# sage_setup: distribution = sagemath-objects
from sage.structure.sage_object cimport SageObject
from sage.structure.parent cimport Parent
from sage.misc.inherit_comparison cimport InheritComparisonMetaclass
cpdef inline parent(x):
"""
Return the parent of the element ``x``.
Usually, this means the mathematical object of which ``x`` is an
element.
INPUT:
- ``x`` -- an element
OUTPUT:
- If ``x`` is a Sage :class:`Element`, return ``x.parent()``.
- Otherwise, return ``type(x)``.
.. SEEALSO::
`Parents, Conversion and Coercion <http://doc.sagemath.org/html/en/tutorial/tour_coercion.html>`_
Section in the Sage Tutorial
EXAMPLES::
sage: a = 42
sage: parent(a)
Integer Ring
sage: b = 42/1
sage: parent(b)
Rational Field
sage: c = 42.0
sage: parent(c) # needs sage.rings.real_mpfr
Real Field with 53 bits of precision
Some more complicated examples::
sage: x = Partition([3,2,1,1,1]) # needs sage.combinat
sage: parent(x) # needs sage.combinat
Partitions
sage: v = vector(RDF, [1,2,3]) # needs sage.modules
sage: parent(v) # needs sage.modules
Vector space of dimension 3 over Real Double Field
The following are not considered to be elements, so the type is
returned::
sage: d = int(42) # Python int
sage: parent(d)
<... 'int'>
sage: L = list(range(10))
sage: parent(L)
<... 'list'>
"""
if isinstance(x, Element):
return (<Element>x)._parent
return type(x)
cdef inline int classify_elements(left, right) noexcept:
"""
Given two objects, at least one which is an :class:`Element`,
classify their type and parent. This is a finer version of
:func:`have_same_parent`.
OUTPUT: the sum of the following bits:
- 0o01: left is an Element
- 0o02: right is an Element
- 0o04: both are Element
- 0o10: left and right have the same type
- 0o20: left and right have the same parent
These are the possible outcomes:
- 0o01: left is an Element, right is not
- 0o02: right is an Element, left is not
- 0o07: both are Element, different types, different parents
- 0o17: both are Element, same type, different parents
- 0o27: both are Element, different types, same parent
- 0o37: both are Element, same type, same parent
"""
if type(left) is type(right):
# We know at least one of the arguments is an Element. So if
# their types are *equal* (fast to check) then they are both
# Elements.
if (<Element>left)._parent is (<Element>right)._parent:
return 0o37
else:
return 0o17
if not isinstance(right, Element):
return 0o01
if not isinstance(left, Element):
return 0o02
if (<Element>left)._parent is (<Element>right)._parent:
return 0o27
else:
return 0o07
# Functions to help understand the result of classify_elements()
cdef inline bint BOTH_ARE_ELEMENT(int cl) noexcept:
return cl & 0o04
cdef inline bint HAVE_SAME_PARENT(int cl) noexcept:
return cl & 0o20
cpdef inline bint have_same_parent(left, right) noexcept:
"""
Return ``True`` if and only if ``left`` and ``right`` have the
same parent.
.. WARNING::
This function assumes that at least one of the arguments is a
Sage :class:`Element`. When in doubt, use the slower
``parent(left) is parent(right)`` instead.
EXAMPLES::
sage: from sage.structure.element import have_same_parent
sage: have_same_parent(1, 3)
True
sage: have_same_parent(1, 1/2)
False
sage: have_same_parent(gap(1), gap(1/2)) # needs sage.libs.gap
True
These have different types but the same parent::
sage: a = RLF(2)
sage: b = exp(a)
sage: type(a)
<... 'sage.rings.real_lazy.LazyWrapper'>
sage: type(b)
<... 'sage.rings.real_lazy.LazyNamedUnop'>
sage: have_same_parent(a, b)
True
"""
return HAVE_SAME_PARENT(classify_elements(left, right))
cdef unary_op_exception(op, x)
cdef bin_op_exception(op, x, y)
cdef class Element(SageObject):
cdef Parent _parent
cpdef _richcmp_(left, right, int op)
cpdef int _cmp_(left, right) except -2
cpdef base_extend(self, R)
cdef getattr_from_category(self, name)
cpdef _act_on_(self, x, bint self_on_left)
cpdef _acted_upon_(self, x, bint self_on_left)
cdef _add_(self, other)
cdef _sub_(self, other)
cdef _neg_(self)
cdef _add_long(self, long n)
cdef _mul_(self, other)
cdef _mul_long(self, long n)
cdef _matmul_(self, other)
cdef _div_(self, other)
cdef _floordiv_(self, other)
cdef _mod_(self, other)
cdef _pow_(self, other)
cdef _pow_int(self, n)
cdef _pow_long(self, long n)
cdef class ElementWithCachedMethod(Element):
cdef public dict _cached_methods
cdef class ModuleElement(Element) # forward declaration
cdef class RingElement(ModuleElement) # forward declaration
cdef class ModuleElement(Element):
cpdef _add_(self, other)
cpdef _sub_(self, other)
cpdef _neg_(self)
# self._rmul_(x) is x * self
cpdef _lmul_(self, Element right)
# self._lmul_(x) is self * x
cpdef _rmul_(self, Element left)
cdef class ModuleElementWithMutability(ModuleElement):
cdef bint _is_immutable
cpdef bint is_immutable(self) noexcept
cpdef bint is_mutable(self) noexcept
cdef class MonoidElement(Element):
cpdef _pow_int(self, n)
cdef class MultiplicativeGroupElement(MonoidElement):
cpdef _div_(self, other)
cdef class AdditiveGroupElement(ModuleElement):
pass
cdef class RingElement(ModuleElement):
cpdef _mul_(self, other)
cpdef _div_(self, other)
cpdef _pow_int(self, n)
cdef class CommutativeRingElement(RingElement):
pass
cdef class IntegralDomainElement(CommutativeRingElement):
pass
cdef class DedekindDomainElement(IntegralDomainElement):
pass
cdef class PrincipalIdealDomainElement(DedekindDomainElement):
pass
cdef class EuclideanDomainElement(PrincipalIdealDomainElement):
cpdef _floordiv_(self, other)
cpdef _mod_(self, other)
cdef class FieldElement(CommutativeRingElement):
cpdef _floordiv_(self, other)
cdef class AlgebraElement(RingElement):
pass
cdef class CommutativeAlgebraElement(CommutativeRingElement):
pass
cdef class Expression(CommutativeRingElement):
pass
cdef class InfinityElement(RingElement):
pass
cdef class Vector(ModuleElementWithMutability):
cdef Py_ssize_t _degree
# Return the dot product using the simple metric
# $e_i \cdot e_j = \delta_{ij}$. The first assumes that the parents
# are equal, both assume that the degrees are equal.
cpdef _dot_product_(Vector left, Vector right)
cpdef _dot_product_coerce_(Vector left, Vector right)
cpdef _pairwise_product_(Vector left, Vector right) # override, call if parents the same
cdef bint is_sparse_c(self) noexcept
cdef bint is_dense_c(self) noexcept
cdef class Matrix(ModuleElement):
# All matrix classes must be written in Cython
cdef Py_ssize_t _nrows
cdef Py_ssize_t _ncols
cdef _vector_times_matrix_(matrix_right, Vector vector_left) # OK to override, AND call directly
cdef _matrix_times_vector_(matrix_left, Vector vector_right) # OK to override, AND call directly
cdef _matrix_times_matrix_(left, Matrix right) # OK to override, AND call directly
cdef bint is_sparse_c(self) noexcept
cdef bint is_dense_c(self) noexcept
