def __init__(self, parent, x, check=True):
"""
The Python constructor.
See :class:`FinitelyPresentedGroupElement` for details.
TESTS::
sage: G = FreeGroup('a, b')
sage: H = G / [G([1]), G([2, 2, 2])]
sage: H([1, 2, 1, -1])
a*b
sage: TestSuite(G).run()
sage: TestSuite(H).run()
sage: G.<a,b> = FreeGroup()
sage: H = G / (G([1]), G([2, 2, 2]))
sage: x = H([1, 2, -1, -2])
sage: TestSuite(x).run()
sage: TestSuite(G.one()).run()
"""
if not isinstance(x, GapElement):
F = parent.free_group()
free_element = F(x)
fp_family = parent.one().gap().FamilyObj()
x = libgap.ElementOfFpGroup(fp_family, free_element.gap())
ElementLibGAP.__init__(self, parent, x)
def __init__(self, parent, x, check=True):
"""
The Python constructor.
See :class:`FinitelyPresentedGroupElement` for details.
TESTS::
sage: G = FreeGroup('a, b')
sage: H = G / [G([1]), G([2, 2, 2])]
sage: H([1, 2, 1, -1])
a*b
sage: TestSuite(G).run()
sage: TestSuite(H).run()
sage: G.<a,b> = FreeGroup()
sage: H = G / (G([1]), G([2, 2, 2]))
sage: x = H([1, 2, -1, -2])
sage: TestSuite(x).run()
sage: TestSuite(G.one()).run()
"""
if not isinstance(x, GapElement):
F = parent.free_group()
free_element = F(x)
fp_family = parent.one().gap().FamilyObj()
x = libgap.ElementOfFpGroup(fp_family, free_element.gap())
ElementLibGAP.__init__(self, parent, x)
def __init__(self, parent, x, check=True):
"""
The Python constructor.
TESTS::
sage: from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap
sage: G = AbelianGroupGap([2,3,4,5])
sage: f = G.aut().an_element()
sage: TestSuite(f).run()
"""
if check:
if not x in parent.gap():
raise ValueError("%s is not in the group %s" % (x, parent))
ElementLibGAP.__init__(self, parent, x)
def __init__(self, parent, M, check=True, convert=True):
r"""
Element of a matrix group over a generic ring.
The group elements are implemented as Sage matrices.
INPUT:
- ``M`` -- a matrix.
- ``parent`` -- the parent.
- ``check`` -- bool (default: ``True``). If true does some
type checking.
- ``convert`` -- bool (default: ``True``). If true convert
``M`` to the right matrix space.
TESTS::
sage: MS = MatrixSpace(GF(3),2,2)
sage: G = MatrixGroup(MS([[1,0],[0,1]]), MS([[1,1],[0,1]]))
sage: G.gen(0)
[1 0]
[0 1]
sage: g = G.random_element()
sage: TestSuite(g).run()
"""
if isinstance(M, GapElement):
ElementLibGAP.__init__(self, parent, M)
return
if convert:
M = parent.matrix_space()(M)
from sage.libs.gap.libgap import libgap
M_gap = libgap(M)
if check:
if not is_Matrix(M):
raise TypeError("M must be a matrix")
if M.parent() is not parent.matrix_space():
raise TypeError("M must be a in the matrix space of the group")
parent._check_matrix(M, M_gap)
ElementLibGAP.__init__(self, parent, M_gap)
def __init__(self, M, parent, check=True, convert=True):
r"""
Element of a matrix group over a generic ring.
The group elements are implemented as Sage matrices.
INPUT:
- ``M`` -- a matrix.
- ``parent`` -- the parent.
- ``check`` -- bool (default: ``True``). If true does some
type checking.
- ``convert`` -- bool (default: ``True``). If true convert
``M`` to the right matrix space.
TESTS::
sage: MS = MatrixSpace(GF(3),2,2)
sage: G = MatrixGroup(MS([[1,0],[0,1]]), MS([[1,1],[0,1]]))
sage: G.gen(0)
[1 0]
[0 1]
sage: g = G.random_element()
sage: TestSuite(g).run()
"""
if isinstance(M, GapElement):
ElementLibGAP.__init__(self, M, parent)
return
if convert:
M = parent.matrix_space()(M)
from sage.libs.gap.libgap import libgap
M_gap = libgap(M)
if check:
if not is_Matrix(M):
raise TypeError('M must be a matrix')
if M.parent() is not parent.matrix_space():
raise TypeError('M must be a in the matrix space of the group')
parent._check_matrix(M, M_gap)
ElementLibGAP.__init__(self, M_gap, parent)
def __init__(self, parent, x):
"""
The Python constructor.
See :class:`FreeGroupElement` for details.
TESTS::
sage: G.<a,b> = FreeGroup()
sage: x = G([1, 2, -1, -1])
sage: x # indirect doctest
a*b*a^-2
sage: y = G([2, 2, 2, 1, -2, -2, -1])
sage: y # indirect doctest
b^3*a*b^-2*a^-1
sage: TestSuite(G).run()
sage: TestSuite(x).run()
"""
if not isinstance(x, GapElement):
try:
l = x.Tietze()
except AttributeError:
l = list(x)
if len(l) > 0:
if min(l) < -parent.ngens() or parent.ngens() < max(l):
raise ValueError('generators not in the group')
if 0 in l:
raise ValueError('zero does not denote a generator')
i = 0
while i < len(l) - 1:
if l[i] == -l[i + 1]:
l.pop(i)
l.pop(i)
if i > 0:
i = i - 1
else:
i = i + 1
AbstractWordTietzeWord = libgap.eval('AbstractWordTietzeWord')
x = AbstractWordTietzeWord(l, parent._gap_gens())
ElementLibGAP.__init__(self, parent, x)
def __init__(self, x, parent):
"""
The Python constructor.
See :class:`FreeGroupElement` for details.
TESTS::
sage: G.<a,b> = FreeGroup()
sage: x = G([1, 2, -1, -1])
sage: x # indirect doctest
a*b*a^-2
sage: y = G([2, 2, 2, 1, -2, -2, -1])
sage: y # indirect doctest
b^3*a*b^-2*a^-1
sage: TestSuite(G).run()
sage: TestSuite(x).run()
"""
if not isinstance(x, GapElement):
try:
l = x.Tietze()
except AttributeError:
l = list(x)
if len(l)>0:
if min(l) < -parent.ngens() or parent.ngens() < max(l):
raise ValueError('generators not in the group')
if 0 in l:
raise ValueError('zero does not denote a generator')
i=0
while i<len(l)-1:
if l[i]==-l[i+1]:
l.pop(i)
l.pop(i)
if i>0:
i=i-1
else:
i=i+1
AbstractWordTietzeWord = libgap.eval('AbstractWordTietzeWord')
x = AbstractWordTietzeWord(l, parent._gap_gens())
ElementLibGAP.__init__(self, x, parent)
def __init__(self, parent, x, check=True):
"""
The Python constructor.
See :class:`AbelianGroupElement_gap` for details.
INPUT:
- ``parent`` -- an instance of :class:`AbelianGroup_gap`
- ``x`` -- an instance of :class:`sage.libs.gap.element.GapElement`
- ``check`` -- boolean (default: ``True``); check
if ``x`` is an element of the group
TESTS::
sage: from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap
sage: G = AbelianGroupGap([3,6])
sage: g = G.an_element()
sage: TestSuite(g).run()
"""
if check and x not in parent.gap():
raise ValueError("%s is not in the group %s" % (x, parent))
ElementLibGAP.__init__(self, parent, x)
def __init__(self, parent, x):
"""
The Python constructor.
See :class:`FreeGroupElement` for details.
TESTS::
sage: from train_track import *
sage: G.<a,b> = FreeGroup()
sage: x = G([1, 2, -1, -1])
sage: x # indirect doctest
a*b*a^-2
sage: y = G([2, 2, 2, 1, -2, -2, -1])
sage: y # indirect doctest
b^3*a*b^-2*a^-1
sage: G("abAbBAB")
a*b*a^-2*b^-1
sage: G(['a','b','A','a','A','B'])
a*b*a^-1*b^-1
sage: TestSuite(G).run()
sage: TestSuite(x).run()
"""
if not isinstance(x, GapElement):
try:
l = x.Tietze()
except AttributeError:
if isinstance(
x, str
): # First check wether x is a string of a generator like 'x0'
try:
x = [parent._names.index(x) + 1]
except ValueError:
try:
x = [-parent._names.index(x.lower()) - 1]
except ValueError:
pass
l = list(x)
for i, a in enumerate(l):
if isinstance(a, (int, Integer)):
if a < -parent.ngens() or parent.ngens() < a or a == 0:
raise ValueError(
'%s does not denote a generator of %s' %
(a, parent))
elif isinstance(a, str):
try:
l[i] = parent._names.index(a) + 1
except ValueError:
try:
l[i] = -parent._names.index(a.lower()) - 1
except ValueError:
raise ValueError('%s is not a generator of %s' %
(a, parent))
i = 0
while i < len(l) - 1:
if l[i] == -l[i + 1]:
l.pop(i)
l.pop(i)
if i > 0:
i = i - 1
else:
i = i + 1
AbstractWordTietzeWord = libgap.eval('AbstractWordTietzeWord')
x = AbstractWordTietzeWord(l, parent._gap_gens())
ElementLibGAP.__init__(self, parent, x)
def __init__(self, parent, x):
"""
The Python constructor.
See :class:`FreeGroupElement` for details.
TESTS::
sage: from train_track import *
sage: G.<a,b> = FreeGroup()
sage: x = G([1, 2, -1, -1])
sage: x # indirect doctest
a*b*a^-2
sage: y = G([2, 2, 2, 1, -2, -2, -1])
sage: y # indirect doctest
b^3*a*b^-2*a^-1
sage: G("abAbBAB")
a*b*a^-2*b^-1
sage: G(['a','b','A','a','A','B'])
a*b*a^-1*b^-1
sage: TestSuite(G).run()
sage: TestSuite(x).run()
"""
if not isinstance(x, GapElement):
try:
l = x.Tietze()
except AttributeError:
if isinstance(x,str): # First check wether x is a string of a generator like 'x0'
try:
x = [parent._names.index(x) + 1]
except ValueError:
try:
x = [-parent._names.index(x.lower()) - 1]
except ValueError:
pass
l = list(x)
for i,a in enumerate(l):
if isinstance(a,(int,Integer)):
if a < -parent.ngens() or parent.ngens() < a or a == 0:
raise ValueError('%s does not denote a generator of %s'%(a,parent))
elif isinstance(a,str):
try:
l[i] = parent._names.index(a) + 1
except ValueError:
try:
l[i] = -parent._names.index(a.lower()) - 1
except ValueError:
raise ValueError('%s is not a generator of %s'%(a,parent))
i=0
while i < len(l)-1:
if l[i] == -l[i+1]:
l.pop(i)
l.pop(i)
if i>0:
i = i-1
else:
i = i+1
AbstractWordTietzeWord = libgap.eval('AbstractWordTietzeWord')
x = AbstractWordTietzeWord(l, parent._gap_gens())
ElementLibGAP.__init__(self, parent, x)