"""
libGAP shared library Interface to GAP
This module implements a fast C library interface to GAP. To use
libGAP you simply call ``libgap`` (the parent of all
:class:`~sage.libs.gap.element.GapElement` instances) and use it to
convert Sage objects into GAP objects.
EXAMPLES::
sage: a = libgap(10)
sage: a
10
sage: type(a)
<type 'sage.libs.gap.element.GapElement_Integer'>
sage: a*a
100
sage: timeit('a*a') # random output
625 loops, best of 3: 898 ns per loop
Compared to the expect interface this is >1000 times faster::
sage: b = gap('10')
sage: timeit('b*b') # random output; long time
125 loops, best of 3: 2.05 ms per loop
If you want to evaluate GAP commands, use the :meth:`Gap.eval` method::
sage: libgap.eval('List([1..10], i->i^2)')
[ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ]
not to be confused with the ``libgap`` call, which converts Sage
objects to GAP objects, for example strings to strings::
sage: libgap('List([1..10], i->i^2)')
"List([1..10], i->i^2)"
sage: type(_)
<type 'sage.libs.gap.element.GapElement_String'>
You can usually use the :meth:`~sage.libs.gap.element.GapElement.sage`
method to convert the resulting GAP element back to its Sage
equivalent::
sage: a.sage()
10
sage: type(_)
<type 'sage.rings.integer.Integer'>
sage: libgap.eval('5/3 + 7*E(3)').sage()
7*zeta3 + 5/3
sage: generators = libgap.AlternatingGroup(4).GeneratorsOfGroup().sage()
sage: generators # a Sage list of Sage permutations!
[(1,2,3), (2,3,4)]
sage: PermutationGroup(generators).cardinality() # computed in Sage
12
sage: libgap.AlternatingGroup(4).Size() # computed in GAP
12
So far, the following GAP data types can be directly converted to the
corresponding Sage datatype:
#. GAP booleans ``true`` / ``false`` to Sage booleans ``True`` /
``False``. The third GAP boolean value ``fail`` raises a
``ValueError``.
#. GAP integers to Sage integers.
#. GAP rational numbers to Sage rational numbers.
#. GAP cyclotomic numbers to Sage cyclotomic numbers.
#. GAP permutations to Sage permutations.
#. The GAP containers ``List`` and ``rec`` are converted to Sage
containers ``list`` and ``dict``. Furthermore, the
:meth:`~sage.libs.gap.element.GapElement.sage` method is applied
recursively to the entries.
Special support is available for the GAP container classes. GAP lists
can be used as follows::
sage: lst = libgap([1,5,7]); lst
[ 1, 5, 7 ]
sage: type(lst)
<type 'sage.libs.gap.element.GapElement_List'>
sage: len(lst)
3
sage: lst[0]
1
sage: [ x^2 for x in lst ]
[1, 25, 49]
sage: type(_[0])
<type 'sage.libs.gap.element.GapElement_Integer'>
Note that you can access the elements of GAP ``List`` objects as you
would expect from Python (with indexing starting at 0), but the
elements are still of type
:class:`~sage.libs.gap.element.GapElement`. The other GAP container
type are records, which are similar to Python dictionaries. You can
construct them directly from Python dictionaries::
sage: libgap({'a':123, 'b':456})
rec( a := 123, b := 456 )
Or get them as results of computations::
sage: rec = libgap.eval('rec(a:=123, b:=456, Sym3:=SymmetricGroup(3))')
sage: rec['Sym3']
Sym( [ 1 .. 3 ] )
sage: dict(rec)
{'a': 123, 'Sym3': Sym( [ 1 .. 3 ] ), 'b': 456}
The output is a Sage dictionary whose keys are Sage strings and whose
Values are instances of :meth:`~sage.libs.gap.element.GapElement`. So,
for example, ``rec['a']`` is not a Sage integer. To recursively
convert the entries into Sage objects, you should use the
:meth:`~sage.libs.gap.element.GapElement.sage` method::
sage: rec.sage()
{'a': 123,
'Sym3': NotImplementedError('cannot construct equivalent Sage object',),
'b': 456}
Now ``rec['a']`` is a Sage integer. We have not implemented the
conversion of the GAP symmetric group to the Sage symmetric group yet,
so you end up with a ``NotImplementedError`` exception object. The
exception is returned and not raised so that you can work with the
partial result.
While we don't directly support matrices yet, you can convert them to
Gap List of Lists. These lists are then easily converted into Sage
using the recursive expansion of the
:meth:`~sage.libs.gap.element.GapElement.sage` method::
sage: M = libgap.eval('BlockMatrix([[1,1,[[1, 2],[ 3, 4]]], [1,2,[[9,10],[11,12]]], [2,2,[[5, 6],[ 7, 8]]]],2,2)')
sage: M
<block matrix of dimensions (2*2)x(2*2)>
sage: M.List() # returns a GAP List of Lists
[ [ 1, 2, 9, 10 ], [ 3, 4, 11, 12 ], [ 0, 0, 5, 6 ], [ 0, 0, 7, 8 ] ]
sage: M.List().sage() # returns a Sage list of lists
[[1, 2, 9, 10], [3, 4, 11, 12], [0, 0, 5, 6], [0, 0, 7, 8]]
sage: matrix(ZZ, _)
[ 1 2 9 10]
[ 3 4 11 12]
[ 0 0 5 6]
[ 0 0 7 8]
Using the libGAP C library from Cython
======================================
The lower-case ``libgap_foobar`` functions are ones that we added to
make the libGAP C shared library. The ``libGAP_foobar`` methods are
the original GAP methods simply prefixed with the string
``libGAP_``. The latter were originally not designed to be in a
library, so some care needs to be taken to call them.
In particular, you must call ``libgap_mark_stack_bottom()`` in every
function that calls into the libGAP C functions. The reason is that
the GAP memory manager will automatically keep objects alive that are
referenced in local (stack-allocated) variables. While convenient,
this requires to look through the stack to find anything that looks
like an address to a memory bag. But this requires vigilance against
the following pattern::
cdef f()
libgap_mark_stack_bottom()
libGAP_function()
cdef g()
libgap_mark_stack_bottom();
f() # f() changed the stack bottom marker
libGAP_function() # boom
The solution is to re-order ``g()`` to first call ``f()``. In order to
catch this error, it is recommended that you wrap calls into libGAP in
``libgap_enter`` / ``libgap_exit`` blocks and not call
``libgap_mark_stack_bottom`` manually. So instead, always write
cdef f()
libgap_enter()
libGAP_function()
libgap_exit()
cdef g()
f()
libgap_enter()
libGAP_function()
libgap_exit()
If you accidentally call ``libgap_enter()`` twice then an error
message is printed to help you debug this::
sage: from sage.libs.gap.util import error_enter_libgap_block_twice
sage: error_enter_libgap_block_twice()
Traceback (most recent call last):
...
RuntimeError: Entered a critical block twice
AUTHORS:
- William Stein, Robert Miller (2009-06-23): first version
- Volker Braun, Dmitrii Pasechnik, Ivan Andrus (2011-03-25, Sage Days 29):
almost complete rewrite; first usable version.
- Volker Braun (2012-08-28, GAP/Singular workshop): update to
gap-4.5.5, make it ready for public consumption.
"""
from gap_includes cimport *
from sage.structure.sage_object cimport SageObject
from sage.structure.parent cimport Parent
from sage.structure.element cimport ModuleElement, RingElement
from sage.rings.all import ZZ
from sage.misc.cachefunc import cached_method
from sage.libs.gap.element cimport *
cdef void report(libGAP_Obj bag):
print libGAP_TNAM_OBJ(bag), <int>libGAP_TNUM_BAG(bag), <int>libGAP_SIZE_BAG(bag)
cdef void print_gasman_objects():
libgap_enter()
libGAP_CallbackForAllBags(report)
libgap_exit()
from sage.misc.lazy_import import is_during_startup
if is_during_startup():
import sys, traceback
print 'Importing libgap during startup!'
traceback.print_stack(None, None, sys.stdout)
class Gap(Parent):
r"""
The libgap interpreter object.
.. NOTE::
This object must be instantiated exactly once by the
libgap. Always use the provided ``libgap`` instance, and never
instantiate :class:`Gap` manually.
EXAMPLES::
sage: libgap.eval('SymmetricGroup(4)')
Sym( [ 1 .. 4 ] )
TESTS::
sage: TestSuite(libgap).run(skip=['_test_category', '_test_elements', '_test_pickling'])
"""
Element = GapElement
def _coerce_map_from_(self, S):
"""
Whether a coercion from `S` exists.
INPUT / OUTPUT:
See :mod:`sage.structure.parent`.
EXAMPLES::
sage: libgap.has_coerce_map_from(ZZ)
True
sage: libgap.has_coerce_map_from(CyclotomicField(5))
True
"""
from sage.rings.all import ZZ, QQ, is_CyclotomicField
if S in (ZZ, QQ) or is_CyclotomicField(S):
return True
def _element_constructor_(self, x):
r"""
Construct elements of this parent class.
INPUT:
- ``x`` -- anything that defines a GAP object.
OUTPUT:
A :class:`GapElement`.
EXAMPLES::
sage: libgap(0) # indirect doctest
0
sage: libgap(ZZ(0))
0
sage: libgap(int(0))
0
"""
if isinstance(x, GapElement):
return x
elif isinstance(x, (list, tuple)):
return make_GapElement_List(self, make_gap_list(x))
elif isinstance(x, dict):
return make_GapElement_Record(self, make_gap_record(x))
elif isinstance(x, bool):
return make_GapElement_Boolean(self, libGAP_True if x else libGAP_False)
elif isinstance(x, int):
return make_GapElement_Integer(self, make_gap_integer(x))
elif isinstance(x, basestring):
return make_GapElement_String(self, make_gap_string(x))
else:
try:
return x._libgap_()
except AttributeError:
pass
x = str(x._gap_init_())
return make_any_gap_element(self, gap_eval(x))
raise ValueError('cannot represent '+str(x)+' as a GAP object')
def _construct_matrix(self, M):
"""
Construct a LibGAP matrix.
INPUT:
- ``M`` -- a matrix.
OUTPUT:
A GAP matrix, that is, a list of lists with entries over a
common ring.
EXAMPLES::
sage: libgap._construct_matrix(identity_matrix(ZZ,2))
[ [ 1, 0 ], [ 0, 1 ] ]
sage: libgap(identity_matrix(ZZ,2)) # syntactic sugar
[ [ 1, 0 ], [ 0, 1 ] ]
sage: libgap(matrix(GF(3),2,2,[4,5,6,7]))
[ [ Z(3)^0, Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
"""
ring = M.base_ring()
try:
gap_ring = self(ring)
except ValueError:
raise TypeError('base ring is not supported by GAP')
M_list = map(list, M.rows())
return make_GapElement_List(self, make_gap_list(M_list))
def eval(self, gap_command):
"""
Evaluate a gap command and wrap the result.
INPUT:
- ``gap_command`` -- a string containing a valid gap command
without the trailing semicolon.
OUTPUT:
A :class:`GapElement`.
EXAMPLES::
sage: libgap.eval('0')
0
sage: libgap.eval('"string"')
"string"
"""
if not isinstance(gap_command, basestring):
gap_command = str(gap_command._gap_init_())
return make_any_gap_element(self, gap_eval(gap_command))
@cached_method
def function_factory(self, function_name):
"""
Return a GAP function wrapper
This is almost the same as calling
``libgap.eval(function_name)``, but faster and makes it
obvious in your code that you are wrapping a function.
INPUT:
- ``function_name`` -- string. The name of a GAP function.
OUTPUT:
A function wrapper
:class:`~sage.libs.gap.element.GapElement_Function` for the
GAP function. Calling it from Sage is equivalent to calling
the wrapped function from GAP.
EXAMPLES::
sage: libgap.function_factory('Print')
<Gap function "Print">
"""
return make_GapElement_Function(self, gap_eval(function_name))
def set_global(self, variable, value):
"""
Set a GAP global variable
INPUT:
- ``variable`` -- string. The variable name.
- ``value`` -- anything that defines a GAP object.
EXAMPLES::
sage: libgap.set_global('FooBar', 1)
sage: libgap.get_global('FooBar')
1
sage: libgap.unset_global('FooBar')
sage: libgap.get_global('FooBar')
Traceback (most recent call last):
...
ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar
"""
is_bound = self.function_factory('IsBoundGlobal')
bind_global = self.function_factory('BindGlobal')
if is_bound(variable):
self.unset_global(variable)
bind_global(variable, value)
def unset_global(self, variable):
"""
Remove a GAP global variable
INPUT:
- ``variable`` -- string. The variable name.
EXAMPLES::
sage: libgap.set_global('FooBar', 1)
sage: libgap.get_global('FooBar')
1
sage: libgap.unset_global('FooBar')
sage: libgap.get_global('FooBar')
Traceback (most recent call last):
...
ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar
"""
make_readwrite = self.function_factory('MakeReadWriteGlobal')
unbind_global = self.function_factory('UnbindGlobal')
make_readwrite(variable)
unbind_global(variable)
def get_global(self, variable):
"""
Get a GAP global variable
INPUT:
- ``variable`` -- string. The variable name.
OUTPUT:
A :class:`~sage.libs.gap.element.GapElement` wrapping the GAP
output. A ``ValueError`` is raised if there is no such
variable in GAP.
EXAMPLES::
sage: libgap.set_global('FooBar', 1)
sage: libgap.get_global('FooBar')
1
sage: libgap.unset_global('FooBar')
sage: libgap.get_global('FooBar')
Traceback (most recent call last):
...
ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar
"""
value_global = self.function_factory('ValueGlobal')
return value_global(variable)
def global_context(self, variable, value):
"""
Temporarily change a global variable
INPUT:
- ``variable`` -- string. The variable name.
- ``value`` -- anything that defines a GAP object.
OUTPUT:
A context manager that sets/reverts the given global variable.
EXAMPLES::
sage: libgap.set_global('FooBar', 1)
sage: with libgap.global_context('FooBar', 2):
....: print libgap.get_global('FooBar')
2
sage: libgap.get_global('FooBar')
1
"""
from sage.libs.gap.context_managers import GlobalVariableContext
return GlobalVariableContext(variable, value)
def _an_element_(self):
r"""
Return a :class:`GapElement`.
OUTPUT:
A :class:`GapElement`.
EXAMPLES::
sage: libgap.an_element() # indirect doctest
0
"""
return self(0)
def zero_element(self):
"""
Return (integer) zero in GAP.
OUTPUT:
A :class:`GapElement`.
EXAMPLES::
sage: libgap.zero_element()
0
"""
return self(0)
def __init__(self):
r"""
The Python constructor.
EXAMPLES::
sage: type(libgap)
<type 'sage.misc.lazy_import.LazyImport'>
sage: type(libgap._get_object())
<class 'sage.libs.gap.libgap.Gap'>
"""
initialize()
libgap_set_gasman_callback(gasman_callback)
from sage.rings.integer_ring import ZZ
Parent.__init__(self, base=ZZ)
def __repr__(self):
r"""
Return a string representation of ``self``.
OUTPUT:
String.
EXAMPLES::
sage: libgap
C library interface to GAP
"""
return 'C library interface to GAP'
def trait_names(self):
"""
Return all Gap function names.
OUTPUT:
A list of strings.
EXAMPLES::
sage: len(libgap.trait_names()) > 1000
True
"""
import gap_functions
return gap_functions.common_gap_functions
def __getattr__(self, name):
r"""
The attributes of the Gap object are the Gap functions.
INPUT:
- ``name`` -- string. The name of the GAP function you want to
call.
OUTPUT:
A :class:`GapElement_Function`. A ``AttributeError`` is raised
if there is no such function.
EXAMPLES::
sage: libgap.List
<Gap function "List">
"""
if name in self.trait_names():
f = make_GapElement_Function(self, gap_eval(str(name)))
assert f.is_function()
self.__dict__[name] = f
return f
else:
raise AttributeError, 'No such attribute: '+name+'.'
def show(self):
"""
Print statistics about the GAP owned object list
Slight complication is that we want to do it without accessing
libgap objects, so we don't create new GapElements as a side
effect.
EXAMPLES::
sage: a = libgap(123)
sage: b = libgap(456)
sage: c = libgap(789)
sage: del b
sage: libgap.show() # random output
11 LibGAP elements currently alive
rec( full := rec( cumulative := 122, deadbags := 9,
deadkb := 0, freekb := 7785, livebags := 304915,
livekb := 47367, time := 33, totalkb := 68608 ),
nfull := 3, npartial := 14 )
"""
print self.count_GAP_objects(), 'LibGAP elements currently alive'
print self.eval('GasmanStatistics()')
def count_GAP_objects(self):
"""
Return the number of GAP objects that are being tracked by
libGAP
OUTPUT:
An integer
EXAMPLES::
sage: libgap.count_GAP_objects() # random output
5
"""
return sum([1 for obj in get_owned_objects()])
def mem(self):
"""
Return information about libGAP memory usage
The GAP workspace is partitioned into 5 pieces (see gasman.c
in the GAP sources for more details):
* The **masterpointer area** contains all the masterpointers of the bags.
* The **old bags area** contains the bodies of all the bags that survived at
least one garbage collection. This area is only scanned for dead bags
during a full garbage collection.
* The **young bags area** contains the bodies of all the bags that have been
allocated since the last garbage collection. This area is scanned for
dead bags during each garbage collection.
* The **allocation area** is the storage that is available for allocation of
new bags. When a new bag is allocated the storage for the body is taken
from the beginning of this area, and this area is correspondingly
reduced. If the body does not fit in the allocation area a garbage
collection is performed.
* The **unavailable area** is the free storage that is not available for
allocation.
OUTPUT:
This function returns a tuple containing 5 integers. Each is
the size (in bytes) of the five partitions of the
workspace. This will potentially change after each GAP garbage
collection.
EXAMPLES::
sage: libgap.collect()
sage: libgap.mem() # random output
(1048576, 6706782, 0, 960930, 0)
sage: libgap.FreeGroup(3)
<free group on the generators [ f1, f2, f3 ]>
sage: libgap.mem() # random output
(1048576, 6706782, 47571, 913359, 0)
sage: libgap.collect()
sage: libgap.mem() # random output
(1048576, 6734785, 0, 998463, 0)
"""
return memory_usage()
def collect(self):
"""
Manually run the garbage collector
EXAMPLES::
sage: a = libgap(123)
sage: del a
sage: libgap.collect()
"""
libgap_enter()
rc = libGAP_CollectBags(0,1)
libgap_exit()
if rc != 1:
raise RuntimeError('Garbage collection failed.')
libgap = Gap()
