def __init__(self, g, parent):
"""
EXAMPLES::
sage: G = WeylGroup(['A',2])
sage: s1 = G.simple_reflection(1)
sage: TestSuite(s1).run()
"""
MatrixGroupElement.__init__(self, g, parent)
self.__matrix = self._MatrixGroupElement__mat
self.__matrix.set_immutable()
self._parent = parent
def __init__(self, g, parent):
"""
EXAMPLES::
sage: G = WeylGroup(['A',2])
sage: s1 = G.simple_reflection(1)
sage: TestSuite(s1).run()
"""
MatrixGroupElement.__init__(self, g, parent)
self.__matrix = self._MatrixGroupElement__mat
self.__matrix.set_immutable()
self._parent = parent
def _latex_(self):
"""
EXAMPLES::
sage: W = WeylGroup(['A',2,1], prefix="s")
sage: [s0,s1,s2]=W.simple_reflections()
sage: latex(s0*s1) # indirect doctest
s_{0}s_{1}
sage: W = WeylGroup(['A',2,1])
sage: [s0,s1,s2]=W.simple_reflections()
sage: latex(s0*s1)
\left(\begin{array}{rrr}
0 & -1 & 2 \\
1 & -1 & 1 \\
0 & 0 & 1
\end{array}\right)
"""
if self._parent._prefix is None:
return MatrixGroupElement._latex_(self)
else:
redword = self.reduced_word()
if len(redword) == 0:
return "1"
else:
return "".join(["%s_{%d}" % (self._parent._prefix, i) for i in redword])
def __repr__(self):
"""
EXAMPLES::
sage: W = WeylGroup(['A',2,1], prefix="s")
sage: [s0,s1,s2]=W.simple_reflections()
sage: s0*s1
s0*s1
sage: W = WeylGroup(['A',2,1])
sage: [s0,s1,s2]=W.simple_reflections()
sage: s0*s1
[ 0 -1 2]
[ 1 -1 1]
[ 0 0 1]
"""
if self._parent._prefix is None:
return MatrixGroupElement.__repr__(self)
else:
redword = self.reduced_word()
if len(redword) == 0:
return "1"
else:
ret = ""
for i in redword[:-1]:
ret += "%s%d*" % (self._parent._prefix, i)
return ret + "%s%d" % (self._parent._prefix, redword[-1])
def __repr__(self):
"""
EXAMPLES::
sage: W = WeylGroup(['A',2,1], prefix="s")
sage: [s0,s1,s2]=W.simple_reflections()
sage: s0*s1
s0*s1
sage: W = WeylGroup(['A',2,1])
sage: [s0,s1,s2]=W.simple_reflections()
sage: s0*s1
[ 0 -1 2]
[ 1 -1 1]
[ 0 0 1]
"""
if self._parent._prefix is None:
return MatrixGroupElement.__repr__(self)
else:
redword = self.reduced_word()
if len(redword) == 0:
return "1"
else:
ret = ""
for i in redword[:-1]:
ret += "%s%d*" % (self._parent._prefix, i)
return ret + "%s%d" % (self._parent._prefix, redword[-1])
def _latex_(self):
"""
EXAMPLES::
sage: W = WeylGroup(['A',2,1], prefix="s")
sage: [s0,s1,s2]=W.simple_reflections()
sage: latex(s0*s1) # indirect doctest
s_{0}s_{1}
sage: W = WeylGroup(['A',2,1])
sage: [s0,s1,s2]=W.simple_reflections()
sage: latex(s0*s1)
\left(\begin{array}{rrr}
0 & -1 & 2 \\
1 & -1 & 1 \\
0 & 0 & 1
\end{array}\right)
"""
if self._parent._prefix is None:
return MatrixGroupElement._latex_(self)
else:
redword = self.reduced_word()
if len(redword) == 0:
return "1"
else:
return "".join(["%s_{%d}"%(self._parent._prefix, i) for i in redword])
