def wrap_FpGroup(libgap_fpgroup):
"""
Wrap a GAP finitely presented group.
This function changes the comparison method of
``libgap_free_group`` to comparison by Python ``id``. If you want
to put the LibGAP free group into a container ``(set, dict)`` then you
should understand the implications of
:meth:`~sage.libs.gap.element.GapElement._set_compare_by_id`. To
be safe, it is recommended that you just work with the resulting
Sage :class:`FinitelyPresentedGroup`.
INPUT:
- ``libgap_fpgroup`` -- a LibGAP finitely presented group
OUTPUT:
A Sage :class:`FinitelyPresentedGroup`.
EXAMPLES:
First construct a LibGAP finitely presented group::
sage: F = libgap.FreeGroup(['a', 'b'])
sage: a_cubed = F.GeneratorsOfGroup()[0] ^ 3
sage: P = F / libgap([ a_cubed ]); P
<fp group of size infinity on the generators [ a, b ]>
sage: type(P)
<type 'sage.libs.gap.element.GapElement'>
Now wrap it::
sage: from sage.groups.finitely_presented import wrap_FpGroup
sage: wrap_FpGroup(P)
Finitely presented group < a, b | a^3 >
"""
assert libgap_fpgroup.IsFpGroup()
libgap_fpgroup._set_compare_by_id()
from sage.groups.free_group import wrap_FreeGroup
free_group = wrap_FreeGroup(libgap_fpgroup.FreeGroupOfFpGroup())
relations = tuple(
free_group(rel.UnderlyingElement())
for rel in libgap_fpgroup.RelatorsOfFpGroup())
return FinitelyPresentedGroup(free_group, relations)
def wrap_FpGroup(libgap_fpgroup):
"""
Wrap a GAP finitely presented group.
This function changes the comparison method of
``libgap_free_group`` to comparison by Python ``id``. If you want
to put the LibGAP free group into a container (set, dict) then you
should understand the implications of
:meth:`~sage.libs.gap.element.GapElement._set_compare_by_id`. To
be safe, it is recommended that you just work with the resulting
Sage :class:`FinitelyPresentedGroup`.
INPUT:
- ``libgap_fpgroup`` -- a LibGAP finitely presented group
OUTPUT:
A Sage :class:`FinitelyPresentedGroup`.
EXAMPLES:
First construct a LibGAP finitely presented group::
sage: F = libgap.FreeGroup(['a', 'b'])
sage: a_cubed = F.GeneratorsOfGroup()[0] ^ 3
sage: P = F / libgap([ a_cubed ]); P
<fp group of size infinity on the generators [ a, b ]>
sage: type(P)
<type 'sage.libs.gap.element.GapElement'>
Now wrap it::
sage: from sage.groups.finitely_presented import wrap_FpGroup
sage: wrap_FpGroup(P)
Finitely presented group < a, b | a^3 >
"""
assert libgap_fpgroup.IsFpGroup()
libgap_fpgroup._set_compare_by_id()
from sage.groups.free_group import wrap_FreeGroup
free_group = wrap_FreeGroup(libgap_fpgroup.FreeGroupOfFpGroup())
relations = tuple( free_group(rel.UnderlyingElement())
for rel in libgap_fpgroup.RelatorsOfFpGroup() )
return FinitelyPresentedGroup(free_group, relations)