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, 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().GeneratorsOfGroup())
ElementLibGAP.__init__(self, parent, x)