def element_order(self, weylelt):
"""
This method returns the order of a given Weyl group element, which should
be specified by the user in the form of products of the generating
reflections, i.e. of the form r1*r2 etc.
For types A-F, this method current works by taking the matrix form of
the specified element, and then finding what power of the matrix is the
identity. It then returns this power.
Examples
========
>>> from sympy.liealgebras.weyl_group import WeylGroup
>>> b = WeylGroup("B4")
>>> b.element_order('r1*r4*r2')
4
"""
n = self.cartan_type.rank()
if self.cartan_type.series == "A":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n + 1):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "D":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "E":
a = self.matrix_form(weylelt)
order = 1
while a != eye(8):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "G":
elts = list(weylelt)
reflections = elts[1::3]
m = self.delete_doubles(reflections)
while self.delete_doubles(m) != m:
m = self.delete_doubles(m)
reflections = m
if len(reflections) % 2 == 1:
return 2
elif len(reflections) == 0:
return 1
else:
if len(reflections) == 1:
return 2
else:
m = len(reflections) // 2
lcm = (6 * m) / igcd(m, 6)
order = lcm / m
return order
if self.cartan_type.series == "F":
a = self.matrix_form(weylelt)
order = 1
while a != eye(4):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "B" or self.cartan_type.series == "C":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n):
a *= self.matrix_form(weylelt)
order += 1
return order
def element_order(self, weylelt):
"""
This method returns the order of a given Weyl group element, which should
be specified by the user in the form of products of the generating
reflections, i.e. of the form r1*r2 etc.
For types A-F, this method current works by taking the matrix form of
the specified element, and then finding what power of the matrix is the
identity. It then returns this power.
Examples
========
>>> from sympy.liealgebras.weyl_group import WeylGroup
>>> b = WeylGroup("B4")
>>> b.element_order('r1*r4*r2')
4
"""
n = self.cartan_type.rank()
if self.cartan_type.series == "A":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n+1):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "D":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "E":
a = self.matrix_form(weylelt)
order = 1
while a != eye(8):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "G":
elts = list(weylelt)
reflections = elts[1::3]
m = self.delete_doubles(reflections)
while self.delete_doubles(m) != m:
m = self.delete_doubles(m)
reflections = m
if len(reflections) % 2 == 1:
return 2
elif len(reflections) == 0:
return 1
else:
if len(reflections) == 1:
return 2
else:
m = len(reflections) // 2
lcm = (6 * m)/ igcd(m, 6)
order = lcm / m
return order
if self.cartan_type.series == 'F':
a = self.matrix_form(weylelt)
order = 1
while a != eye(4):
a *= self.matrix_form(weylelt)
order += 1
return order
if self.cartan_type.series == "B" or self.cartan_type.series == "C":
a = self.matrix_form(weylelt)
order = 1
while a != eye(n):
a *= self.matrix_form(weylelt)
order += 1
return order