sqrt5.cpp

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#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
#if PY_MAJOR_VERSION < 3
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
{
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_ASSUME_SAFE_MACROS
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    if (strcmp(default_encoding_c, "ascii") == 0) {
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
    } else {
        char ascii_chars[128];
        int c;
        for (c = 0; c < 128; c++) {
            ascii_chars[c] = c;
        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif


/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */

static PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static PyObject *__pyx_empty_unicode;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;


static const char *__pyx_f[] = {
  "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx",
  "memory.pxd",
  "sage_object.pxd",
  "element.pxd",
  "stdsage.pxd",
  "code/alex/psage/psage/ellcurve/lseries/stringsource",
  "type.pxd",
  "bool.pxd",
  "complex.pxd",
  "category_object.pxd",
  "coerce_dict.pxd",
  "inherit_comparison.pxd",
  "parent.pxd",
  "parent_old.pxd",
  "parent_base.pxd",
  "parent_gens.pxd",
  "ring.pxd",
  "map.pxd",
  "morphism.pxd",
  "integer.pxd",
  "binary_tree.pxd",
  "polynomial_compiled.pxd",
  "polynomial_element.pxd",
  "ntl_ZZX.pxd",
  "ntl_ZZ.pxd",
  "number_field_element.pxd",
  "number_field_element_quadratic.pxd",
  "code/alex/psage/psage/modform/hilbert/sqrt5/sqrt5_fast.pxd",
  "intlist.pxd",
  "signals.pxi",
  "stdsage.pxi",
  "interrupt.pxi",
};

/*--- Type declarations ---*/
struct __pyx_obj_4sage_9structure_11sage_object_SageObject;
struct __pyx_obj_4sage_9structure_15category_object_CategoryObject;
struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict;
struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict;
struct __pyx_obj_4sage_4misc_18inherit_comparison_InheritComparisonMetaclass;
struct __pyx_obj_4sage_9structure_7element_Element;
struct __pyx_obj_4sage_9structure_7element_ElementWithCachedMethod;
struct __pyx_obj_4sage_9structure_7element_ModuleElement;
struct __pyx_obj_4sage_9structure_7element_MonoidElement;
struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement;
struct __pyx_obj_4sage_9structure_7element_AdditiveGroupElement;
struct __pyx_obj_4sage_9structure_7element_RingElement;
struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement;
struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement;
struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement;
struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement;
struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement;
struct __pyx_obj_4sage_9structure_7element_FieldElement;
struct __pyx_obj_4sage_9structure_7element_AlgebraElement;
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement;
struct __pyx_obj_4sage_9structure_7element_InfinityElement;
struct __pyx_obj_4sage_9structure_7element_Vector;
struct __pyx_obj_4sage_9structure_7element_Matrix;
struct __pyx_obj_4sage_9structure_7element_CoercionModel;
struct __pyx_obj_4sage_9structure_6parent_Parent;
struct __pyx_obj_4sage_9structure_10parent_old_Parent;
struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase;
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens;
struct __pyx_obj_4sage_5rings_4ring_Ring;
struct __pyx_obj_4sage_5rings_4ring_CommutativeRing;
struct __pyx_obj_4sage_5rings_4ring_IntegralDomain;
struct __pyx_obj_4sage_5rings_4ring_DedekindDomain;
struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain;
struct __pyx_obj_4sage_5rings_4ring_EuclideanDomain;
struct __pyx_obj_4sage_5rings_4ring_Field;
struct __pyx_obj_4sage_5rings_4ring_Algebra;
struct __pyx_obj_4sage_5rings_4ring_CommutativeAlgebra;
struct __pyx_obj_4sage_10categories_3map_Map;
struct __pyx_obj_4sage_10categories_3map_Section;
struct __pyx_obj_4sage_10categories_3map_FormalCompositeMap;
struct __pyx_obj_4sage_10categories_8morphism_Morphism;
struct __pyx_obj_4sage_10categories_8morphism_SetMorphism;
struct __pyx_obj_4sage_5rings_7integer_Integer;
struct __pyx_obj_4sage_5rings_7integer_int_to_Z;
struct __pyx_obj_4sage_4misc_11binary_tree_BinaryTree;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_var_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_add_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd;
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd;
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial;
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense;
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact;
struct __pyx_obj_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX;
struct __pyx_obj_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ;
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement;
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute;
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative;
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute;
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_OrderElement_relative;
struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic;
struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic;
struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract;
struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement;
struct __pyx_obj_4sage_5stats_7intlist_IntList;
struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius;
struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator;
struct __pyx_obj___pyx_scope_struct____Pyx_CFunc_object____object____object____int___to_py;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action;
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action;

/* "sage/structure/parent.pxd":102
 * 
 * # Flags for Parent.flags
 * cdef enum:             # <<<<<<<<<<<<<<
 *     # If this flag is set, call __richcmp__ on elements without
 *     # coercion. This allows a completely custom comparison function.
 */
enum  {
  __pyx_e_4sage_9structure_6parent_Parent_richcmp_element_without_coercion = 1
};

/* "sage/structure/parent.pxd":38
 * 
 *     # Called from the __init__ method to set up coercion.
 *     cdef int init_coerce(self, bint warn=*) except -1             # <<<<<<<<<<<<<<
 * 
 *     # returns whether or not there is a Morphism from S to self
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce {
  int __pyx_n;
  int warn;
};

/* "sage/structure/parent.pxd":55
 *     # returns the Action by/on self on/by S
 *     # corresponding to op and self_on_left
 *     cpdef get_action(self, S, op=*, bint self_on_left=*, self_el=*, S_el=*)             # <<<<<<<<<<<<<<
 *     cpdef _get_action_(self, S, op, bint self_on_left)
 * 
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action {
  int __pyx_n;
  PyObject *op;
  int self_on_left;
  PyObject *self_el;
  PyObject *S_el;
};

/* "sage/structure/parent.pxd":68
 *     cdef discover_coerce_map_from(self, S)
 *     cdef discover_convert_map_from(self, S)
 *     cdef discover_action(self, S, op, bint self_on_left, self_el=*, S_el=*)             # <<<<<<<<<<<<<<
 * 
 *     # List consisting of Morphisms (from anything to self)
 */
struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action {
  int __pyx_n;
  PyObject *self_el;
  PyObject *S_el;
};
struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args;

/* "map.pxd":15
 *     # these methods require x is an element of domain, and returns an element with parent codomain
 *     cpdef Element _call_(self, x)
 *     cpdef Element _call_with_args(self, x, args=*, kwds=*)             # <<<<<<<<<<<<<<
 * 
 *     cdef public domain    # will be either a weakref or a constant map
 */
struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args {
  int __pyx_n;
  PyObject *args;
  PyObject *kwds;
};
struct __pyx_t_4sage_4misc_11binary_tree_binary_tree_node;

/* "sage/misc/binary_tree.pxd":1
 * cdef struct binary_tree_node:             # <<<<<<<<<<<<<<
 *     int key
 *     binary_tree_node *left
 */
struct __pyx_t_4sage_4misc_11binary_tree_binary_tree_node {
  int key;
  struct __pyx_t_4sage_4misc_11binary_tree_binary_tree_node *left;
  struct __pyx_t_4sage_4misc_11binary_tree_binary_tree_node *right;
  void *value;
};

/* "psage/modform/hilbert/sqrt5/sqrt5_fast.pxd":5
 * 
 * # Residue element
 * ctypedef long residue_element[2]             # <<<<<<<<<<<<<<
 * 
 * cdef class ResidueRingElement
 */
typedef long __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element[2];

/* "sage/structure/sage_object.pxd":9
 * 
 * 
 * cdef class SageObject:             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_11sage_object_SageObject {
  PyObject_HEAD
};


/* "sage/structure/category_object.pxd":15
 * cpdef check_default_category(default_category, category)
 * 
 * cdef class CategoryObject(SageObject):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 *     cdef _category
 */
struct __pyx_obj_4sage_9structure_15category_object_CategoryObject {
  struct __pyx_obj_4sage_9structure_11sage_object_SageObject __pyx_base;
  struct __pyx_vtabstruct_4sage_9structure_15category_object_CategoryObject *__pyx_vtab;
  PyObject *__cached_methods;
  PyObject *_category;
  PyObject *_base;
  PyObject *_names;
  PyObject *_factory_data;
  PyObject *__weakref__;
  long _hash_value;
};


/* "sage/structure/coerce_dict.pxd":7
 * 
 * @cython.final
 * cdef class MonoDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */
struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict *__pyx_vtab;
  PyObject *__weakref__;
  size_t mask;
  size_t used;
  size_t fill;
  struct __pyx_t_4sage_9structure_11coerce_dict_mono_cell *table;
  int weak_values;
  PyObject *eraser;
};


/* "sage/structure/coerce_dict.pxd":23
 * 
 * @cython.final
 * cdef class TripleDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */
struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict *__pyx_vtab;
  PyObject *__weakref__;
  size_t mask;
  size_t used;
  size_t fill;
  struct __pyx_t_4sage_9structure_11coerce_dict_triple_cell *table;
  int weak_values;
  PyObject *eraser;
};


/* "sage/misc/inherit_comparison.pxd":3
 * cimport sage.misc.cython_metaclass
 * 
 * cdef class InheritComparisonMetaclass(type):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_4misc_18inherit_comparison_InheritComparisonMetaclass {
  PyHeapTypeObject __pyx_base;
};


/* "sage/structure/element.pxd":169
 * 
 * 
 * cdef class Element(SageObject):             # <<<<<<<<<<<<<<
 *     cdef Parent _parent
 *     cpdef _richcmp_(left, right, int op)
 */
struct __pyx_obj_4sage_9structure_7element_Element {
  struct __pyx_obj_4sage_9structure_11sage_object_SageObject __pyx_base;
  struct __pyx_vtabstruct_4sage_9structure_7element_Element *__pyx_vtab;
  struct __pyx_obj_4sage_9structure_6parent_Parent *_parent;
};


/* "sage/structure/element.pxd":192
 * 
 * 
 * cdef class ElementWithCachedMethod(Element):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 * 
 */
struct __pyx_obj_4sage_9structure_7element_ElementWithCachedMethod {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
  PyObject *__cached_methods;
};


/* "sage/structure/element.pxd":195
 *     cdef public dict __cached_methods
 * 
 * cdef class ModuleElement(Element)       # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration
 */
struct __pyx_obj_4sage_9structure_7element_ModuleElement {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
};


/* "sage/structure/element.pxd":208
 *     cpdef _rmul_(self, RingElement left)
 * 
 * cdef class MonoidElement(Element):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_MonoidElement {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
};


/* "sage/structure/element.pxd":211
 *     pass
 * 
 * cdef class MultiplicativeGroupElement(MonoidElement):             # <<<<<<<<<<<<<<
 *     cpdef _div_(self, right)
 * 
 */
struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement {
  struct __pyx_obj_4sage_9structure_7element_MonoidElement __pyx_base;
};


/* "sage/structure/element.pxd":214
 *     cpdef _div_(self, right)
 * 
 * cdef class AdditiveGroupElement(ModuleElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_AdditiveGroupElement {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
};


/* "sage/structure/element.pxd":197
 * cdef class ModuleElement(Element)       # forward declaration
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class ModuleElement(Element):
 */
struct __pyx_obj_4sage_9structure_7element_RingElement {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
};


/* "sage/structure/element.pxd":220
 *     cpdef _div_(self, right)
 * 
 * cdef class CommutativeRingElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":223
 *     pass
 * 
 * cdef class IntegralDomainElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":226
 *     pass
 * 
 * cdef class DedekindDomainElement(IntegralDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement {
  struct __pyx_obj_4sage_9structure_7element_IntegralDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":229
 *     pass
 * 
 * cdef class PrincipalIdealDomainElement(DedekindDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement {
  struct __pyx_obj_4sage_9structure_7element_DedekindDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":232
 *     pass
 * 
 * cdef class EuclideanDomainElement(PrincipalIdealDomainElement):             # <<<<<<<<<<<<<<
 *     cpdef _floordiv_(self, right)
 *     cpdef _mod_(self, right)
 */
struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement {
  struct __pyx_obj_4sage_9structure_7element_PrincipalIdealDomainElement __pyx_base;
};


/* "sage/structure/element.pxd":236
 *     cpdef _mod_(self, right)
 * 
 * cdef class FieldElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     cpdef _floordiv_(self, right)
 * 
 */
struct __pyx_obj_4sage_9structure_7element_FieldElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":239
 *     cpdef _floordiv_(self, right)
 * 
 * cdef class AlgebraElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_AlgebraElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":242
 *     pass
 * 
 * cdef class CommutativeAlgebraElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement {
  struct __pyx_obj_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};


/* "sage/structure/element.pxd":245
 *     pass
 * 
 * cdef class InfinityElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_9structure_7element_InfinityElement {
  struct __pyx_obj_4sage_9structure_7element_RingElement __pyx_base;
};


/* "sage/structure/element.pxd":249
 * 
 * 
 * cdef class Vector(ModuleElement):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _degree
 * 
 */
struct __pyx_obj_4sage_9structure_7element_Vector {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
  Py_ssize_t _degree;
};


/* "sage/structure/element.pxd":264
 * 
 * 
 * cdef class Matrix(ModuleElement):             # <<<<<<<<<<<<<<
 *     # All matrix classes must be written in Cython
 *     cdef Py_ssize_t _nrows
 */
struct __pyx_obj_4sage_9structure_7element_Matrix {
  struct __pyx_obj_4sage_9structure_7element_ModuleElement __pyx_base;
  Py_ssize_t _nrows;
  Py_ssize_t _ncols;
};


/* "sage/structure/element.pxd":277
 * 
 * 
 * cdef class CoercionModel:             # <<<<<<<<<<<<<<
 *     cpdef canonical_coercion(self, x, y)
 *     cpdef bin_op(self, x, y, op)
 */
struct __pyx_obj_4sage_9structure_7element_CoercionModel {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel *__pyx_vtab;
};


/* "sage/structure/parent.pxd":12
 * from sage.structure.coerce_dict cimport MonoDict, TripleDict
 * 
 * cdef class Parent(category_object.CategoryObject):             # <<<<<<<<<<<<<<
 *     cdef public _element_constructor
 *     cdef public _convert_method_name
 */
struct __pyx_obj_4sage_9structure_6parent_Parent {
  struct __pyx_obj_4sage_9structure_15category_object_CategoryObject __pyx_base;
  PyObject *_element_constructor;
  PyObject *_convert_method_name;
  int _element_init_pass_parent;
  PyObject *_initial_coerce_list;
  PyObject *_initial_action_list;
  PyObject *_initial_convert_list;
  int _coercions_used;
  int flags;
  PyObject *_cache_an_element;
  PyObject *_coerce_from_list;
  PyObject *_registered_domains;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_coerce_from_hash;
  PyObject *_action_list;
  struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *_action_hash;
  PyObject *_convert_from_list;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_convert_from_hash;
  PyObject *_embedding;
};


/* "parent_old.pxd":15
 * 
 * 
 * cdef class Parent(parent.Parent):             # <<<<<<<<<<<<<<
 * 
 *     # returns a Morphism from S to self, or None
 */
struct __pyx_obj_4sage_9structure_10parent_old_Parent {
  struct __pyx_obj_4sage_9structure_6parent_Parent __pyx_base;
  struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *_has_coerce_map_from;
};


/* "parent_base.pxd":11
 * from .parent_old cimport Parent as Parent_old
 * 
 * cdef class ParentWithBase(Parent_old):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase {
  struct __pyx_obj_4sage_9structure_10parent_old_Parent __pyx_base;
};


/* "sage/structure/parent_gens.pxd":18
 * 
 * 
 * cdef class ParentWithGens(ParentWithBase):             # <<<<<<<<<<<<<<
 *     cdef public object _gens
 *     cdef public object _latex_names
 */
struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens {
  struct __pyx_obj_4sage_9structure_11parent_base_ParentWithBase __pyx_base;
  PyObject *_gens;
  PyObject *_latex_names;
  PyObject *_list;
};


/* "sage/rings/ring.pxd":5
 * cpdef bint _is_Field(x) except -2
 * 
 * cdef class Ring(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _zero_element
 *     cdef public object _one_element
 */
struct __pyx_obj_4sage_5rings_4ring_Ring {
  struct __pyx_obj_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
  PyObject *_zero_element;
  PyObject *_one_element;
  PyObject *_zero_ideal;
  PyObject *_unit_ideal;
  PyObject *__ideal_monoid;
};


/* "sage/rings/ring.pxd":13
 *     cdef _an_element_c_impl(self)
 * 
 * cdef class CommutativeRing(Ring):             # <<<<<<<<<<<<<<
 *     cdef public object __fraction_field
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_CommutativeRing {
  struct __pyx_obj_4sage_5rings_4ring_Ring __pyx_base;
  PyObject *__fraction_field;
};


/* "sage/rings/ring.pxd":16
 *     cdef public object __fraction_field
 * 
 * cdef class IntegralDomain(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_IntegralDomain {
  struct __pyx_obj_4sage_5rings_4ring_CommutativeRing __pyx_base;
};


/* "sage/rings/ring.pxd":19
 *     pass
 * 
 * cdef class DedekindDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_DedekindDomain {
  struct __pyx_obj_4sage_5rings_4ring_IntegralDomain __pyx_base;
};


/* "sage/rings/ring.pxd":23
 * 
 * 
 * cdef class PrincipalIdealDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain {
  struct __pyx_obj_4sage_5rings_4ring_IntegralDomain __pyx_base;
};


/* "sage/rings/ring.pxd":26
 *     pass
 * 
 * cdef class EuclideanDomain(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_EuclideanDomain {
  struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};


/* "sage/rings/ring.pxd":29
 *     pass
 * 
 * cdef class Field(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_Field {
  struct __pyx_obj_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};


/* "sage/rings/ring.pxd":32
 *     pass
 * 
 * cdef class Algebra(Ring):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_4ring_Algebra {
  struct __pyx_obj_4sage_5rings_4ring_Ring __pyx_base;
};


/* "sage/rings/ring.pxd":35
 *     pass
 * 
 * cdef class CommutativeAlgebra(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_5rings_4ring_CommutativeAlgebra {
  struct __pyx_obj_4sage_5rings_4ring_CommutativeRing __pyx_base;
};


/* "map.pxd":4
 * from sage.structure.element cimport Element
 * 
 * cdef class Map(Element):             # <<<<<<<<<<<<<<
 *     cdef object __weakref__
 * 
 */
struct __pyx_obj_4sage_10categories_3map_Map {
  struct __pyx_obj_4sage_9structure_7element_Element __pyx_base;
  PyObject *__weakref__;
  int _coerce_cost;
  PyObject *domain;
  PyObject *codomain;
  struct __pyx_obj_4sage_9structure_6parent_Parent *_codomain;
  PyObject *_category_for;
  PyObject *_repr_type_str;
};


/* "map.pxd":25
 * 
 * 
 * cdef class Section(Map):             # <<<<<<<<<<<<<<
 *     cdef Map _inverse
 * 
 */
struct __pyx_obj_4sage_10categories_3map_Section {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
  struct __pyx_obj_4sage_10categories_3map_Map *_inverse;
};


/* "map.pxd":28
 *     cdef Map _inverse
 * 
 * cdef class FormalCompositeMap(Map):             # <<<<<<<<<<<<<<
 *     cdef __list
 */
struct __pyx_obj_4sage_10categories_3map_FormalCompositeMap {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
  PyObject *__pyx___list;
};


/* "sage/categories/morphism.pxd":5
 * from .map cimport Map
 * 
 * cdef class Morphism(Map):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_10categories_8morphism_Morphism {
  struct __pyx_obj_4sage_10categories_3map_Map __pyx_base;
};


/* "sage/categories/morphism.pxd":8
 *     pass
 * 
 * cdef class SetMorphism(Morphism):             # <<<<<<<<<<<<<<
 *     cdef object _function
 *     cpdef bint _eq_c_impl(left, Element right)
 */
struct __pyx_obj_4sage_10categories_8morphism_SetMorphism {
  struct __pyx_obj_4sage_10categories_8morphism_Morphism __pyx_base;
  PyObject *_function;
};


/* "sage/rings/integer.pxd":7
 * from sage.categories.morphism cimport Morphism
 * 
 * cdef class Integer(EuclideanDomainElement):             # <<<<<<<<<<<<<<
 *     cdef mpz_t value
 * 
 */
struct __pyx_obj_4sage_5rings_7integer_Integer {
  struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement __pyx_base;
  mpz_t value;
};


/* "sage/rings/integer.pxd":37
 * cdef Integer smallInteger(long value)
 * 
 * cdef class int_to_Z(Morphism):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_5rings_7integer_int_to_Z {
  struct __pyx_obj_4sage_10categories_8morphism_Morphism __pyx_base;
};


/* "sage/misc/binary_tree.pxd":27
 * 
 * 
 * cdef class BinaryTree:             # <<<<<<<<<<<<<<
 *     cdef binary_tree_node *head
 */
struct __pyx_obj_4sage_4misc_11binary_tree_BinaryTree {
  PyObject_HEAD
  struct __pyx_t_4sage_4misc_11binary_tree_binary_tree_node *head;
};


/* "polynomial_compiled.pxd":7
 * cdef class generic_pd
 * 
 * cdef class CompiledPolynomialFunction:             # <<<<<<<<<<<<<<
 *     cdef generic_pd _dag
 *     cdef object _coeffs
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *__pyx_vtab;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *_dag;
  PyObject *_coeffs;
};


/* "polynomial_compiled.pxd":5
 * 
 * 
 * cdef class generic_pd             # <<<<<<<<<<<<<<
 * 
 * cdef class CompiledPolynomialFunction:
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *__pyx_vtab;
  PyObject *value;
  int refs;
  int hits;
  int label;
};


/* "polynomial_compiled.pxd":24
 *     cdef void reset(self)
 * 
 * cdef class dummy_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd link
 *     cdef void fill(dummy_pd self, generic_pd link)
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *link;
};


/* "polynomial_compiled.pxd":28
 *     cdef void fill(dummy_pd self, generic_pd link)
 * 
 * cdef class var_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_var_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  int index;
};


/* "polynomial_compiled.pxd":31
 *     cdef int index
 * 
 * cdef class univar_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};


/* "polynomial_compiled.pxd":34
 *     pass
 * 
 * cdef class coeff_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  int index;
};


/* "polynomial_compiled.pxd":38
 * 
 * 
 * cdef class unary_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd operand
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *operand;
};


/* "polynomial_compiled.pxd":41
 *     cdef generic_pd operand
 * 
 * cdef class sqr_pd(unary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd __pyx_base;
};


/* "polynomial_compiled.pxd":44
 *     pass
 * 
 * cdef class pow_pd(unary_pd):             # <<<<<<<<<<<<<<
 *     cdef object exponent
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd __pyx_base;
  PyObject *exponent;
};


/* "polynomial_compiled.pxd":48
 * 
 * 
 * cdef class binary_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd left, right
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *left;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *right;
};


/* "polynomial_compiled.pxd":51
 *     cdef generic_pd left, right
 * 
 * cdef class add_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_add_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
};


/* "polynomial_compiled.pxd":54
 *     pass
 * 
 * cdef class mul_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
};


/* "polynomial_compiled.pxd":57
 *     pass
 * 
 * cdef class abc_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd {
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
  int index;
};


/* "sage/rings/polynomial/polynomial_element.pxd":8
 * 
 * 
 * cdef class Polynomial(CommutativeAlgebraElement):             # <<<<<<<<<<<<<<
 *     cdef char _is_gen
 *     cdef CompiledPolynomialFunction _compiled
 */
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial {
  struct __pyx_obj_4sage_9structure_7element_CommutativeAlgebraElement __pyx_base;
  char _is_gen;
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *_compiled;
};


/* "sage/rings/polynomial/polynomial_element.pxd":29
 *     cdef get_unsafe(self, Py_ssize_t i)
 * 
 * cdef class Polynomial_generic_dense(Polynomial):             # <<<<<<<<<<<<<<
 *     cdef Polynomial_generic_dense _new_c(self, list coeffs, Parent P)
 *     cdef list __coeffs
 */
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense {
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial __pyx_base;
  PyObject *__pyx___coeffs;
};


/* "sage/rings/polynomial/polynomial_element.pxd":34
 *     cdef int __normalize(self) except -1
 * 
 * cdef class Polynomial_generic_dense_inexact(Polynomial_generic_dense):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact {
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense __pyx_base;
};


/* "sage/libs/ntl/ntl_ZZX.pxd":3
 * from .types cimport ZZX_c
 * 
 * cdef class ntl_ZZX(object):             # <<<<<<<<<<<<<<
 *     cdef ZZX_c x
 *     cdef void setitem_from_int(ntl_ZZX self, long i, int value)
 */
struct __pyx_obj_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX *__pyx_vtab;
  ZZX x;
};


/* "sage/libs/ntl/ntl_ZZ.pxd":3
 * from sage.libs.ntl.types cimport ZZ_c
 * 
 * cdef class ntl_ZZ(object):             # <<<<<<<<<<<<<<
 *     cdef ZZ_c x
 *     cdef int get_as_int(ntl_ZZ self)
 */
struct __pyx_obj_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ *__pyx_vtab;
  ZZ x;
};


/* "number_field_element.pxd":11
 * from sage.libs.ntl.ntl_ZZ cimport ntl_ZZ
 * 
 * cdef class NumberFieldElement(FieldElement):             # <<<<<<<<<<<<<<
 *     cdef ZZX_c __numerator
 *     cdef ZZ_c __denominator
 */
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement {
  struct __pyx_obj_4sage_9structure_7element_FieldElement __pyx_base;
  ZZX __pyx___numerator;
  ZZ __pyx___denominator;
  struct __pyx_obj_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX *__pyx___fld_numerator;
  struct __pyx_obj_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ *__pyx___fld_denominator;
  PyObject *__pyx___multiplicative_order;
  PyObject *__pyx___pari;
  PyObject *__pyx___matrix;
};


/* "number_field_element.pxd":38
 * 
 * 
 * cdef class NumberFieldElement_absolute(NumberFieldElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute {
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement __pyx_base;
};


/* "number_field_element.pxd":41
 *     pass
 * 
 * cdef class NumberFieldElement_relative(NumberFieldElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative {
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement __pyx_base;
};


/* "number_field_element.pxd":46
 * # TODO: cyclotomic and/or quadratic classes? (Both for differing implementations and speed).
 * 
 * cdef class OrderElement_absolute(NumberFieldElement_absolute):             # <<<<<<<<<<<<<<
 *     cdef object _number_field
 * 
 */
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute {
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute __pyx_base;
  PyObject *_number_field;
};


/* "number_field_element.pxd":49
 *     cdef object _number_field
 * 
 * cdef class OrderElement_relative(NumberFieldElement_relative):             # <<<<<<<<<<<<<<
 *     cdef object _number_field
 */
struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_OrderElement_relative {
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative __pyx_base;
  PyObject *_number_field;
};


/* "sage/rings/number_field/number_field_element_quadratic.pxd":6
 * 
 * 
 * cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):             # <<<<<<<<<<<<<<
 *     # (a + b sqrt(D)) / denom
 *     cdef mpz_t a, b, denom
 */
struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic {
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute __pyx_base;
  mpz_t a;
  mpz_t b;
  mpz_t denom;
  struct __pyx_obj_4sage_5rings_7integer_Integer *D;
  int standard_embedding;
};


/* "sage/rings/number_field/number_field_element_quadratic.pxd":19
 * 
 * 
 * cdef class OrderElement_quadratic(NumberFieldElement_quadratic):             # <<<<<<<<<<<<<<
 *     pass
 */
struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic {
  struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic __pyx_base;
};


/* "psage/modform/hilbert/sqrt5/sqrt5_fast.pxd":9
 * cdef class ResidueRingElement
 * 
 * cdef class ResidueRing_abstract(CommutativeRing):             # <<<<<<<<<<<<<<
 *     cdef object P, F
 *     cdef public object element_class, _residue_field
 */
struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract {
  struct __pyx_obj_4sage_5rings_4ring_CommutativeRing __pyx_base;
  PyObject *P;
  PyObject *F;
  PyObject *element_class;
  PyObject *_residue_field;
  long n0;
  long n1;
  long p;
  long e;
  long _cardinality;
  long im_gen0;
};


/* "psage/modform/hilbert/sqrt5/sqrt5_fast.pxd":7
 * ctypedef long residue_element[2]
 * 
 * cdef class ResidueRingElement             # <<<<<<<<<<<<<<
 * 
 * cdef class ResidueRing_abstract(CommutativeRing):
 */
struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement {
  PyObject_HEAD
  struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_vtab;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element x;
  struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *_parent;
};


/* "sage/stats/intlist.pxd":8
 * #############################################################################
 * 
 * cdef class IntList:             # <<<<<<<<<<<<<<
 *     cdef int* _values
 *     cdef Py_ssize_t _length
 */
struct __pyx_obj_4sage_5stats_7intlist_IntList {
  PyObject_HEAD
  struct __pyx_vtabstruct_4sage_5stats_7intlist_IntList *__pyx_vtab;
  int *_values;
  Py_ssize_t _length;
};


/* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":123
 * cdef long UNKNOWN = 2**31 - 1
 * 
 * cdef class TracesOfFrobenius:             # <<<<<<<<<<<<<<
 *     cdef long bound, table_size
 *     cdef long* primes
 */
struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius {
  PyObject_HEAD
  long bound;
  long table_size;
  long *primes;
  long *sqrt5;
  long *ap;
  mpz_t Ax;
  mpz_t Ay;
  mpz_t Bx;
  mpz_t By;
  PyObject *E;
  PyObject *j;
  PyObject *c_quo;
};


/* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":365
 *     return C
 * 
 * cdef class InertTraceCalculator:             # <<<<<<<<<<<<<<
 *     cdef public dict tables
 * 
 */
struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator {
  PyObject_HEAD
  struct __pyx_vtabstruct_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_vtab;
  PyObject *tables;
};


/* "cfunc.to_py":64
 * 
 * @cname("__Pyx_CFunc_object____object____object____int___to_py")
 * cdef object __Pyx_CFunc_object____object____object____int___to_py(object (*f)(object, object, int) ):             # <<<<<<<<<<<<<<
 *     def wrap(object arg0, object arg1, int arg2):
 *         """wrap(arg0, arg1, arg2: 'int')"""
 */
struct __pyx_obj___pyx_scope_struct____Pyx_CFunc_object____object____object____int___to_py {
  PyObject_HEAD
  PyObject *(*__pyx_v_f)(PyObject *, PyObject *, int);
};



/* "sage/structure/category_object.pxd":15
 * cpdef check_default_category(default_category, category)
 * 
 * cdef class CategoryObject(SageObject):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 *     cdef _category
 */

struct __pyx_vtabstruct_4sage_9structure_15category_object_CategoryObject {
  PyObject *(*getattr_from_category)(struct __pyx_obj_4sage_9structure_15category_object_CategoryObject *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_9structure_15category_object_CategoryObject *__pyx_vtabptr_4sage_9structure_15category_object_CategoryObject;


/* "sage/structure/coerce_dict.pxd":7
 * 
 * @cython.final
 * cdef class MonoDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */

struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict {
  struct __pyx_t_4sage_9structure_11coerce_dict_mono_cell *(*lookup)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *);
  PyObject *(*get)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *);
  PyObject *(*set)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *, PyObject *, PyObject *);
  int (*resize)(struct __pyx_obj_4sage_9structure_11coerce_dict_MonoDict *);
};
static struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_MonoDict *__pyx_vtabptr_4sage_9structure_11coerce_dict_MonoDict;


/* "sage/structure/coerce_dict.pxd":23
 * 
 * @cython.final
 * cdef class TripleDict:             # <<<<<<<<<<<<<<
 *     cdef __weakref__
 *     cdef size_t mask
 */

struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict {
  struct __pyx_t_4sage_9structure_11coerce_dict_triple_cell *(*lookup)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *);
  PyObject *(*get)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *);
  PyObject *(*set)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *, PyObject *, PyObject *, PyObject *, PyObject *);
  int (*resize)(struct __pyx_obj_4sage_9structure_11coerce_dict_TripleDict *);
};
static struct __pyx_vtabstruct_4sage_9structure_11coerce_dict_TripleDict *__pyx_vtabptr_4sage_9structure_11coerce_dict_TripleDict;


/* "sage/structure/element.pxd":169
 * 
 * 
 * cdef class Element(SageObject):             # <<<<<<<<<<<<<<
 *     cdef Parent _parent
 *     cpdef _richcmp_(left, right, int op)
 */

struct __pyx_vtabstruct_4sage_9structure_7element_Element {
  PyObject *(*_richcmp_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int, int __pyx_skip_dispatch);
  int (*_cmp_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*base_extend)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*getattr_from_category)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_act_on_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*_acted_upon_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*_add_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_sub_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_neg_)(struct __pyx_obj_4sage_9structure_7element_Element *);
  PyObject *(*_add_long)(struct __pyx_obj_4sage_9structure_7element_Element *, long);
  PyObject *(*_mul_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_mul_long)(struct __pyx_obj_4sage_9structure_7element_Element *, long);
  PyObject *(*_div_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_floordiv_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
  PyObject *(*_mod_)(struct __pyx_obj_4sage_9structure_7element_Element *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Element *__pyx_vtabptr_4sage_9structure_7element_Element;


/* "sage/structure/element.pxd":192
 * 
 * 
 * cdef class ElementWithCachedMethod(Element):             # <<<<<<<<<<<<<<
 *     cdef public dict __cached_methods
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_ElementWithCachedMethod {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_ElementWithCachedMethod *__pyx_vtabptr_4sage_9structure_7element_ElementWithCachedMethod;


/* "sage/structure/element.pxd":195
 *     cdef public dict __cached_methods
 * 
 * cdef class ModuleElement(Element)       # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration
 */

struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
  PyObject *(*_sub_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_neg_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, int __pyx_skip_dispatch);
  PyObject *(*_lmul_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
  PyObject *(*_rmul_)(struct __pyx_obj_4sage_9structure_7element_ModuleElement *, struct __pyx_obj_4sage_9structure_7element_RingElement *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement *__pyx_vtabptr_4sage_9structure_7element_ModuleElement;


/* "sage/structure/element.pxd":197
 * cdef class ModuleElement(Element)       # forward declaration
 * 
 * cdef class RingElement(ModuleElement)   # forward declaration             # <<<<<<<<<<<<<<
 * 
 * cdef class ModuleElement(Element):
 */

struct __pyx_vtabstruct_4sage_9structure_7element_RingElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  PyObject *(*_div_)(struct __pyx_obj_4sage_9structure_7element_RingElement *, PyObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_RingElement *__pyx_vtabptr_4sage_9structure_7element_RingElement;


/* "sage/structure/element.pxd":208
 *     cpdef _rmul_(self, RingElement left)
 * 
 * cdef class MonoidElement(Element):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement *__pyx_vtabptr_4sage_9structure_7element_MonoidElement;


/* "sage/structure/element.pxd":211
 *     pass
 * 
 * cdef class MultiplicativeGroupElement(MonoidElement):             # <<<<<<<<<<<<<<
 *     cpdef _div_(self, right)
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_MultiplicativeGroupElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_MonoidElement __pyx_base;
  PyObject *(*_div_)(struct __pyx_obj_4sage_9structure_7element_MultiplicativeGroupElement *, PyObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_MultiplicativeGroupElement *__pyx_vtabptr_4sage_9structure_7element_MultiplicativeGroupElement;


/* "sage/structure/element.pxd":214
 *     cpdef _div_(self, right)
 * 
 * cdef class AdditiveGroupElement(ModuleElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_AdditiveGroupElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_AdditiveGroupElement *__pyx_vtabptr_4sage_9structure_7element_AdditiveGroupElement;


/* "sage/structure/element.pxd":220
 *     cpdef _div_(self, right)
 * 
 * cdef class CommutativeRingElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement *__pyx_vtabptr_4sage_9structure_7element_CommutativeRingElement;


/* "sage/structure/element.pxd":223
 *     pass
 * 
 * cdef class IntegralDomainElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement *__pyx_vtabptr_4sage_9structure_7element_IntegralDomainElement;


/* "sage/structure/element.pxd":226
 *     pass
 * 
 * cdef class DedekindDomainElement(IntegralDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_IntegralDomainElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement *__pyx_vtabptr_4sage_9structure_7element_DedekindDomainElement;


/* "sage/structure/element.pxd":229
 *     pass
 * 
 * cdef class PrincipalIdealDomainElement(DedekindDomainElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_DedekindDomainElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement *__pyx_vtabptr_4sage_9structure_7element_PrincipalIdealDomainElement;


/* "sage/structure/element.pxd":232
 *     pass
 * 
 * cdef class EuclideanDomainElement(PrincipalIdealDomainElement):             # <<<<<<<<<<<<<<
 *     cpdef _floordiv_(self, right)
 *     cpdef _mod_(self, right)
 */

struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_PrincipalIdealDomainElement __pyx_base;
  PyObject *(*_floordiv_)(struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_mod_)(struct __pyx_obj_4sage_9structure_7element_EuclideanDomainElement *, PyObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement *__pyx_vtabptr_4sage_9structure_7element_EuclideanDomainElement;


/* "sage/structure/element.pxd":236
 *     cpdef _mod_(self, right)
 * 
 * cdef class FieldElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     cpdef _floordiv_(self, right)
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
  PyObject *(*_floordiv_)(struct __pyx_obj_4sage_9structure_7element_FieldElement *, PyObject *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement *__pyx_vtabptr_4sage_9structure_7element_FieldElement;


/* "sage/structure/element.pxd":239
 *     cpdef _floordiv_(self, right)
 * 
 * cdef class AlgebraElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_AlgebraElement *__pyx_vtabptr_4sage_9structure_7element_AlgebraElement;


/* "sage/structure/element.pxd":242
 *     pass
 * 
 * cdef class CommutativeAlgebraElement(CommutativeRingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeRingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement *__pyx_vtabptr_4sage_9structure_7element_CommutativeAlgebraElement;


/* "sage/structure/element.pxd":245
 *     pass
 * 
 * cdef class InfinityElement(RingElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_InfinityElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_RingElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_7element_InfinityElement *__pyx_vtabptr_4sage_9structure_7element_InfinityElement;


/* "sage/structure/element.pxd":249
 * 
 * 
 * cdef class Vector(ModuleElement):             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t _degree
 * 
 */

struct __pyx_vtabstruct_4sage_9structure_7element_Vector {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  PyObject *(*_dot_product_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  PyObject *(*_dot_product_coerce_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  PyObject *(*_pairwise_product_)(struct __pyx_obj_4sage_9structure_7element_Vector *, struct __pyx_obj_4sage_9structure_7element_Vector *, int __pyx_skip_dispatch);
  int (*is_sparse_c)(struct __pyx_obj_4sage_9structure_7element_Vector *);
  int (*is_dense_c)(struct __pyx_obj_4sage_9structure_7element_Vector *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Vector *__pyx_vtabptr_4sage_9structure_7element_Vector;


/* "sage/structure/element.pxd":264
 * 
 * 
 * cdef class Matrix(ModuleElement):             # <<<<<<<<<<<<<<
 *     # All matrix classes must be written in Cython
 *     cdef Py_ssize_t _nrows
 */

struct __pyx_vtabstruct_4sage_9structure_7element_Matrix {
  struct __pyx_vtabstruct_4sage_9structure_7element_ModuleElement __pyx_base;
  PyObject *(*_vector_times_matrix_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Vector *);
  PyObject *(*_matrix_times_vector_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Vector *);
  PyObject *(*_matrix_times_matrix_)(struct __pyx_obj_4sage_9structure_7element_Matrix *, struct __pyx_obj_4sage_9structure_7element_Matrix *);
  int (*is_sparse_c)(struct __pyx_obj_4sage_9structure_7element_Matrix *);
  int (*is_dense_c)(struct __pyx_obj_4sage_9structure_7element_Matrix *);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_Matrix *__pyx_vtabptr_4sage_9structure_7element_Matrix;


/* "sage/structure/element.pxd":277
 * 
 * 
 * cdef class CoercionModel:             # <<<<<<<<<<<<<<
 *     cpdef canonical_coercion(self, x, y)
 *     cpdef bin_op(self, x, y, op)
 */

struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel {
  PyObject *(*canonical_coercion)(struct __pyx_obj_4sage_9structure_7element_CoercionModel *, PyObject *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*bin_op)(struct __pyx_obj_4sage_9structure_7element_CoercionModel *, PyObject *, PyObject *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*richcmp)(struct __pyx_obj_4sage_9structure_7element_CoercionModel *, PyObject *, PyObject *, int, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_7element_CoercionModel *__pyx_vtabptr_4sage_9structure_7element_CoercionModel;


/* "sage/structure/parent.pxd":12
 * from sage.structure.coerce_dict cimport MonoDict, TripleDict
 * 
 * cdef class Parent(category_object.CategoryObject):             # <<<<<<<<<<<<<<
 *     cdef public _element_constructor
 *     cdef public _convert_method_name
 */

struct __pyx_vtabstruct_4sage_9structure_6parent_Parent {
  struct __pyx_vtabstruct_4sage_9structure_15category_object_CategoryObject __pyx_base;
  int (*get_flag)(struct __pyx_obj_4sage_9structure_6parent_Parent *, int);
  int (*is_coercion_cached)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*is_conversion_cached)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_coercion)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_conversion)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*register_embedding)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*_richcmp)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int, int __pyx_skip_dispatch);
  int (*_cmp_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  int (*is_exact)(struct __pyx_obj_4sage_9structure_6parent_Parent *, int __pyx_skip_dispatch);
  int (*init_coerce)(struct __pyx_obj_4sage_9structure_6parent_Parent *, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_init_coerce *__pyx_optional_args);
  int (*has_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_internal_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_coerce_map_from_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_internal_convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_convert_map_from_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*get_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_get_action *__pyx_optional_args);
  PyObject *(*_get_action_)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*coerce)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*an_element)(struct __pyx_obj_4sage_9structure_6parent_Parent *, int __pyx_skip_dispatch);
  PyObject *(*_generic_convert_map)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*discover_coerce_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *);
  PyObject *(*discover_convert_map_from)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *);
  PyObject *(*discover_action)(struct __pyx_obj_4sage_9structure_6parent_Parent *, PyObject *, PyObject *, int, struct __pyx_opt_args_4sage_9structure_6parent_6Parent_discover_action *__pyx_optional_args);
};
static struct __pyx_vtabstruct_4sage_9structure_6parent_Parent *__pyx_vtabptr_4sage_9structure_6parent_Parent;
static CYTHON_INLINE int __pyx_f_4sage_9structure_6parent_6Parent_get_flag(struct __pyx_obj_4sage_9structure_6parent_Parent *, int);


/* "parent_old.pxd":15
 * 
 * 
 * cdef class Parent(parent.Parent):             # <<<<<<<<<<<<<<
 * 
 *     # returns a Morphism from S to self, or None
 */

struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent {
  struct __pyx_vtabstruct_4sage_9structure_6parent_Parent __pyx_base;
  PyObject *(*coerce_map_from_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*coerce_map_from_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*get_action_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*get_action_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, PyObject *, int);
  PyObject *(*has_coerce_map_from_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*has_coerce_map_from_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*_coerce_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *, int __pyx_skip_dispatch);
  PyObject *(*_coerce_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, PyObject *);
  PyObject *(*_an_element_c_impl)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *);
  PyObject *(*_an_element_c)(struct __pyx_obj_4sage_9structure_10parent_old_Parent *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent *__pyx_vtabptr_4sage_9structure_10parent_old_Parent;


/* "parent_base.pxd":11
 * from .parent_old cimport Parent as Parent_old
 * 
 * cdef class ParentWithBase(Parent_old):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase {
  struct __pyx_vtabstruct_4sage_9structure_10parent_old_Parent __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase *__pyx_vtabptr_4sage_9structure_11parent_base_ParentWithBase;


/* "sage/structure/parent_gens.pxd":18
 * 
 * 
 * cdef class ParentWithGens(ParentWithBase):             # <<<<<<<<<<<<<<
 *     cdef public object _gens
 *     cdef public object _latex_names
 */

struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens {
  struct __pyx_vtabstruct_4sage_9structure_11parent_base_ParentWithBase __pyx_base;
};
static struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens *__pyx_vtabptr_4sage_9structure_11parent_gens_ParentWithGens;


/* "sage/rings/ring.pxd":5
 * cpdef bint _is_Field(x) except -2
 * 
 * cdef class Ring(ParentWithGens):             # <<<<<<<<<<<<<<
 *     cdef public object _zero_element
 *     cdef public object _one_element
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Ring {
  struct __pyx_vtabstruct_4sage_9structure_11parent_gens_ParentWithGens __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Ring *__pyx_vtabptr_4sage_5rings_4ring_Ring;


/* "sage/rings/ring.pxd":13
 *     cdef _an_element_c_impl(self)
 * 
 * cdef class CommutativeRing(Ring):             # <<<<<<<<<<<<<<
 *     cdef public object __fraction_field
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Ring __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing *__pyx_vtabptr_4sage_5rings_4ring_CommutativeRing;


/* "sage/rings/ring.pxd":16
 *     cdef public object __fraction_field
 * 
 * cdef class IntegralDomain(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain *__pyx_vtabptr_4sage_5rings_4ring_IntegralDomain;


/* "sage/rings/ring.pxd":19
 *     pass
 * 
 * cdef class DedekindDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_DedekindDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_DedekindDomain *__pyx_vtabptr_4sage_5rings_4ring_DedekindDomain;


/* "sage/rings/ring.pxd":23
 * 
 * 
 * cdef class PrincipalIdealDomain(IntegralDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_IntegralDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain *__pyx_vtabptr_4sage_5rings_4ring_PrincipalIdealDomain;


/* "sage/rings/ring.pxd":26
 *     pass
 * 
 * cdef class EuclideanDomain(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_EuclideanDomain {
  struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_EuclideanDomain *__pyx_vtabptr_4sage_5rings_4ring_EuclideanDomain;


/* "sage/rings/ring.pxd":29
 *     pass
 * 
 * cdef class Field(PrincipalIdealDomain):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Field {
  struct __pyx_vtabstruct_4sage_5rings_4ring_PrincipalIdealDomain __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Field *__pyx_vtabptr_4sage_5rings_4ring_Field;


/* "sage/rings/ring.pxd":32
 *     pass
 * 
 * cdef class Algebra(Ring):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_Algebra {
  struct __pyx_vtabstruct_4sage_5rings_4ring_Ring __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_Algebra *__pyx_vtabptr_4sage_5rings_4ring_Algebra;


/* "sage/rings/ring.pxd":35
 *     pass
 * 
 * cdef class CommutativeAlgebra(CommutativeRing):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeAlgebra {
  struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeAlgebra *__pyx_vtabptr_4sage_5rings_4ring_CommutativeAlgebra;


/* "map.pxd":4
 * from sage.structure.element cimport Element
 * 
 * cdef class Map(Element):             # <<<<<<<<<<<<<<
 *     cdef object __weakref__
 * 
 */

struct __pyx_vtabstruct_4sage_10categories_3map_Map {
  struct __pyx_vtabstruct_4sage_9structure_7element_Element __pyx_base;
  PyObject *(*_update_slots)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *);
  PyObject *(*_extra_slots)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *);
  struct __pyx_obj_4sage_9structure_7element_Element *(*_call_)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_Element *(*_call_with_args)(struct __pyx_obj_4sage_10categories_3map_Map *, PyObject *, int __pyx_skip_dispatch, struct __pyx_opt_args_4sage_10categories_3map_3Map__call_with_args *__pyx_optional_args);
};
static struct __pyx_vtabstruct_4sage_10categories_3map_Map *__pyx_vtabptr_4sage_10categories_3map_Map;


/* "map.pxd":25
 * 
 * 
 * cdef class Section(Map):             # <<<<<<<<<<<<<<
 *     cdef Map _inverse
 * 
 */

struct __pyx_vtabstruct_4sage_10categories_3map_Section {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_3map_Section *__pyx_vtabptr_4sage_10categories_3map_Section;


/* "map.pxd":28
 *     cdef Map _inverse
 * 
 * cdef class FormalCompositeMap(Map):             # <<<<<<<<<<<<<<
 *     cdef __list
 */

struct __pyx_vtabstruct_4sage_10categories_3map_FormalCompositeMap {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_3map_FormalCompositeMap *__pyx_vtabptr_4sage_10categories_3map_FormalCompositeMap;


/* "sage/categories/morphism.pxd":5
 * from .map cimport Map
 * 
 * cdef class Morphism(Map):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism {
  struct __pyx_vtabstruct_4sage_10categories_3map_Map __pyx_base;
};
static struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism *__pyx_vtabptr_4sage_10categories_8morphism_Morphism;


/* "sage/categories/morphism.pxd":8
 *     pass
 * 
 * cdef class SetMorphism(Morphism):             # <<<<<<<<<<<<<<
 *     cdef object _function
 *     cpdef bint _eq_c_impl(left, Element right)
 */

struct __pyx_vtabstruct_4sage_10categories_8morphism_SetMorphism {
  struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism __pyx_base;
  int (*_eq_c_impl)(struct __pyx_obj_4sage_10categories_8morphism_SetMorphism *, struct __pyx_obj_4sage_9structure_7element_Element *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_10categories_8morphism_SetMorphism *__pyx_vtabptr_4sage_10categories_8morphism_SetMorphism;


/* "sage/rings/integer.pxd":7
 * from sage.categories.morphism cimport Morphism
 * 
 * cdef class Integer(EuclideanDomainElement):             # <<<<<<<<<<<<<<
 *     cdef mpz_t value
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_7integer_Integer {
  struct __pyx_vtabstruct_4sage_9structure_7element_EuclideanDomainElement __pyx_base;
  int (*_to_ZZ)(struct __pyx_obj_4sage_5rings_7integer_Integer *, ZZ *);
  void (*set_from_mpz)(struct __pyx_obj_4sage_5rings_7integer_Integer *, __mpz_struct *);
  PyObject *(*hash_c)(struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_pari_)(struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  PyObject *(*_shift_helper)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *, int, int __pyx_skip_dispatch);
  PyObject *(*_and)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_or)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  PyObject *(*_xor)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  size_t (*_exact_log_log2_iter)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  size_t (*_exact_log_mpfi_log)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_9structure_7element_RingElement *(*_valuation)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  PyObject *(*_val_unit)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  struct __pyx_obj_4sage_5rings_7integer_Integer *(*_divide_knowing_divisible_by)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  int (*_is_power_of)(struct __pyx_obj_4sage_5rings_7integer_Integer *, struct __pyx_obj_4sage_5rings_7integer_Integer *);
  int (*_pseudoprime_is_prime)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *);
  PyObject *(*_pari_divisors_small)(struct __pyx_obj_4sage_5rings_7integer_Integer *, int __pyx_skip_dispatch);
  PyObject *(*_reduce_set)(struct __pyx_obj_4sage_5rings_7integer_Integer *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_5rings_7integer_Integer *__pyx_vtabptr_4sage_5rings_7integer_Integer;


/* "sage/rings/integer.pxd":37
 * cdef Integer smallInteger(long value)
 * 
 * cdef class int_to_Z(Morphism):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_5rings_7integer_int_to_Z {
  struct __pyx_vtabstruct_4sage_10categories_8morphism_Morphism __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_7integer_int_to_Z *__pyx_vtabptr_4sage_5rings_7integer_int_to_Z;


/* "polynomial_compiled.pxd":5
 * 
 * 
 * cdef class generic_pd             # <<<<<<<<<<<<<<
 * 
 * cdef class CompiledPolynomialFunction:
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd {
  int (*eval)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *, PyObject *, PyObject *);
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *(*nodummies)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *);
  void (*reset)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *);
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd;


/* "polynomial_compiled.pxd":7
 * cdef class generic_pd
 * 
 * cdef class CompiledPolynomialFunction:             # <<<<<<<<<<<<<<
 *     cdef generic_pd _dag
 *     cdef object _coeffs
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction {
  PyObject *(*_parse_structure)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *);
  struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *(*_get_gap)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *, struct __pyx_obj_4sage_4misc_11binary_tree_BinaryTree *, int);
  void (*_fill_gaps_binary)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *, struct __pyx_obj_4sage_4misc_11binary_tree_BinaryTree *);
  PyObject *(*eval)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction;


/* "polynomial_compiled.pxd":24
 *     cdef void reset(self)
 * 
 * cdef class dummy_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd link
 *     cdef void fill(dummy_pd self, generic_pd link)
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
  void (*fill)(struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd *, struct __pyx_obj_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd *);
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd;


/* "polynomial_compiled.pxd":28
 *     cdef void fill(dummy_pd self, generic_pd link)
 * 
 * cdef class var_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_var_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_var_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_var_pd;


/* "polynomial_compiled.pxd":31
 *     cdef int index
 * 
 * cdef class univar_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd;


/* "polynomial_compiled.pxd":34
 *     pass
 * 
 * cdef class coeff_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd;


/* "polynomial_compiled.pxd":38
 * 
 * 
 * cdef class unary_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd operand
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd;


/* "polynomial_compiled.pxd":41
 *     cdef generic_pd operand
 * 
 * cdef class sqr_pd(unary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd;


/* "polynomial_compiled.pxd":44
 *     pass
 * 
 * cdef class pow_pd(unary_pd):             # <<<<<<<<<<<<<<
 *     cdef object exponent
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd;


/* "polynomial_compiled.pxd":48
 * 
 * 
 * cdef class binary_pd(generic_pd):             # <<<<<<<<<<<<<<
 *     cdef generic_pd left, right
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd;


/* "polynomial_compiled.pxd":51
 *     cdef generic_pd left, right
 * 
 * cdef class add_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_add_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_add_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_add_pd;


/* "polynomial_compiled.pxd":54
 *     pass
 * 
 * cdef class mul_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd;


/* "polynomial_compiled.pxd":57
 *     pass
 * 
 * cdef class abc_pd(binary_pd):             # <<<<<<<<<<<<<<
 *     cdef int index
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd *__pyx_vtabptr_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd;


/* "sage/rings/polynomial/polynomial_element.pxd":8
 * 
 * 
 * cdef class Polynomial(CommutativeAlgebraElement):             # <<<<<<<<<<<<<<
 *     cdef char _is_gen
 *     cdef CompiledPolynomialFunction _compiled
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial {
  struct __pyx_vtabstruct_4sage_9structure_7element_CommutativeAlgebraElement __pyx_base;
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *(*truncate)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, long, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *(*inverse_series_trunc)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, long, int __pyx_skip_dispatch);
  long (*_hash_c)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *);
  PyObject *(*constant_coefficient)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *(*_new_constant_poly)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, PyObject *, struct __pyx_obj_4sage_9structure_6parent_Parent *, int __pyx_skip_dispatch);
  int (*is_zero)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, int __pyx_skip_dispatch);
  int (*is_one)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *(*_mul_trunc_)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, long, int __pyx_skip_dispatch);
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *(*_power_trunc)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, unsigned long, long, int __pyx_skip_dispatch);
  PyObject *(*_inplace_truncate)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, long);
  PyObject *(*get_unsafe)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial *, Py_ssize_t);
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial *__pyx_vtabptr_4sage_5rings_10polynomial_18polynomial_element_Polynomial;


/* "sage/rings/polynomial/polynomial_element.pxd":29
 *     cdef get_unsafe(self, Py_ssize_t i)
 * 
 * cdef class Polynomial_generic_dense(Polynomial):             # <<<<<<<<<<<<<<
 *     cdef Polynomial_generic_dense _new_c(self, list coeffs, Parent P)
 *     cdef list __coeffs
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial __pyx_base;
  struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense *(*_new_c)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense *, PyObject *, struct __pyx_obj_4sage_9structure_6parent_Parent *);
  int (*__pyx___normalize)(struct __pyx_obj_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense *);
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense *__pyx_vtabptr_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense;


/* "sage/rings/polynomial/polynomial_element.pxd":34
 *     cdef int __normalize(self) except -1
 * 
 * cdef class Polynomial_generic_dense_inexact(Polynomial_generic_dense):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact {
  struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact *__pyx_vtabptr_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact;


/* "sage/libs/ntl/ntl_ZZX.pxd":3
 * from .types cimport ZZX_c
 * 
 * cdef class ntl_ZZX(object):             # <<<<<<<<<<<<<<
 *     cdef ZZX_c x
 *     cdef void setitem_from_int(ntl_ZZX self, long i, int value)
 */

struct __pyx_vtabstruct_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX {
  void (*setitem_from_int)(struct __pyx_obj_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX *, long, int);
  int (*getitem_as_int)(struct __pyx_obj_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX *, long);
};
static struct __pyx_vtabstruct_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX *__pyx_vtabptr_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX;


/* "sage/libs/ntl/ntl_ZZ.pxd":3
 * from sage.libs.ntl.types cimport ZZ_c
 * 
 * cdef class ntl_ZZ(object):             # <<<<<<<<<<<<<<
 *     cdef ZZ_c x
 *     cdef int get_as_int(ntl_ZZ self)
 */

struct __pyx_vtabstruct_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ {
  int (*get_as_int)(struct __pyx_obj_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ *);
  void (*set_from_int)(struct __pyx_obj_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ *, int);
};
static struct __pyx_vtabstruct_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ *__pyx_vtabptr_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ;


/* "number_field_element.pxd":11
 * from sage.libs.ntl.ntl_ZZ cimport ntl_ZZ
 * 
 * cdef class NumberFieldElement(FieldElement):             # <<<<<<<<<<<<<<
 *     cdef ZZX_c __numerator
 *     cdef ZZ_c __denominator
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement {
  struct __pyx_vtabstruct_4sage_9structure_7element_FieldElement __pyx_base;
  PyObject *(*_new)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *);
  PyObject *(*number_field)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *);
  void (*_ntl_coeff_as_mpz)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, __mpz_struct *, long);
  void (*_ntl_denom_as_mpz)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, __mpz_struct *);
  void (*_reduce_c_)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *);
  PyObject *(*_coefficients)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, int __pyx_skip_dispatch);
  int (*is_rational)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, int __pyx_skip_dispatch);
  int (*is_one)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, int __pyx_skip_dispatch);
  int (*_randomize)(struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *, PyObject *, PyObject *, PyObject *);
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *__pyx_vtabptr_4sage_5rings_12number_field_20number_field_element_NumberFieldElement;


/* "number_field_element.pxd":38
 * 
 * 
 * cdef class NumberFieldElement_absolute(NumberFieldElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute *__pyx_vtabptr_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute;


/* "number_field_element.pxd":41
 *     pass
 * 
 * cdef class NumberFieldElement_relative(NumberFieldElement):             # <<<<<<<<<<<<<<
 *     pass
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative *__pyx_vtabptr_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative;


/* "number_field_element.pxd":46
 * # TODO: cyclotomic and/or quadratic classes? (Both for differing implementations and speed).
 * 
 * cdef class OrderElement_absolute(NumberFieldElement_absolute):             # <<<<<<<<<<<<<<
 *     cdef object _number_field
 * 
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute *__pyx_vtabptr_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute;


/* "number_field_element.pxd":49
 *     cdef object _number_field
 * 
 * cdef class OrderElement_relative(NumberFieldElement_relative):             # <<<<<<<<<<<<<<
 *     cdef object _number_field
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_OrderElement_relative {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_OrderElement_relative *__pyx_vtabptr_4sage_5rings_12number_field_20number_field_element_OrderElement_relative;


/* "sage/rings/number_field/number_field_element_quadratic.pxd":6
 * 
 * 
 * cdef class NumberFieldElement_quadratic(NumberFieldElement_absolute):             # <<<<<<<<<<<<<<
 *     # (a + b sqrt(D)) / denom
 *     cdef mpz_t a, b, denom
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute __pyx_base;
  struct __pyx_obj_4sage_5rings_12number_field_20number_field_element_NumberFieldElement *(*galois_conjugate)(struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic *, int __pyx_skip_dispatch);
  int (*is_sqrt_disc)(struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic *);
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic *__pyx_vtabptr_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic;


/* "sage/rings/number_field/number_field_element_quadratic.pxd":19
 * 
 * 
 * cdef class OrderElement_quadratic(NumberFieldElement_quadratic):             # <<<<<<<<<<<<<<
 *     pass
 */

struct __pyx_vtabstruct_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic {
  struct __pyx_vtabstruct_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic __pyx_base;
};
static struct __pyx_vtabstruct_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic *__pyx_vtabptr_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic;


/* "psage/modform/hilbert/sqrt5/sqrt5_fast.pxd":7
 * ctypedef long residue_element[2]
 * 
 * cdef class ResidueRingElement             # <<<<<<<<<<<<<<
 * 
 * cdef class ResidueRing_abstract(CommutativeRing):
 */

struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement {
  long (*index)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch);
  PyObject *(*parent)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch);
  PyObject *(*new_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *);
  int (*is_unit)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch);
  int (*is_square)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch);
  PyObject *(*sqrt)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_vtabptr_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement;


/* "psage/modform/hilbert/sqrt5/sqrt5_fast.pxd":9
 * cdef class ResidueRingElement
 * 
 * cdef class ResidueRing_abstract(CommutativeRing):             # <<<<<<<<<<<<<<
 *     cdef object P, F
 *     cdef public object element_class, _residue_field
 */

struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract {
  struct __pyx_vtabstruct_4sage_5rings_4ring_CommutativeRing __pyx_base;
  PyObject *(*element_to_residue_field)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  void (*add)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *, long *);
  void (*sub)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *, long *);
  void (*mul)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *, long *);
  int (*inv)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*is_unit)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  void (*neg)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *(*new_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *);
  int (*coefficients)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *, struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic *);
  int (*coerce_from_nf)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, struct __pyx_obj_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic *);
  int (*element_is_1)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  int (*element_is_0)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  void (*set_element_to_1)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  void (*set_element_to_0)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  void (*set_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*set_element_from_tuple)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, PyObject *);
  int (*cmp_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*pow)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *, long);
  int (*is_square)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  int (*sqrt)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*ith_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long);
  long (*cardinality)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, int __pyx_skip_dispatch);
  void (*unsafe_ith_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long);
  int (*next_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*is_last_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  long (*index_of_element)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  long (*index_of_element_in_P)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  int (*next_element_in_P)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *, long *);
  int (*is_last_element_in_P)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
  PyObject *(*element_to_str)(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, long *);
};
static struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_vtabptr_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract;


/* "sage/stats/intlist.pxd":8
 * #############################################################################
 * 
 * cdef class IntList:             # <<<<<<<<<<<<<<
 *     cdef int* _values
 *     cdef Py_ssize_t _length
 */

struct __pyx_vtabstruct_4sage_5stats_7intlist_IntList {
  int (*prod)(struct __pyx_obj_4sage_5stats_7intlist_IntList *, int __pyx_skip_dispatch);
  int (*sum)(struct __pyx_obj_4sage_5stats_7intlist_IntList *, int __pyx_skip_dispatch);
};
static struct __pyx_vtabstruct_4sage_5stats_7intlist_IntList *__pyx_vtabptr_4sage_5stats_7intlist_IntList;


/* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":365
 *     return C
 * 
 * cdef class InertTraceCalculator:             # <<<<<<<<<<<<<<
 *     cdef public dict tables
 * 
 */

struct __pyx_vtabstruct_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator {
  long (*trace_of_frobenius)(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *, PyObject *, PyObject *, long, int __pyx_skip_dispatch);
  int (*cube_table)(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *, struct __pyx_obj_4sage_5stats_7intlist_IntList *, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *);
  int (*init_squares_table)(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *, struct __pyx_obj_4sage_5stats_7intlist_IntList *, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *);
  int (*elliptic_curve_from_j)(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *, long *, long *, long *, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *);
  int (*ap_via_enumeration)(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *, int *, int *, long *, long *, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *, struct __pyx_obj_4sage_5stats_7intlist_IntList *, struct __pyx_obj_4sage_5stats_7intlist_IntList *);
};
static struct __pyx_vtabstruct_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_vtabptr_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator;

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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

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static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);

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static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig);

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static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);

static long __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_trace_of_frobenius(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, PyObject *__pyx_v_j0, PyObject *__pyx_v_c_quo0, long __pyx_v_p, int __pyx_skip_dispatch); /* proto*/
static int __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_cube_table(CYTHON_UNUSED struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_cubes, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R); /* proto*/
static int __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_init_squares_table(CYTHON_UNUSED struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_squares, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R); /* proto*/
static int __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_elliptic_curve_from_j(CYTHON_UNUSED struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, long *__pyx_v_a4, long *__pyx_v_a6, long *__pyx_v_j, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R); /* proto*/
static int __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_ap_via_enumeration(CYTHON_UNUSED struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, int *__pyx_v_ap, int *__pyx_v_c_quo, long *__pyx_v_a4, long *__pyx_v_a6, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_squares, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_cubes); /* proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_6parent_6Parent_get_flag(struct __pyx_obj_4sage_9structure_6parent_Parent *__pyx_v_self, int __pyx_v_flag); /* proto*/

/* Module declarations from 'libc.stdint' */

/* Module declarations from 'libc.string' */

/* Module declarations from 'libc.stdio' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

/* Module declarations from 'cpython.version' */

/* Module declarations from 'cpython.ref' */

/* Module declarations from 'cpython.exc' */

/* Module declarations from 'cpython.module' */

/* Module declarations from 'cpython.mem' */

/* Module declarations from 'cpython.tuple' */

/* Module declarations from 'cpython.list' */

/* Module declarations from 'cpython.sequence' */

/* Module declarations from 'cpython.mapping' */

/* Module declarations from 'cpython.iterator' */

/* Module declarations from 'cpython.number' */

/* Module declarations from 'cpython.int' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.bool' */
static PyTypeObject *__pyx_ptype_7cpython_4bool_bool = 0;

/* Module declarations from 'cpython.long' */

/* Module declarations from 'cpython.float' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.complex' */
static PyTypeObject *__pyx_ptype_7cpython_7complex_complex = 0;

/* Module declarations from 'cpython.string' */

/* Module declarations from 'cpython.unicode' */

/* Module declarations from 'cpython.dict' */

/* Module declarations from 'cpython.instance' */

/* Module declarations from 'cpython.function' */

/* Module declarations from 'cpython.method' */

/* Module declarations from 'cpython.weakref' */

/* Module declarations from 'cpython.getargs' */

/* Module declarations from 'cpython.pythread' */

/* Module declarations from 'cpython.pystate' */

/* Module declarations from 'cpython.cobject' */

/* Module declarations from 'cpython.oldbuffer' */

/* Module declarations from 'cpython.set' */

/* Module declarations from 'cpython.buffer' */

/* Module declarations from 'cpython.bytes' */

/* Module declarations from 'cpython.pycapsule' */

/* Module declarations from 'cpython' */

/* Module declarations from 'cpython.object' */

/* Module declarations from 'sage.structure.sage_object' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11sage_object_SageObject = 0;
static CYTHON_INLINE PyObject *__pyx_f_4sage_9structure_11sage_object_richcmp_not_equal(PyObject *, PyObject *, int, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_11sage_object_rich_to_bool(int, int, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_11sage_object_rich_to_bool_sgn(int, int, int __pyx_skip_dispatch); /*proto*/

/* Module declarations from 'sage.structure.category_object' */
static PyTypeObject *__pyx_ptype_4sage_9structure_15category_object_CategoryObject = 0;

/* Module declarations from 'cython' */

/* Module declarations from 'sage.structure.coerce_dict' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11coerce_dict_MonoDict = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_11coerce_dict_TripleDict = 0;

/* Module declarations from 'sage.misc.cython_metaclass' */

/* Module declarations from 'sage.misc' */

/* Module declarations from 'sage.misc.inherit_comparison' */
static PyTypeObject *__pyx_ptype_4sage_4misc_18inherit_comparison_InheritComparisonMetaclass = 0;

/* Module declarations from 'sage.structure.element' */
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Element = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_ElementWithCachedMethod = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_ModuleElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_RingElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_MonoidElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_MultiplicativeGroupElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_AdditiveGroupElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_CommutativeRingElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_IntegralDomainElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_DedekindDomainElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_PrincipalIdealDomainElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_EuclideanDomainElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_FieldElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_AlgebraElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_CommutativeAlgebraElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_InfinityElement = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Vector = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_Matrix = 0;
static PyTypeObject *__pyx_ptype_4sage_9structure_7element_CoercionModel = 0;
static struct __pyx_obj_4sage_9structure_7element_CoercionModel **__pyx_vp_4sage_9structure_7element_coercion_model = 0;
#define __pyx_v_4sage_9structure_7element_coercion_model (*__pyx_vp_4sage_9structure_7element_coercion_model)
static CYTHON_INLINE PyObject *__pyx_f_4sage_9structure_7element_parent(PyObject *, int __pyx_skip_dispatch); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_7element_classify_elements(PyObject *, PyObject *); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_7element_HAVE_SAME_PARENT(int); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_9structure_7element_have_same_parent(PyObject *, PyObject *, int __pyx_skip_dispatch); /*proto*/

/* Module declarations from 'sage.structure' */

/* Module declarations from 'sage' */

/* Module declarations from 'sage.structure.parent' */
static PyTypeObject *__pyx_ptype_4sage_9structure_6parent_Parent = 0;

/* Module declarations from 'sage.structure.parent_old' */
static PyTypeObject *__pyx_ptype_4sage_9structure_10parent_old_Parent = 0;

/* Module declarations from 'sage.structure.parent_base' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_base_ParentWithBase = 0;

/* Module declarations from 'sage.structure.parent_gens' */
static PyTypeObject *__pyx_ptype_4sage_9structure_11parent_gens_ParentWithGens = 0;

/* Module declarations from 'sage.rings.ring' */
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Ring = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_CommutativeRing = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_IntegralDomain = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_DedekindDomain = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_PrincipalIdealDomain = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_EuclideanDomain = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Field = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_Algebra = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_4ring_CommutativeAlgebra = 0;

/* Module declarations from 'sage.libs.gmp.types' */

/* Module declarations from 'sage.libs.ntl.types' */

/* Module declarations from 'sage.categories.map' */
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_Map = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_Section = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_3map_FormalCompositeMap = 0;

/* Module declarations from 'sage.categories.morphism' */
static PyTypeObject *__pyx_ptype_4sage_10categories_8morphism_Morphism = 0;
static PyTypeObject *__pyx_ptype_4sage_10categories_8morphism_SetMorphism = 0;

/* Module declarations from 'sage.rings.integer' */
static PyTypeObject *__pyx_ptype_4sage_5rings_7integer_Integer = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_7integer_int_to_Z = 0;

/* Module declarations from 'sage.misc.binary_tree' */
static PyTypeObject *__pyx_ptype_4sage_4misc_11binary_tree_BinaryTree = 0;

/* Module declarations from 'sage.rings.polynomial.polynomial_compiled' */
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_generic_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_CompiledPolynomialFunction = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_dummy_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_var_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_univar_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_coeff_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_unary_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_sqr_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_pow_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_binary_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_add_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_mul_pd = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_19polynomial_compiled_abc_pd = 0;

/* Module declarations from 'sage.rings.polynomial.polynomial_element' */
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_18polynomial_element_Polynomial = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_10polynomial_18polynomial_element_Polynomial_generic_dense_inexact = 0;

/* Module declarations from 'sage.libs.ntl.ntl_ZZX' */
static PyTypeObject *__pyx_ptype_4sage_4libs_3ntl_7ntl_ZZX_ntl_ZZX = 0;

/* Module declarations from 'sage.libs.ntl.ntl_ZZ' */
static PyTypeObject *__pyx_ptype_4sage_4libs_3ntl_6ntl_ZZ_ntl_ZZ = 0;

/* Module declarations from 'sage.rings.number_field.number_field_element' */
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_20number_field_element_NumberFieldElement = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_absolute = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_20number_field_element_NumberFieldElement_relative = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_20number_field_element_OrderElement_absolute = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_20number_field_element_OrderElement_relative = 0;

/* Module declarations from 'sage.rings.number_field.number_field_element_quadratic' */
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_30number_field_element_quadratic_NumberFieldElement_quadratic = 0;
static PyTypeObject *__pyx_ptype_4sage_5rings_12number_field_30number_field_element_quadratic_OrderElement_quadratic = 0;

/* Module declarations from 'psage.modform.hilbert.sqrt5.sqrt5_fast' */
static PyTypeObject *__pyx_ptype_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement = 0;
static PyTypeObject *__pyx_ptype_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract = 0;

/* Module declarations from 'sage.libs.gmp.mpz' */

/* Module declarations from 'cysignals.__init__' */

/* Module declarations from 'cysignals' */

/* Module declarations from 'cysignals.signals' */
static cysigs_t *__pyx_vp_9cysignals_7signals_cysigs = 0;
#define cysigs (*__pyx_vp_9cysignals_7signals_cysigs)
static void (*__pyx_f_9cysignals_7signals_print_backtrace)(void); /*proto*/
static void (*__pyx_f_9cysignals_7signals__sig_on_interrupt_received)(void); /*proto*/
static void (*__pyx_f_9cysignals_7signals__sig_on_recover)(void); /*proto*/
static void (*__pyx_f_9cysignals_7signals__sig_off_warning)(char const *, int); /*proto*/

/* Module declarations from 'libc.stdlib' */

/* Module declarations from 'cysignals.memory' */
static CYTHON_INLINE void *sig_malloc(size_t); /*proto*/
static CYTHON_INLINE void *sig_realloc(void *, size_t); /*proto*/
static CYTHON_INLINE void *sig_calloc(size_t, size_t); /*proto*/
static CYTHON_INLINE void sig_free(void *); /*proto*/
static CYTHON_INLINE size_t __pyx_f_9cysignals_6memory_mul_overflowcheck(size_t, size_t); /*proto*/
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_allocarray(size_t, size_t); /*proto*/
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_reallocarray(void *, size_t, size_t); /*proto*/
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_malloc(size_t); /*proto*/
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_realloc(void *, size_t); /*proto*/
static CYTHON_INLINE void *__pyx_f_9cysignals_6memory_check_calloc(size_t, size_t); /*proto*/

/* Module declarations from 'sage.ext.stdsage' */
static CYTHON_INLINE PyObject *__pyx_f_4sage_3ext_7stdsage_PY_NEW(PyTypeObject *); /*proto*/
static CYTHON_INLINE int __pyx_f_4sage_3ext_7stdsage_HAS_DICTIONARY(PyObject *); /*proto*/

/* Module declarations from 'sage.stats.intlist' */
static PyTypeObject *__pyx_ptype_4sage_5stats_7intlist_IntList = 0;

/* Module declarations from 'code.alex.psage.psage.ellcurve.lseries.sqrt5' */
static PyTypeObject *__pyx_ptype_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius = 0;
static PyTypeObject *__pyx_ptype_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator = 0;
static PyTypeObject *__pyx_ptype___pyx_scope_struct____Pyx_CFunc_object____object____object____int___to_py = 0;
static long __pyx_v_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_UNKNOWN;
static long __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_ap_via_enumeration(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *, int __pyx_skip_dispatch); /*proto*/
static unsigned long __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_sqrt_mod(unsigned long, unsigned long, int __pyx_skip_dispatch); /*proto*/
static PyObject *__Pyx_CFunc_object____object____object____int___to_py(PyObject *(*)(PyObject *, PyObject *, int)); /*proto*/
#define __Pyx_MODULE_NAME "code.alex.psage.psage.ellcurve.lseries.sqrt5"
int __pyx_module_is_main_code__alex__psage__psage__ellcurve__lseries__sqrt5 = 0;

/* Implementation of 'code.alex.psage.psage.ellcurve.lseries.sqrt5' */
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_builtin_IndexError;
static PyObject *__pyx_builtin_NotImplementedError;
static PyObject *__pyx_builtin_MemoryError;
static PyObject *__pyx_builtin_AttributeError;
static const char __pyx_k_C[] = "C";
static const char __pyx_k_E[] = "E";
static const char __pyx_k_F[] = "F";
static const char __pyx_k_N[] = "N";
static const char __pyx_k_R[] = "R";
static const char __pyx_k_a[] = "a";
static const char __pyx_k_c[] = "c";
static const char __pyx_k_p[] = "p";
static const char __pyx_k_s[] = "s";
static const char __pyx_k_x[] = "x";
static const char __pyx_k_y[] = "y";
static const char __pyx_k_a4[] = "a4";
static const char __pyx_k_a6[] = "a6";
static const char __pyx_k_ap[] = "ap";
static const char __pyx_k_j0[] = "j0";
static const char __pyx_k_op[] = "op";
static const char __pyx_k_gen[] = "gen";
static const char __pyx_k_arg0[] = "arg0";
static const char __pyx_k_arg1[] = "arg1";
static const char __pyx_k_arg2[] = "arg2";
static const char __pyx_k_keys[] = "keys";
static const char __pyx_k_left[] = "left";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_math[] = "math";
static const char __pyx_k_pari[] = "pari";
static const char __pyx_k_sqrt[] = "sqrt";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_wrap[] = "wrap";
static const char __pyx_k_bound[] = "bound";
static const char __pyx_k_c_quo[] = "c_quo";
static const char __pyx_k_ideal[] = "ideal";
static const char __pyx_k_parts[] = "parts";
static const char __pyx_k_prime[] = "prime";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_right[] = "right";
static const char __pyx_k_sqrt5[] = "sqrt5";
static const char __pyx_k_aplist[] = "aplist";
static const char __pyx_k_c_quo0[] = "c_quo0";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_parent[] = "parent";
static const char __pyx_k_primes[] = "primes";
static const char __pyx_k_tables[] = "tables";
static const char __pyx_k_squares[] = "squares";
static const char __pyx_k_verbose[] = "verbose";
static const char __pyx_k_prime_pi[] = "prime_pi";
static const char __pyx_k_sage_all[] = "sage.all";
static const char __pyx_k_smalljac[] = "smalljac";
static const char __pyx_k_algorithm[] = "algorithm";
static const char __pyx_k_IndexError[] = "IndexError";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_pyx_vtable[] = "__pyx_vtable__";
static const char __pyx_k_MemoryError[] = "MemoryError";
static const char __pyx_k_ResidueRing[] = "ResidueRing";
static const char __pyx_k_cfunc_to_py[] = "cfunc.to_py";
static const char __pyx_k_deprecation[] = "deprecation";
static const char __pyx_k_get_verbose[] = "get_verbose";
static const char __pyx_k_inert_table[] = "inert_table";
static const char __pyx_k_prime_range[] = "prime_range";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_a_invariants[] = "a_invariants";
static const char __pyx_k_inert_primes[] = "inert_primes";
static const char __pyx_k_stringsource[] = "stringsource";
static const char __pyx_k_AttributeError[] = "AttributeError";
static const char __pyx_k_naive_i_s_a__s[] = "naive i=%s, a_{%s}";
static const char __pyx_k_sage_ext_memory[] = "sage.ext.memory";
static const char __pyx_k_elliptic_curve_ap[] = "elliptic_curve_ap";
static const char __pyx_k_trace_of_frobenius[] = "trace_of_frobenius";
static const char __pyx_k_NotImplementedError[] = "NotImplementedError";
static const char __pyx_k_compute_naive_trace[] = "_compute_naive_trace";
static const char __pyx_k_compute_split_traces[] = "_compute_split_traces";
static const char __pyx_k_sage_misc_superseded[] = "sage.misc.superseded";
static const char __pyx_k_init_memory_functions[] = "init_memory_functions";
static const char __pyx_k_initialize_coefficients[] = "_initialize_coefficients";
static const char __pyx_k_i_must_be_between_0_and_s[] = "i must be between 0 and %s";
static const char __pyx_k_Pyx_CFunc_object____object[] = "__Pyx_CFunc_object____object____object____int___to_py.<locals>.wrap";
static const char __pyx_k_failed_to_allocate_s_bytes[] = "failed to allocate %s bytes";
static const char __pyx_k_initialize_prime_ap_tables[] = "_initialize_prime_ap_tables";
static const char __pyx_k_memory_assumption_violated[] = "memory assumption violated";
static const char __pyx_k_ellap_ellinit_0_0_0_s_s_1_s[] = "ellap(ellinit([0,0,0,%s,%s],1),%s)";
static const char __pyx_k_failed_to_allocate_s_s_bytes[] = "failed to allocate %s * %s bytes";
static const char __pyx_k_psage_libs_smalljac_wrapper1[] = "psage.libs.smalljac.wrapper1";
static const char __pyx_k_residue_ring_must_be_a_field[] = "residue ring must be a field";
static const char __pyx_k_unpickle_InertTraceCalculator[] = "unpickle_InertTraceCalculator";
static const char __pyx_k_File_sqrt5_pyx_starting_at_line[] = "File: sqrt5.pyx (starting at line 1)\n\nFast Cython code needed to compute L-series of elliptic curves over F = Q(sqrt(5)).\n\nUSES:\n\n   - The fast residue class rings defined in\n     psage.modform.hilbert.sqrt5.sqrt5_fast for naive enumeration.\n\n   - Drew Sutherlands smalljac for point counting\n\n   - Lcalc for evaluating the L-series\n\n   - Dokchitser as well.\n\n   - Computes the *root number* in addition to the L-series.\n\n";
static const char __pyx_k_compute_inert_and_ramified_trac[] = "_compute_inert_and_ramified_traces";
static const char __pyx_k_compute_remaining_traces_naivel[] = "_compute_remaining_traces_naively";
static const char __pyx_k_projects_68c8b2b8_03ba_44d4_a0d[] = "/projects/68c8b2b8-03ba-44d4-a0d1-5d771c8cb465/code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx";
static const char __pyx_k_Inert_trace_calculator_with_prec[] = "Inert trace calculator with precomputed tables for p in {%s}";
static const char __pyx_k_code_alex_psage_psage_ellcurve_l[] = "code.alex.psage.psage.ellcurve.lseries.sqrt5";
static const char __pyx_k_import_cysignals_signals_pxi_ins[] = "import \"cysignals/signals.pxi\" instead of \"sage/ext/interrupt.pxi\"";
static const char __pyx_k_psage_modform_hilbert_sqrt5_sqrt[] = "psage.modform.hilbert.sqrt5.sqrt5";
static const char __pyx_k_skipping_inert_table_computation[] = "skipping inert table computation for p=%s (%s)";
static const char __pyx_k_psage_modform_hilbert_sqrt5_sqrt_2[] = "psage.modform.hilbert.sqrt5.sqrt5_fast";
static PyObject *__pyx_n_s_AttributeError;
static PyObject *__pyx_n_s_C;
static PyObject *__pyx_n_s_E;
static PyObject *__pyx_n_s_F;
static PyObject *__pyx_n_s_IndexError;
static PyObject *__pyx_kp_s_Inert_trace_calculator_with_prec;
static PyObject *__pyx_n_s_MemoryError;
static PyObject *__pyx_n_s_N;
static PyObject *__pyx_n_s_NotImplementedError;
static PyObject *__pyx_n_s_Pyx_CFunc_object____object;
static PyObject *__pyx_n_s_R;
static PyObject *__pyx_n_s_ResidueRing;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s_a;
static PyObject *__pyx_n_s_a4;
static PyObject *__pyx_n_s_a6;
static PyObject *__pyx_n_s_a_invariants;
static PyObject *__pyx_n_s_algorithm;
static PyObject *__pyx_n_s_ap;
static PyObject *__pyx_n_s_aplist;
static PyObject *__pyx_n_s_arg0;
static PyObject *__pyx_n_s_arg1;
static PyObject *__pyx_n_s_arg2;
static PyObject *__pyx_n_s_bound;
static PyObject *__pyx_n_s_c;
static PyObject *__pyx_n_s_c_quo;
static PyObject *__pyx_n_s_c_quo0;
static PyObject *__pyx_n_s_cfunc_to_py;
static PyObject *__pyx_n_s_code_alex_psage_psage_ellcurve_l;
static PyObject *__pyx_n_s_compute_inert_and_ramified_trac;
static PyObject *__pyx_n_s_compute_naive_trace;
static PyObject *__pyx_n_s_compute_remaining_traces_naivel;
static PyObject *__pyx_n_s_compute_split_traces;
static PyObject *__pyx_n_s_deprecation;
static PyObject *__pyx_kp_s_ellap_ellinit_0_0_0_s_s_1_s;
static PyObject *__pyx_n_s_elliptic_curve_ap;
static PyObject *__pyx_kp_s_failed_to_allocate_s_bytes;
static PyObject *__pyx_kp_s_failed_to_allocate_s_s_bytes;
static PyObject *__pyx_n_s_gen;
static PyObject *__pyx_n_s_get_verbose;
static PyObject *__pyx_kp_s_i_must_be_between_0_and_s;
static PyObject *__pyx_n_s_ideal;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_kp_s_import_cysignals_signals_pxi_ins;
static PyObject *__pyx_n_s_inert_primes;
static PyObject *__pyx_n_s_inert_table;
static PyObject *__pyx_n_s_init_memory_functions;
static PyObject *__pyx_n_s_initialize_coefficients;
static PyObject *__pyx_n_s_initialize_prime_ap_tables;
static PyObject *__pyx_n_s_j0;
static PyObject *__pyx_n_s_keys;
static PyObject *__pyx_n_s_left;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_math;
static PyObject *__pyx_kp_s_memory_assumption_violated;
static PyObject *__pyx_kp_s_naive_i_s_a__s;
static PyObject *__pyx_n_s_op;
static PyObject *__pyx_n_s_p;
static PyObject *__pyx_n_s_parent;
static PyObject *__pyx_n_s_pari;
static PyObject *__pyx_n_s_parts;
static PyObject *__pyx_n_s_prime;
static PyObject *__pyx_n_s_prime_pi;
static PyObject *__pyx_n_s_prime_range;
static PyObject *__pyx_n_s_primes;
static PyObject *__pyx_kp_s_projects_68c8b2b8_03ba_44d4_a0d;
static PyObject *__pyx_n_s_psage_libs_smalljac_wrapper1;
static PyObject *__pyx_n_s_psage_modform_hilbert_sqrt5_sqrt;
static PyObject *__pyx_n_s_psage_modform_hilbert_sqrt5_sqrt_2;
static PyObject *__pyx_n_s_pyx_vtable;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_kp_s_residue_ring_must_be_a_field;
static PyObject *__pyx_n_s_right;
static PyObject *__pyx_n_s_s;
static PyObject *__pyx_n_s_sage_all;
static PyObject *__pyx_n_s_sage_ext_memory;
static PyObject *__pyx_n_s_sage_misc_superseded;
static PyObject *__pyx_kp_s_skipping_inert_table_computation;
static PyObject *__pyx_n_s_smalljac;
static PyObject *__pyx_n_s_sqrt;
static PyObject *__pyx_n_s_sqrt5;
static PyObject *__pyx_n_s_squares;
static PyObject *__pyx_kp_s_stringsource;
static PyObject *__pyx_n_s_tables;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_trace_of_frobenius;
static PyObject *__pyx_n_s_unpickle_InertTraceCalculator;
static PyObject *__pyx_n_s_verbose;
static PyObject *__pyx_n_s_wrap;
static PyObject *__pyx_n_s_x;
static PyObject *__pyx_n_s_y;
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_ap_via_enumeration(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_v_a4, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_v_a6); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_2sqrt_mod(CYTHON_UNUSED PyObject *__pyx_self, unsigned long __pyx_v_a, unsigned long __pyx_v_p); /* proto */
static int __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius___cinit__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self); /* proto */
static int __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_2__init__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_E, long __pyx_v_bound); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_4_initialize_prime_ap_tables(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, long __pyx_v_bound); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_6_initialize_coefficients(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_E); /* proto */
static void __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_8__dealloc__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_10_tables(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_12aplist(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_14_compute_split_traces(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_algorithm); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_16_compute_inert_and_ramified_traces(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_T); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_18_compute_remaining_traces_naively(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_20_compute_naive_trace(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_22prime(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, long __pyx_v_i); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_17TracesOfFrobenius_24_compute_traces(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius *__pyx_v_self, PyObject *__pyx_v_inert_table, CYTHON_UNUSED PyObject *__pyx_v_algorithm); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_4inert_primes(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_N); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_6unpickle_InertTraceCalculator(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_tables); /* proto */
static int __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator___init__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_2__repr__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_4__reduce__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_6trace_of_frobenius(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, PyObject *__pyx_v_j0, PyObject *__pyx_v_c_quo0, long __pyx_v_p); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_8init_table(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, int __pyx_v_p); /* proto */
static PyObject *__pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_6tables___get__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self); /* proto */
static int __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_6tables_2__set__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, PyObject *__pyx_v_value); /* proto */
static int __pyx_pf_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_6tables_4__del__(struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4sage_9structure_11sage_object_richcmp_not_equal(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_x, PyObject *__pyx_v_y, int __pyx_v_op); /* proto */
static PyObject *__pyx_pf_4sage_9structure_11sage_object_2rich_to_bool(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_op, int __pyx_v_c); /* proto */
static PyObject *__pyx_pf_4sage_9structure_11sage_object_4rich_to_bool_sgn(CYTHON_UNUSED PyObject *__pyx_self, int __pyx_v_op, int __pyx_v_c); /* proto */
static PyObject *__pyx_pf_4sage_9structure_7element_parent(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_x); /* proto */
static PyObject *__pyx_pf_4sage_9structure_7element_2have_same_parent(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_left, PyObject *__pyx_v_right); /* proto */
static PyObject *__pyx_pf_11cfunc_dot_to_py_53__Pyx_CFunc_object____object____object____int___to_py_wrap(PyObject *__pyx_self, PyObject *__pyx_v_arg0, PyObject *__pyx_v_arg1, int __pyx_v_arg2); /* proto */
static PyObject *__pyx_tp_new_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_TracesOfFrobenius(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new___pyx_scope_struct____Pyx_CFunc_object____object____object____int___to_py(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static __Pyx_CachedCFunction __pyx_umethod_PyDict_Type_keys = {0, &__pyx_n_s_keys, 0, 0, 0};
static PyObject *__pyx_int_0;
static PyObject *__pyx_int_1;
static PyObject *__pyx_int_2;
static PyObject *__pyx_int_3;
static PyObject *__pyx_int_4;
static PyObject *__pyx_int_5;
static PyObject *__pyx_int_8;
static PyObject *__pyx_int_16;
static PyObject *__pyx_int_24;
static PyObject *__pyx_int_36;
static PyObject *__pyx_int_64;
static PyObject *__pyx_int_216;
static PyObject *__pyx_int_432;
static PyObject *__pyx_int_20002;
static PyObject *__pyx_int_neg_27;
static PyObject *__pyx_int_neg_48;
static PyObject *__pyx_int_neg_54;
static PyObject *__pyx_int_neg_64;
static PyObject *__pyx_int_neg_864;
static PyObject *__pyx_int_neg_110592;
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_codeobj__4;
static PyObject *__pyx_codeobj__7;
static PyObject *__pyx_codeobj__9;

/* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":56
 * from psage.modform.hilbert.sqrt5.sqrt5_fast import ResidueRing
 * 
 * cpdef long ap_via_enumeration(ResidueRingElement a4, ResidueRingElement a6) except -1:             # <<<<<<<<<<<<<<
 *     """
 *     Compute the trace of Frobenius `a_p` on the elliptic curve defined
 */

static PyObject *__pyx_pw_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_1ap_via_enumeration(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static long __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_ap_via_enumeration(struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_v_a4, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *__pyx_v_a6, CYTHON_UNUSED int __pyx_skip_dispatch) {
  long __pyx_v_i;
  long __pyx_v_cnt;
  struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R = 0;
  long __pyx_v_p;
  CYTHON_UNUSED long __pyx_v_n;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_x;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_z;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_w;
  long __pyx_r;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  int __pyx_t_2;
  long __pyx_t_3;
  long __pyx_t_4;
  int __pyx_t_5;
  __Pyx_RefNannySetupContext("ap_via_enumeration", 0);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":77
 *         120
 *     """
 *     cdef long i, cnt = 1  # point at infinity             # <<<<<<<<<<<<<<
 *     cdef ResidueRing_abstract R = a4.parent()
 * 
 */
  __pyx_v_cnt = 1;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":78
 *     """
 *     cdef long i, cnt = 1  # point at infinity
 *     cdef ResidueRing_abstract R = a4.parent()             # <<<<<<<<<<<<<<
 * 
 *     if R.e != 1:
 */
  __pyx_t_1 = ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRingElement *)__pyx_v_a4->__pyx_vtab)->parent(__pyx_v_a4, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 78, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract))))) __PYX_ERR(0, 78, __pyx_L1_error)
  __pyx_v_R = ((struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_t_1);
  __pyx_t_1 = 0;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":80
 *     cdef ResidueRing_abstract R = a4.parent()
 * 
 *     if R.e != 1:             # <<<<<<<<<<<<<<
 *         raise ValueError, "residue ring must be a field"
 * 
 */
  __pyx_t_2 = ((__pyx_v_R->e != 1) != 0);
  if (__pyx_t_2) {

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":81
 * 
 *     if R.e != 1:
 *         raise ValueError, "residue ring must be a field"             # <<<<<<<<<<<<<<
 * 
 *     cdef long p = R.p
 */
    __Pyx_Raise(__pyx_builtin_ValueError, __pyx_kp_s_residue_ring_must_be_a_field, 0, 0);
    __PYX_ERR(0, 81, __pyx_L1_error)

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":80
 *     cdef ResidueRing_abstract R = a4.parent()
 * 
 *     if R.e != 1:             # <<<<<<<<<<<<<<
 *         raise ValueError, "residue ring must be a field"
 * 
 */
  }

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":83
 *         raise ValueError, "residue ring must be a field"
 * 
 *     cdef long p = R.p             # <<<<<<<<<<<<<<
 *     cdef long n = p*(p-1)/2
 *     cdef residue_element x, z, w
 */
  __pyx_t_3 = __pyx_v_R->p;
  __pyx_v_p = __pyx_t_3;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":84
 * 
 *     cdef long p = R.p
 *     cdef long n = p*(p-1)/2             # <<<<<<<<<<<<<<
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    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->set_element_to_1(__pyx_v_R, __pyx_v_a6);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":459
 *             R.set_element_to_0(a4)
 *             R.set_element_to_1(a6)
 *             return 0             # <<<<<<<<<<<<<<
 * 
 *         if R.cmp_element(j, k) == 0:   # if j==1728
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":456
 *         k[0] = 1728 % R.p; k[1] = 0
 * 
 *         if R.element_is_0(j):   # if j==0             # <<<<<<<<<<<<<<
 *             R.set_element_to_0(a4)
 *             R.set_element_to_1(a6)
 */
  }

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":461
 *             return 0
 * 
 *         if R.cmp_element(j, k) == 0:   # if j==1728             # <<<<<<<<<<<<<<
 *             R.set_element_to_1(a4)
 *             R.set_element_to_0(a6)
 */
  __pyx_t_1 = ((((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->cmp_element(__pyx_v_R, __pyx_v_j, __pyx_v_k) == 0) != 0);
  if (__pyx_t_1) {

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":462
 * 
 *         if R.cmp_element(j, k) == 0:   # if j==1728
 *             R.set_element_to_1(a4)             # <<<<<<<<<<<<<<
 *             R.set_element_to_0(a6)
 *             return 0
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->set_element_to_1(__pyx_v_R, __pyx_v_a4);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":463
 *         if R.cmp_element(j, k) == 0:   # if j==1728
 *             R.set_element_to_1(a4)
 *             R.set_element_to_0(a6)             # <<<<<<<<<<<<<<
 *             return 0
 * 
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->set_element_to_0(__pyx_v_R, __pyx_v_a6);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":464
 *             R.set_element_to_1(a4)
 *             R.set_element_to_0(a6)
 *             return 0             # <<<<<<<<<<<<<<
 * 
 *         # -3 and -2
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":461
 *             return 0
 * 
 *         if R.cmp_element(j, k) == 0:   # if j==1728             # <<<<<<<<<<<<<<
 *             R.set_element_to_1(a4)
 *             R.set_element_to_0(a6)
 */
  }

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":467
 * 
 *         # -3 and -2
 *         m_three[0] = R.p - 3; m_three[1] = 0             # <<<<<<<<<<<<<<
 *         m_two[0] = R.p - 2; m_two[1] = 0
 * 
 */
  (__pyx_v_m_three[0]) = (__pyx_v_R->p - 3);
  (__pyx_v_m_three[1]) = 0;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":468
 *         # -3 and -2
 *         m_three[0] = R.p - 3; m_three[1] = 0
 *         m_two[0] = R.p - 2; m_two[1] = 0             # <<<<<<<<<<<<<<
 * 
 *         # k = j-1728
 */
  (__pyx_v_m_two[0]) = (__pyx_v_R->p - 2);
  (__pyx_v_m_two[1]) = 0;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":471
 * 
 *         # k = j-1728
 *         R.sub(k, j, k)             # <<<<<<<<<<<<<<
 * 
 *         # a4 = -3*j*k
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->sub(__pyx_v_R, __pyx_v_k, __pyx_v_j, __pyx_v_k);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":474
 * 
 *         # a4 = -3*j*k
 *         R.mul(a4, m_three, j)             # <<<<<<<<<<<<<<
 *         R.mul(a4, a4, k)
 * 
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_a4, __pyx_v_m_three, __pyx_v_j);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":475
 *         # a4 = -3*j*k
 *         R.mul(a4, m_three, j)
 *         R.mul(a4, a4, k)             # <<<<<<<<<<<<<<
 * 
 *         # a6 = -2*j*k^2
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_a4, __pyx_v_a4, __pyx_v_k);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":478
 * 
 *         # a6 = -2*j*k^2
 *         R.mul(a6, m_two, j)             # <<<<<<<<<<<<<<
 *         R.mul(a6, a6, k)
 *         R.mul(a6, a6, k)
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_a6, __pyx_v_m_two, __pyx_v_j);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":479
 *         # a6 = -2*j*k^2
 *         R.mul(a6, m_two, j)
 *         R.mul(a6, a6, k)             # <<<<<<<<<<<<<<
 *         R.mul(a6, a6, k)
 * 
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_a6, __pyx_v_a6, __pyx_v_k);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":480
 *         R.mul(a6, m_two, j)
 *         R.mul(a6, a6, k)
 *         R.mul(a6, a6, k)             # <<<<<<<<<<<<<<
 * 
 * 
 */
  ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_a6, __pyx_v_a6, __pyx_v_k);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":446
 *         return 0
 * 
 *     cdef int elliptic_curve_from_j(self,             # <<<<<<<<<<<<<<
 *                                    residue_element a4,
 *                                    residue_element a6,
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_AddTraceback("code.alex.psage.psage.ellcurve.lseries.sqrt5.InertTraceCalculator.elliptic_curve_from_j", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
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/* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":483
 * 
 * 
 *     cdef int ap_via_enumeration(self, int* ap, int* c_quo,             # <<<<<<<<<<<<<<
 *                                 residue_element a4, residue_element a6,
 *                                 ResidueRing_abstract R,
 */

static int __pyx_f_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_20InertTraceCalculator_ap_via_enumeration(CYTHON_UNUSED struct __pyx_obj_4code_4alex_5psage_5psage_8ellcurve_7lseries_5sqrt5_InertTraceCalculator *__pyx_v_self, int *__pyx_v_ap, int *__pyx_v_c_quo, long *__pyx_v_a4, long *__pyx_v_a6, struct __pyx_obj_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *__pyx_v_R, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_squares, struct __pyx_obj_4sage_5stats_7intlist_IntList *__pyx_v_cubes) {
  long __pyx_v_i;
  long __pyx_v_cnt;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_x;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_z;
  __pyx_t_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_residue_element __pyx_v_w;
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  __Pyx_RefNannyDeclarations
  long __pyx_t_1;
  long __pyx_t_2;
  int __pyx_t_3;
  long __pyx_t_4;
  int __pyx_t_5;
  __Pyx_RefNannySetupContext("ap_via_enumeration", 0);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":488
 *                                 IntList squares,
 *                                 IntList cubes) except -1:
 *         assert R.p >= 7             # <<<<<<<<<<<<<<
 *         cdef long i, j, cnt = 1  # start 1 because of point at infinity
 *         cdef residue_element x, z, w
 */
  #ifndef CYTHON_WITHOUT_ASSERTIONS
  if (unlikely(!Py_OptimizeFlag)) {
    if (unlikely(!((__pyx_v_R->p >= 7) != 0))) {
      PyErr_SetNone(PyExc_AssertionError);
      __PYX_ERR(0, 488, __pyx_L1_error)
    }
  }
  #endif

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":489
 *                                 IntList cubes) except -1:
 *         assert R.p >= 7
 *         cdef long i, j, cnt = 1  # start 1 because of point at infinity             # <<<<<<<<<<<<<<
 *         cdef residue_element x, z, w
 *         for i in range(R.cardinality()):
 */
  __pyx_v_cnt = 1;

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":491
 *         cdef long i, j, cnt = 1  # start 1 because of point at infinity
 *         cdef residue_element x, z, w
 *         for i in range(R.cardinality()):             # <<<<<<<<<<<<<<
 *             R.unsafe_ith_element(x, i)
 *             R.unsafe_ith_element(z, cubes._values[i])  # z = x^3
 */
  __pyx_t_1 = ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->cardinality(__pyx_v_R, 0);
  for (__pyx_t_2 = 0; __pyx_t_2 < __pyx_t_1; __pyx_t_2+=1) {
    __pyx_v_i = __pyx_t_2;

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":492
 *         cdef residue_element x, z, w
 *         for i in range(R.cardinality()):
 *             R.unsafe_ith_element(x, i)             # <<<<<<<<<<<<<<
 *             R.unsafe_ith_element(z, cubes._values[i])  # z = x^3
 *             R.mul(w, a4, x)  # w = a4*x
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->unsafe_ith_element(__pyx_v_R, __pyx_v_x, __pyx_v_i);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":493
 *         for i in range(R.cardinality()):
 *             R.unsafe_ith_element(x, i)
 *             R.unsafe_ith_element(z, cubes._values[i])  # z = x^3             # <<<<<<<<<<<<<<
 *             R.mul(w, a4, x)  # w = a4*x
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->unsafe_ith_element(__pyx_v_R, __pyx_v_z, (__pyx_v_cubes->_values[__pyx_v_i]));

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":494
 *             R.unsafe_ith_element(x, i)
 *             R.unsafe_ith_element(z, cubes._values[i])  # z = x^3
 *             R.mul(w, a4, x)  # w = a4*x             # <<<<<<<<<<<<<<
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->mul(__pyx_v_R, __pyx_v_w, __pyx_v_a4, __pyx_v_x);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":495
 *             R.unsafe_ith_element(z, cubes._values[i])  # z = x^3
 *             R.mul(w, a4, x)  # w = a4*x
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x             # <<<<<<<<<<<<<<
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6
 *             if R.element_is_0(z):
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->add(__pyx_v_R, __pyx_v_z, __pyx_v_z, __pyx_v_w);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":496
 *             R.mul(w, a4, x)  # w = a4*x
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6             # <<<<<<<<<<<<<<
 *             if R.element_is_0(z):
 *                 cnt += 1
 */
    ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->add(__pyx_v_R, __pyx_v_z, __pyx_v_z, __pyx_v_a6);

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":497
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6
 *             if R.element_is_0(z):             # <<<<<<<<<<<<<<
 *                 cnt += 1
 *             else:
 */
    __pyx_t_3 = (((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->element_is_0(__pyx_v_R, __pyx_v_z) != 0);
    if (__pyx_t_3) {

      /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":498
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6
 *             if R.element_is_0(z):
 *                 cnt += 1             # <<<<<<<<<<<<<<
 *             else:
 *                 if squares._values[R.index_of_element(z)]:  # assumes p!=2.
 */
      __pyx_v_cnt = (__pyx_v_cnt + 1);

      /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":497
 *             R.add(z, z, w)   # z = z + w = x^3 + a4*x
 *             R.add(z, z, a6)  # z = x^3 + a4*x + a6
 *             if R.element_is_0(z):             # <<<<<<<<<<<<<<
 *                 cnt += 1
 *             else:
 */
      goto __pyx_L5;
    }

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":500
 *                 cnt += 1
 *             else:
 *                 if squares._values[R.index_of_element(z)]:  # assumes p!=2.             # <<<<<<<<<<<<<<
 *                     cnt += 2
 * 
 */
    /*else*/ {
      __pyx_t_4 = ((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->index_of_element(__pyx_v_R, __pyx_v_z); if (unlikely(__pyx_t_4 == -1L)) __PYX_ERR(0, 500, __pyx_L1_error)
      __pyx_t_3 = ((__pyx_v_squares->_values[__pyx_t_4]) != 0);
      if (__pyx_t_3) {

        /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":501
 *             else:
 *                 if squares._values[R.index_of_element(z)]:  # assumes p!=2.
 *                     cnt += 2             # <<<<<<<<<<<<<<
 * 
 *         ap[0] = R.cardinality() + 1 - cnt
 */
        __pyx_v_cnt = (__pyx_v_cnt + 2);

        /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":500
 *                 cnt += 1
 *             else:
 *                 if squares._values[R.index_of_element(z)]:  # assumes p!=2.             # <<<<<<<<<<<<<<
 *                     cnt += 2
 * 
 */
      }
    }
    __pyx_L5:;
  }

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":503
 *                     cnt += 2
 * 
 *         ap[0] = R.cardinality() + 1 - cnt             # <<<<<<<<<<<<<<
 * 
 *         # Now compute c4/c6 = a4/(18*a6)
 */
  (__pyx_v_ap[0]) = ((((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->cardinality(__pyx_v_R, 0) + 1) - __pyx_v_cnt);

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":506
 * 
 *         # Now compute c4/c6 = a4/(18*a6)
 *         if R.element_is_0(a6):             # <<<<<<<<<<<<<<
 *             c_quo[0] = -1   # signifies "infinity"
 *         else:
 */
  __pyx_t_3 = (((struct __pyx_vtabstruct_5psage_7modform_7hilbert_5sqrt5_10sqrt5_fast_ResidueRing_abstract *)__pyx_v_R->__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_base.__pyx_vtab)->element_is_0(__pyx_v_R, __pyx_v_a6) != 0);
  if (__pyx_t_3) {

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":507
 *         # Now compute c4/c6 = a4/(18*a6)
 *         if R.element_is_0(a6):
 *             c_quo[0] = -1   # signifies "infinity"             # <<<<<<<<<<<<<<
 *         else:
 *             x[0] = 18 % R.p;  x[1] = 0  # x = 18
 */
    (__pyx_v_c_quo[0]) = -1;

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":506
 * 
 *         # Now compute c4/c6 = a4/(18*a6)
 *         if R.element_is_0(a6):             # <<<<<<<<<<<<<<
 *             c_quo[0] = -1   # signifies "infinity"
 *         else:
 */
    goto __pyx_L7;
  }

  /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":509
 *             c_quo[0] = -1   # signifies "infinity"
 *         else:
 *             x[0] = 18 % R.p;  x[1] = 0  # x = 18             # <<<<<<<<<<<<<<
 *             R.mul(z, x, a6)             # z = 18*a6
 *             R.inv(w, z)                 # w = 1/(18*a6)
 */
  /*else*/ {
    if (unlikely(__pyx_v_R->p == 0)) {
      PyErr_SetString(PyExc_ZeroDivisionError, "integer division or modulo by zero");
      __PYX_ERR(0, 509, __pyx_L1_error)
    }
    (__pyx_v_x[0]) = __Pyx_mod_long(18, __pyx_v_R->p);
    (__pyx_v_x[1]) = 0;

    /* "code/alex/psage/psage/ellcurve/lseries/sqrt5.pyx":510
 *         else:
 *             x[0] = 18 % R.p;  x[1] = 0  # x = 18
 *             R.mul(z, x, a6)             # z = 18*a6             # <<<<<<<<<<<<<<
 *             R.inv(w, z)                 # w = 1/(18*a6)
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        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

/* ParseKeywords */
  static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

/* ArgTypeTest */
  static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
}
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (likely(Py_TYPE(obj) == type)) return 1;
        #if PY_MAJOR_VERSION == 2
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
    }
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
    return 0;
}

/* KeywordStringCheck */
  static CYTHON_INLINE int __Pyx_CheckKeywordStrings(
    PyObject *kwdict,
    const char* function_name,
    int kw_allowed)
{
    PyObject* key = 0;
    Py_ssize_t pos = 0;
#if CYTHON_COMPILING_IN_PYPY
    if (!kw_allowed && PyDict_Next(kwdict, &pos, &key, 0))
        goto invalid_keyword;
    return 1;
#else
    while (PyDict_Next(kwdict, &pos, &key, 0)) {
        #if PY_MAJOR_VERSION < 3
        if (unlikely(!PyString_CheckExact(key)) && unlikely(!PyString_Check(key)))
        #endif
            if (unlikely(!PyUnicode_Check(key)))
                goto invalid_keyword_type;
    }
    if ((!kw_allowed) && unlikely(key))
        goto invalid_keyword;
    return 1;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    return 0;
#endif
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
    return 0;
}

/* PyCFunctionFastCall */
  #if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
    PyObject *self = PyCFunction_GET_SELF(func);
    assert(PyCFunction_Check(func));
    assert(METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST)));
    assert(nargs >= 0);
    assert(nargs == 0 || args != NULL);
    /* _PyCFunction_FastCallDict() must not be called with an exception set,
       because it may clear it (directly or indirectly) and so the
       caller loses its exception */
    assert(!PyErr_Occurred());
    return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs, NULL);
}
#endif  // CYTHON_FAST_PYCCALL

/* PyFunctionFastCall */
  #if CYTHON_FAST_PYCALL
#include "frameobject.h"
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = PyThreadState_GET();
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
       PyFrame_New() that doesn't take locals, but does
       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = f->f_localsplus;
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
#if PY_MAJOR_VERSION >= 3
    PyObject *kwdefs;
#endif
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
        return NULL;
    }
    if (
#if PY_MAJOR_VERSION >= 3
            co->co_kwonlyargcount == 0 &&
#endif
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
            args = &PyTuple_GET_ITEM(argdefs, 0);
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
        k = &PyTuple_GET_ITEM(kwtuple, 0);
        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
            Py_INCREF(k[i]);
            Py_INCREF(k[i+1]);
            i += 2;
        }
        nk = i / 2;
    }
    else {
        kwtuple = NULL;
        k = NULL;
    }
    closure = PyFunction_GET_CLOSURE(func);
#if PY_MAJOR_VERSION >= 3
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
#endif
    if (argdefs != NULL) {
        d = &PyTuple_GET_ITEM(argdefs, 0);
        nd = Py_SIZE(argdefs);
    }
    else {
        d = NULL;
        nd = 0;
    }
#if PY_MAJOR_VERSION >= 3
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, kwdefs, closure);
#else
    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, closure);
#endif
    Py_XDECREF(kwtuple);
done:
    Py_LeaveRecursiveCall();
    return result;
}
#endif  // CPython < 3.6
#endif  // CYTHON_FAST_PYCALL

/* PyObjectCall */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *result;
    ternaryfunc call = func->ob_type->tp_call;
    if (unlikely(!call))
        return PyObject_Call(func, arg, kw);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = (*call)(func, arg, kw);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallMethO */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = PyCFunction_GET_FUNCTION(func);
    self = PyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallOneArg */
  #if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, &arg, 1);
    }
#endif
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
#if CYTHON_FAST_PYCCALL
        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
#endif
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_Pack(1, arg);
    if (unlikely(!args)) return NULL;
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
#endif

/* GetModuleGlobalName */
    static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if !CYTHON_AVOID_BORROWED_REFS
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

/* None */
      static CYTHON_INLINE long __Pyx_mod_long(long a, long b) {
    long r = a % b;
    r += ((r != 0) & ((r ^ b) < 0)) * b;
    return r;
}

/* PyObjectCallNoArg */
      #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, NULL, 0);
    }
#endif
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

/* RaiseTooManyValuesToUnpack */
        static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

/* RaiseNeedMoreValuesToUnpack */
        static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

/* IterFinish */
        static CYTHON_INLINE int __Pyx_IterFinish(void) {
#if CYTHON_FAST_THREAD_STATE
    PyThreadState *tstate = PyThreadState_GET();
    PyObject* exc_type = tstate->curexc_type;
    if (unlikely(exc_type)) {
        if (likely(exc_type == PyExc_StopIteration) || PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration)) {
            PyObject *exc_value, *exc_tb;
            exc_value = tstate->curexc_value;
            exc_tb = tstate->curexc_traceback;
            tstate->curexc_type = 0;
            tstate->curexc_value = 0;
            tstate->curexc_traceback = 0;
            Py_DECREF(exc_type);
            Py_XDECREF(exc_value);
            Py_XDECREF(exc_tb);
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#else
    if (unlikely(PyErr_Occurred())) {
        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
            PyErr_Clear();
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#endif
}

/* UnpackItemEndCheck */
        static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
    if (unlikely(retval)) {
        Py_DECREF(retval);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    } else {
        return __Pyx_IterFinish();
    }
    return 0;
}

/* GetItemInt */
        static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return NULL;
                    PyErr_Clear();
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

/* BytesEquals */
        static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

/* UnicodeEquals */
        static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

/* SaveResetException */
        #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#endif

/* PyErrExceptionMatches */
        #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
    PyObject *exc_type = tstate->curexc_type;
    if (exc_type == err) return 1;
    if (unlikely(!exc_type)) return 0;
    return PyErr_GivenExceptionMatches(exc_type, err);
}
#endif

/* GetException */
        #if CYTHON_FAST_THREAD_STATE
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
#endif
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_FAST_THREAD_STATE
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_FAST_THREAD_STATE
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_FAST_THREAD_STATE
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

/* Import */
          static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_VERSION_HEX < 0x03030000
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    {
        #if PY_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
            #else
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

/* ImportFrom */
          static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Format(PyExc_ImportError,
        #if PY_MAJOR_VERSION < 3
            "cannot import name %.230s", PyString_AS_STRING(name));
        #else
            "cannot import name %S", name);
        #endif
    }
    return value;
}

/* PyIntBinop */
          #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = (long)((unsigned long)a - b);
            if (likely((x^a) >= 0 || (x^~b) >= 0))
                return PyInt_FromLong(x);
            return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
#ifdef HAVE_LONG_LONG
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
#endif
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2);
            }
        }
                x = a - b;
            return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
        long_long:
                llx = lla - llb;
            return PyLong_FromLongLong(llx);
#endif
        
        
    }
    #endif
    if (PyFloat_CheckExact(op1)) {
        const long b = intval;
        double a = PyFloat_AS_DOUBLE(op1);
            double result;
            PyFPE_START_PROTECT("subtract", return NULL)
            result = ((double)a) - (double)b;
            PyFPE_END_PROTECT(result)
            return PyFloat_FromDouble(result);
    }
    return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2);
}
#endif

/* PyIntBinop */
          #if !CYTHON_COMPILING_IN_PYPY
static PyObject* __Pyx_PyInt_RemainderObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) {
    #if PY_MAJOR_VERSION < 3
    if (likely(PyInt_CheckExact(op1))) {
        const long b = intval;
        long x;
        long a = PyInt_AS_LONG(op1);
            x = a % b;
            x += ((x != 0) & ((x ^ b) < 0)) * b;
            return PyInt_FromLong(x);
    }
    #endif
    #if CYTHON_USE_PYLONG_INTERNALS
    if (likely(PyLong_CheckExact(op1))) {
        const long b = intval;
        long a, x;
#ifdef HAVE_LONG_LONG
        const PY_LONG_LONG llb = intval;
        PY_LONG_LONG lla, llx;
#endif
        const digit* digits = ((PyLongObject*)op1)->ob_digit;
        const Py_ssize_t size = Py_SIZE(op1);
        if (likely(__Pyx_sst_abs(size) <= 1)) {
            a = likely(size) ? digits[0] : 0;
            if (size == -1) a = -a;
        } else {
            switch (size) {
                case -2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 2:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case -3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 3:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case -4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                case 4:
                    if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                        a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        break;
#ifdef HAVE_LONG_LONG
                    } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) {
                        lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0]));
                        goto long_long;
#endif
                    }
                default: return PyLong_Type.tp_as_number->nb_remainder(op1, op2);
            }
        }
                x = a % b;
                x += ((x != 0) & ((x ^ b) < 0)) * b;
            return PyLong_FromLong(x);
#ifdef HAVE_LONG_LONG
        long_long:
                llx = lla % llb;
                llx += ((llx != 0) & ((llx ^ llb) < 0)) * llb;
            return PyLong_FromLongLong(llx);
#endif
        
        
    }
    #endif
    return (inplace ? PyNumber_InPlaceRemainder : PyNumber_Remainder)(op1, op2);
}
#endif

/* UnpackUnboundCMethod */
          static int __Pyx_TryUnpackUnboundCMethod(__Pyx_CachedCFunction* target) {
    PyObject *method;
    method = __Pyx_PyObject_GetAttrStr(target->type, *target->method_name);
    if (unlikely(!method))
        return -1;
    target->method = method;
#if CYTHON_COMPILING_IN_CPYTHON
    #if PY_MAJOR_VERSION >= 3
    if (likely(PyObject_TypeCheck(method, &PyMethodDescr_Type)))
    #endif
    {
        PyMethodDescrObject *descr = (PyMethodDescrObject*) method;
        target->func = descr->d_method->ml_meth;
        target->flag = descr->d_method->ml_flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST);
    }
#endif
    return 0;
}

/* CallUnboundCMethod0 */
          static PyObject* __Pyx__CallUnboundCMethod0(__Pyx_CachedCFunction* cfunc, PyObject* self) {
    PyObject *args, *result = NULL;
    if (unlikely(!cfunc->method) && unlikely(__Pyx_TryUnpackUnboundCMethod(cfunc) < 0)) return NULL;
#if CYTHON_ASSUME_SAFE_MACROS
    args = PyTuple_New(1);
    if (unlikely(!args)) goto bad;
    Py_INCREF(self);
    PyTuple_SET_ITEM(args, 0, self);
#else
    args = PyTuple_Pack(1, self);
    if (unlikely(!args)) goto bad;
#endif
    result = __Pyx_PyObject_Call(cfunc->method, args, NULL);
    Py_DECREF(args);
bad:
    return result;
}

/* py_dict_keys */
          static CYTHON_INLINE PyObject* __Pyx_PyDict_Keys(PyObject* d) {
    if (PY_MAJOR_VERSION >= 3)
        return __Pyx_CallUnboundCMethod0(&__pyx_umethod_PyDict_Type_keys, d);
    else
        return PyDict_Keys(d);
}

/* FetchCommonType */
          static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
    PyObject* fake_module;
    PyTypeObject* cached_type = NULL;
    fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
    if (!fake_module) return NULL;
    Py_INCREF(fake_module);
    cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
    if (cached_type) {
        if (!PyType_Check((PyObject*)cached_type)) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s is not a type object",
                type->tp_name);
            goto bad;
        }
        if (cached_type->tp_basicsize != type->tp_basicsize) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s has the wrong size, try recompiling",
                type->tp_name);
            goto bad;
        }
    } else {
        if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
        PyErr_Clear();
        if (PyType_Ready(type) < 0) goto bad;
        if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
            goto bad;
        Py_INCREF(type);
        cached_type = type;
    }
done:
    Py_DECREF(fake_module);
    return cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}

/* CythonFunction */
          static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *closure)
{
    if (unlikely(op->func_doc == NULL)) {
        if (op->func.m_ml->ml_doc) {
#if PY_MAJOR_VERSION >= 3
            op->func_doc = PyUnicode_FromString(op->func.m_ml->ml_doc);
#else
            op->func_doc = PyString_FromString(op->func.m_ml->ml_doc);
#endif
            if (unlikely(op->func_doc == NULL))
                return NULL;
        } else {
            Py_INCREF(Py_None);
            return Py_None;
        }
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp = op->func_doc;
    if (value == NULL) {
        value = Py_None;
    }
    Py_INCREF(value);
    op->func_doc = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_name == NULL)) {
#if PY_MAJOR_VERSION >= 3
        op->func_name = PyUnicode_InternFromString(op->func.m_ml->ml_name);
#else
        op->func_name = PyString_InternFromString(op->func.m_ml->ml_name);
#endif
        if (unlikely(op->func_name == NULL))
            return NULL;
    }
    Py_INCREF(op->func_name);
    return op->func_name;
}
static int
__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    tmp = op->func_name;
    Py_INCREF(value);
    op->func_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_qualname);
    return op->func_qualname;
}
static int
__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    tmp = op->func_qualname;
    Py_INCREF(value);
    op->func_qualname = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_self(__pyx_CyFunctionObject *m, CYTHON_UNUSED void *closure)
{
    PyObject *self;
    self = m->func_closure;
    if (self == NULL)
        self = Py_None;
    Py_INCREF(self);
    return self;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_dict == NULL)) {
        op->func_dict = PyDict_New();
        if (unlikely(op->func_dict == NULL))
            return NULL;
    }
    Py_INCREF(op->func_dict);
    return op->func_dict;
}
static int
__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
    if (unlikely(value == NULL)) {
        PyErr_SetString(PyExc_TypeError,
               "function's dictionary may not be deleted");
        return -1;
    }
    if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
               "setting function's dictionary to a non-dict");
        return -1;
    }
    tmp = op->func_dict;
    Py_INCREF(value);
    op->func_dict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_globals);
    return op->func_globals;
}
static PyObject *
__Pyx_CyFunction_get_closure(CYTHON_UNUSED __pyx_CyFunctionObject *op)
{
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
    int result = 0;
    PyObject *res = op->defaults_getter((PyObject *) op);
    if (unlikely(!res))
        return -1;
    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
    Py_INCREF(op->defaults_tuple);
    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
    Py_INCREF(op->defaults_kwdict);
    #else
    op->defaults_tuple = PySequence_ITEM(res, 0);
    if (unlikely(!op->defaults_tuple)) result = -1;
    else {
        op->defaults_kwdict = PySequence_ITEM(res, 1);
        if (unlikely(!op->defaults_kwdict)) result = -1;
    }
    #endif
    Py_DECREF(res);
    return result;
}
static int
__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyTuple_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__defaults__ must be set to a tuple object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_tuple;
    op->defaults_tuple = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_tuple;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
            result = op->defaults_tuple;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__kwdefaults__ must be set to a dict object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_kwdict;
    op->defaults_kwdict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_kwdict;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
            result = op->defaults_kwdict;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value || value == Py_None) {
        value = NULL;
    } else if (!PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__annotations__ must be set to a dict object");
        return -1;
    }
    Py_XINCREF(value);
    tmp = op->func_annotations;
    op->func_annotations = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op) {
    PyObject* result = op->func_annotations;
    if (unlikely(!result)) {
        result = PyDict_New();
        if (unlikely(!result)) return NULL;
        op->func_annotations = result;
    }
    Py_INCREF(result);
    return result;
}
static PyGetSetDef __pyx_CyFunction_getsets[] = {
    {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
    {(char *) "__self__", (getter)__Pyx_CyFunction_get_self, 0, 0, 0},
    {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {(char *) "__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
    {(char *) "__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
    {0, 0, 0, 0, 0}
};
static PyMemberDef __pyx_CyFunction_members[] = {
    {(char *) "__module__", T_OBJECT, offsetof(__pyx_CyFunctionObject, func.m_module), PY_WRITE_RESTRICTED, 0},
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, CYTHON_UNUSED PyObject *args)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromString(m->func.m_ml->ml_name);
#else
    return PyString_FromString(m->func.m_ml->ml_name);
#endif
}
static PyMethodDef __pyx_CyFunction_methods[] = {
    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
    {0, 0, 0, 0}
};
#if PY_VERSION_HEX < 0x030500A0
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
#else
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func.m_weakreflist)
#endif
static PyObject *__Pyx_CyFunction_New(PyTypeObject *type, PyMethodDef *ml, int flags, PyObject* qualname,
                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
    __pyx_CyFunctionObject *op = PyObject_GC_New(__pyx_CyFunctionObject, type);
    if (op == NULL)
        return NULL;
    op->flags = flags;
    __Pyx_CyFunction_weakreflist(op) = NULL;
    op->func.m_ml = ml;
    op->func.m_self = (PyObject *) op;
    Py_XINCREF(closure);
    op->func_closure = closure;
    Py_XINCREF(module);
    op->func.m_module = module;
    op->func_dict = NULL;
    op->func_name = NULL;
    Py_INCREF(qualname);
    op->func_qualname = qualname;
    op->func_doc = NULL;
    op->func_classobj = NULL;
    op->func_globals = globals;
    Py_INCREF(op->func_globals);
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults_pyobjects = 0;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_kwdict = NULL;
    op->defaults_getter = NULL;
    op->func_annotations = NULL;
    PyObject_GC_Track(op);
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
    Py_CLEAR(m->func.m_module);
    Py_CLEAR(m->func_dict);
    Py_CLEAR(m->func_name);
    Py_CLEAR(m->func_qualname);
    Py_CLEAR(m->func_doc);
    Py_CLEAR(m->func_globals);
    Py_CLEAR(m->func_code);
    Py_CLEAR(m->func_classobj);
    Py_CLEAR(m->defaults_tuple);
    Py_CLEAR(m->defaults_kwdict);
    Py_CLEAR(m->func_annotations);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_XDECREF(pydefaults[i]);
        PyObject_Free(m->defaults);
        m->defaults = NULL;
    }
    return 0;
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    if (__Pyx_CyFunction_weakreflist(m) != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    PyObject_GC_Del(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    Py_VISIT(m->func_closure);
    Py_VISIT(m->func.m_module);
    Py_VISIT(m->func_dict);
    Py_VISIT(m->func_name);
    Py_VISIT(m->func_qualname);
    Py_VISIT(m->func_doc);
    Py_VISIT(m->func_globals);
    Py_VISIT(m->func_code);
    Py_VISIT(m->func_classobj);
    Py_VISIT(m->defaults_tuple);
    Py_VISIT(m->defaults_kwdict);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_VISIT(pydefaults[i]);
    }
    return 0;
}
static PyObject *__Pyx_CyFunction_descr_get(PyObject *func, PyObject *obj, PyObject *type)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    if (m->flags & __Pyx_CYFUNCTION_STATICMETHOD) {
        Py_INCREF(func);
        return func;
    }
    if (m->flags & __Pyx_CYFUNCTION_CLASSMETHOD) {
        if (type == NULL)
            type = (PyObject *)(Py_TYPE(obj));
        return __Pyx_PyMethod_New(func, type, (PyObject *)(Py_TYPE(type)));
    }
    if (obj == Py_None)
        obj = NULL;
    return __Pyx_PyMethod_New(func, obj, type);
}
static PyObject*
__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromFormat("<cyfunction %U at %p>",
                                op->func_qualname, (void *)op);
#else
    return PyString_FromFormat("<cyfunction %s at %p>",
                               PyString_AsString(op->func_qualname), (void *)op);
#endif
}
static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
    PyCFunctionObject* f = (PyCFunctionObject*)func;
    PyCFunction meth = f->m_ml->ml_meth;
    Py_ssize_t size;
    switch (f->m_ml->ml_flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
    case METH_VARARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0))
            return (*meth)(self, arg);
        break;
    case METH_VARARGS | METH_KEYWORDS:
        return (*(PyCFunctionWithKeywords)meth)(self, arg, kw);
    case METH_NOARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 0))
                return (*meth)(self, NULL);
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    case METH_O:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 1)) {
                PyObject *result, *arg0 = PySequence_ITEM(arg, 0);
                if (unlikely(!arg0)) return NULL;
                result = (*meth)(self, arg0);
                Py_DECREF(arg0);
                return result;
            }
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags in "
                        "__Pyx_CyFunction_Call. METH_OLDARGS is no "
                        "longer supported!");
        return NULL;
    }
    PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments",
                 f->m_ml->ml_name);
    return NULL;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    return __Pyx_CyFunction_CallMethod(func, ((PyCFunctionObject*)func)->m_self, arg, kw);
}
static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
    PyObject *result;
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        Py_ssize_t argc;
        PyObject *new_args;
        PyObject *self;
        argc = PyTuple_GET_SIZE(args);
        new_args = PyTuple_GetSlice(args, 1, argc);
        if (unlikely(!new_args))
            return NULL;
        self = PyTuple_GetItem(args, 0);
        if (unlikely(!self)) {
            Py_DECREF(new_args);
            return NULL;
        }
        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
        Py_DECREF(new_args);
    } else {
        result = __Pyx_CyFunction_Call(func, args, kw);
    }
    return result;
}
static PyTypeObject __pyx_CyFunctionType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    "cython_function_or_method",
    sizeof(__pyx_CyFunctionObject),
    0,
    (destructor) __Pyx_CyFunction_dealloc,
    0,
    0,
    0,
#if PY_MAJOR_VERSION < 3
    0,
#else
    0,
#endif
    (reprfunc) __Pyx_CyFunction_repr,
    0,
    0,
    0,
    0,
    __Pyx_CyFunction_CallAsMethod,
    0,
    0,
    0,
    0,
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,
    0,
    (traverseproc) __Pyx_CyFunction_traverse,
    (inquiry) __Pyx_CyFunction_clear,
    0,
#if PY_VERSION_HEX < 0x030500A0
    offsetof(__pyx_CyFunctionObject, func_weakreflist),
#else
    offsetof(PyCFunctionObject, m_weakreflist),
#endif
    0,
    0,
    __pyx_CyFunction_methods,
    __pyx_CyFunction_members,
    __pyx_CyFunction_getsets,
    0,
    0,
    __Pyx_CyFunction_descr_get,
    0,
    offsetof(__pyx_CyFunctionObject, func_dict),
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
#if PY_VERSION_HEX >= 0x030400a1
    0,
#endif
};
static int __pyx_CyFunction_init(void) {
    __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type);
    if (__pyx_CyFunctionType == NULL) {
        return -1;
    }
    return 0;
}
static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults = PyObject_Malloc(size);
    if (!m->defaults)
        return PyErr_NoMemory();
    memset(m->defaults, 0, size);
    m->defaults_pyobjects = pyobjects;
    return m->defaults;
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_tuple = tuple;
    Py_INCREF(tuple);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_kwdict = dict;
    Py_INCREF(dict);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->func_annotations = dict;
    Py_INCREF(dict);
}

/* SetVTable */
              static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
#if PY_VERSION_HEX >= 0x02070000
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
#else
    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
#endif
    if (!ob)
        goto bad;
    if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
        goto bad;
    Py_DECREF(ob);
    return 0;
bad:
    Py_XDECREF(ob);
    return -1;
}

/* GetVTable */
              static void* __Pyx_GetVtable(PyObject *dict) {
    void* ptr;
    PyObject *ob = PyObject_GetItem(dict, __pyx_n_s_pyx_vtable);
    if (!ob)
        goto bad;
#if PY_VERSION_HEX >= 0x02070000
    ptr = PyCapsule_GetPointer(ob, 0);
#else
    ptr = PyCObject_AsVoidPtr(ob);
#endif
    if (!ptr && !PyErr_Occurred())
        PyErr_SetString(PyExc_RuntimeError, "invalid vtable found for imported type");
    Py_DECREF(ob);
    return ptr;
bad:
    Py_XDECREF(ob);
    return NULL;
}

/* CodeObjectCache */
              static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_code_cache.count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

/* AddTraceback */
              #include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        0,
        0,
        0,
        0,
        0,
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple, /*PyObject *consts,*/
        __pyx_empty_tuple, /*PyObject *names,*/
        __pyx_empty_tuple, /*PyObject *varnames,*/
        __pyx_empty_tuple, /*PyObject *freevars,*/
        __pyx_empty_tuple, /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        py_line,
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

/* CIntFromPyVerify */
              #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* CIntToPy */
              static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

/* CIntToPy */
              static CYTHON_INLINE PyObject* __Pyx_PyInt_From_unsigned_long(unsigned long value) {
    const unsigned long neg_one = (unsigned long) -1, const_zero = (unsigned long) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(unsigned long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(unsigned long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(unsigned long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(unsigned long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(unsigned long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(unsigned long),
                                     little, !is_unsigned);
    }
}

/* CIntToPy */
              static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

/* CIntFromPy */
              static CYTHON_INLINE unsigned long __Pyx_PyInt_As_unsigned_long(PyObject *x) {
    const unsigned long neg_one = (unsigned long) -1, const_zero = (unsigned long) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(unsigned long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(unsigned long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (unsigned long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (unsigned long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(unsigned long, digit, digits[0])
                case 2:
                    if (8 * sizeof(unsigned long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) >= 2 * PyLong_SHIFT) {
                            return (unsigned long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) >= 3 * PyLong_SHIFT) {
                            return (unsigned long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) >= 4 * PyLong_SHIFT) {
                            return (unsigned long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (unsigned long) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(unsigned long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(unsigned long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (unsigned long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(unsigned long, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(unsigned long,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(unsigned long) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned long) (((unsigned long)-1)*(((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(unsigned long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 2 * PyLong_SHIFT) {
                            return (unsigned long) ((((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(unsigned long) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned long) (((unsigned long)-1)*(((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 3 * PyLong_SHIFT) {
                            return (unsigned long) ((((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(unsigned long) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned long) (((unsigned long)-1)*(((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(unsigned long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(unsigned long) - 1 > 4 * PyLong_SHIFT) {
                            return (unsigned long) ((((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(unsigned long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(unsigned long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(unsigned long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            unsigned long val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (unsigned long) -1;
        }
    } else {
        unsigned long val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (unsigned long) -1;
        val = __Pyx_PyInt_As_unsigned_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to unsigned long");
    return (unsigned long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to unsigned long");
    return (unsigned long) -1;
}

/* CIntFromPy */
              static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (long) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

/* CIntFromPy */
              static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

/* CheckBinaryVersion */
              static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

/* ModuleImport */
              #ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

/* TypeImport */
              #ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

/* VoidPtrImport */
              #ifndef __PYX_HAVE_RT_ImportVoidPtr
#define __PYX_HAVE_RT_ImportVoidPtr
static int __Pyx_ImportVoidPtr(PyObject *module, const char *name, void **p, const char *sig) {
    PyObject *d = 0;
    PyObject *cobj = 0;
    d = PyObject_GetAttrString(module, (char *)"__pyx_capi__");
    if (!d)
        goto bad;
    cobj = PyDict_GetItemString(d, name);
    if (!cobj) {
        PyErr_Format(PyExc_ImportError,
            "%.200s does not export expected C variable %.200s",
                PyModule_GetName(module), name);
        goto bad;
    }
#if PY_VERSION_HEX >= 0x02070000
    if (!PyCapsule_IsValid(cobj, sig)) {
        PyErr_Format(PyExc_TypeError,
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), name, sig, PyCapsule_GetName(cobj));
        goto bad;
    }
    *p = PyCapsule_GetPointer(cobj, sig);
#else
    {const char *desc, *s1, *s2;
    desc = (const char *)PyCObject_GetDesc(cobj);
    if (!desc)
        goto bad;
    s1 = desc; s2 = sig;
    while (*s1 != '\0' && *s1 == *s2) { s1++; s2++; }
    if (*s1 != *s2) {
        PyErr_Format(PyExc_TypeError,
            "C variable %.200s.%.200s has wrong signature (expected %.500s, got %.500s)",
             PyModule_GetName(module), name, sig, desc);
        goto bad;
    }
    *p = PyCObject_AsVoidPtr(cobj);}
#endif
    if (!(*p))
        goto bad;
    Py_DECREF(d);
    return 0;
bad:
    Py_XDECREF(d);
    return -1;
}
#endif

/* InitStrings */
              static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if CYTHON_COMPILING_IN_CPYTHON && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
#if PY_VERSION_HEX < 0x03030000
        char* defenc_c;
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
        if (!defenc) return NULL;
        defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        {
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
            char* c;
            for (c = defenc_c; c < end; c++) {
                if ((unsigned char) (*c) >= 128) {
                    PyUnicode_AsASCIIString(o);
                    return NULL;
                }
            }
        }
#endif
        *length = PyBytes_GET_SIZE(defenc);
        return defenc_c;
#else
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (PyUnicode_IS_ASCII(o)) {
            *length = PyUnicode_GET_LENGTH(o);
            return PyUnicode_AsUTF8(o);
        } else {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
#else
        return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
    } else
#endif
#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return __Pyx_NewRef(x);
#if CYTHON_USE_TYPE_SLOTS
  m = Py_TYPE(x)->tp_as_number;
  #if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
  #else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
  #endif
#else
  res = PyNumber_Int(x);
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_TypeError,
                    "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b))) {
    if (sizeof(Py_ssize_t) >= sizeof(long))
        return PyInt_AS_LONG(b);
    else
        return PyInt_AsSsize_t(x);
  }
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    const digit* digits = ((PyLongObject*)b)->ob_digit;
    const Py_ssize_t size = Py_SIZE(b);
    if (likely(__Pyx_sst_abs(size) <= 1)) {
        ival = likely(size) ? digits[0] : 0;
        if (size == -1) ival = -ival;
        return ival;
    } else {
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */