Coverage for local/lib/python2.7/site-packages/sage/libs/gap/libgap.pyx : 86%

""" 

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) 

{'Sym3': Sym( [ 1 .. 3 ] ), 'a': 123, '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() 

{'Sym3': NotImplementedError('cannot construct equivalent Sage object',), 

'a': 123, 

'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. 

""" 

############################################################################### 

# Copyright (C) 2009, William Stein <wstein@gmail.com> 

# Copyright (C) 2012, Volker Braun <vbraun.name@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# as published by the Free Software Foundation; either version 2 of 

# the License, or (at your option) any later version. 

# http://www.gnu.org/licenses/ 

############################################################################### 

############################################################################## 

# 

# If you want to add support for converting some GAP datatype to its 

# Sage equivalent, you have two options. Either 

# 

# 1. add an if-clause to GapElement.sage(). This is the easiest 

# option and you should probably start with it first 

# 

# 2. Subclass GapElement to GapElement_Mydatatype. In that case you 

# need to write the derived class, a factory function to 

# instantiate it (GapElement cannot be instantiated by __init__), 

# and add an if-clause in make_GapElement. See GapElement_List, 

# for example. The advantage of this more complicated approach is 

# that you can then add extra methods to your data type. For 

# example, GapElement_List instances can access the individual 

# elements with the usual gapelement[i] syntax. 

# 

# TODO 

# 

# Not all GAP types have their own GapElement. We should wrap more 

# stuff. Talk to me (Volker) if you want to work on that. 

# 

############################################################################## 

from __future__ import print_function, absolute_import 

from .gap_includes cimport * 

from sage.structure.sage_object cimport SageObject 

from sage.structure.parent cimport Parent 

from sage.structure.element cimport ModuleElement, RingElement, Vector 

from sage.rings.all import ZZ 

from sage.misc.cachefunc import cached_method 

from sage.misc.superseded import deprecated_function_alias 

from sage.libs.gap.element cimport * 

############################################################################ 

### Debugging ############################################################## 

############################################################################ 

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) 

############################################################################ 

### Gap ################################################################### 

############################################################################ 

# The libGap interpreter object Gap is the parent of the GapElements 

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)['x','y']) 

True 

""" 

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 

sage: libgap(vector((0,1,2))) 

[ 0, 1, 2 ] 

sage: libgap(vector((1/3,2/3,4/5))) 

[ 1/3, 2/3, 4/5 ] 

sage: libgap(vector((1/3, 0.8, 3))) 

[ 0.333333, 0.8, 3. ] 

""" 

if isinstance(x, GapElement): 

return x 

elif isinstance(x, (list, tuple, Vector)): 

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): 

# attention: must come before int 

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)) 

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 ] ] 

TESTS: 

We gracefully handle the case that the conversion fails (:trac:`18039`):: 

sage: F.<a> = GF(9, modulus="first_lexicographic") 

sage: libgap(Matrix(F, [[a]])) 

Traceback (most recent call last): 

... 

NotImplementedError: conversion of (Givaro) finite field element to GAP not implemented except for fields defined by Conway polynomials. 

""" 

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(self): 

""" 

Return (integer) zero in GAP. 

OUTPUT: 

A :class:`GapElement`. 

EXAMPLES:: 

sage: libgap.zero() 

0 

""" 

return self(0) 

def one(self): 

r""" 

Return (integer) one in GAP. 

EXAMPLES:: 

sage: libgap.one() 

1 

sage: parent(_) 

C library interface to GAP 

""" 

return self(1) 

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' 

@cached_method 

def __dir__(self): 

""" 

Customize tab completion 

EXAMPLES:: 

sage: 'OctaveAlgebra' in dir(libgap) 

True 

""" 

from sage.libs.gap.gap_functions import common_gap_functions 

return dir(self.__class__) + list(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 dir(self.__class__): 

return getattr(self.__class__, name) 

from sage.libs.gap.gap_functions import common_gap_functions 

if name in common_gap_functions: 

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('{} LibGAP elements currently alive'.format(self.count_GAP_objects())) 

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()