本文整理汇总了Python中sage.combinat.root_system.root_system.RootSystem.weyl_group方法的典型用法代码示例。如果您正苦于以下问题：Python RootSystem.weyl_group方法的具体用法？Python RootSystem.weyl_group怎么用？Python RootSystem.weyl_group使用的例子？那么, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类sage.combinat.root_system.root_system.RootSystem的用法示例。
在下文中一共展示了RootSystem.weyl_group方法的1个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: __init__
# 需要导入模块: from sage.combinat.root_system.root_system import RootSystem [as 别名]
# 或者: from sage.combinat.root_system.root_system.RootSystem import weyl_group [as 别名]
def __init__(self, cartan_type, prefix, finite=True):
r"""
EXAMPLES::
sage: from sage.combinat.root_system.fundamental_group import FundamentalGroupOfExtendedAffineWeylGroup
sage: F = FundamentalGroupOfExtendedAffineWeylGroup(['A',3,1])
sage: F in Groups().Commutative().Finite()
True
sage: TestSuite(F).run()
"""
def leading_support(beta):
r"""
Given a dictionary with one key, return this key
"""
supp = beta.support()
assert len(supp) == 1
return supp[0]
self._cartan_type = cartan_type
self._prefix = prefix
special_node = cartan_type.special_node()
self._special_nodes = cartan_type.special_nodes()
# initialize dictionaries with the entries for the distinguished special node
# dictionary of inverse elements
inverse_dict = {}
inverse_dict[special_node] = special_node
# dictionary for the action of special automorphisms by permutations of the affine Dynkin nodes
auto_dict = {}
for i in cartan_type.index_set():
auto_dict[special_node,i] = i
# dictionary for the finite Weyl component of the special automorphisms
reduced_words_dict = {}
reduced_words_dict[0] = tuple([])
if cartan_type.dual().is_untwisted_affine():
# this combines the computations for an untwisted affine type and its affine dual
cartan_type = cartan_type.dual()
if cartan_type.is_untwisted_affine():
cartan_type_classical = cartan_type.classical()
I = [i for i in cartan_type_classical.index_set()]
Q = RootSystem(cartan_type_classical).root_lattice()
alpha = Q.simple_roots()
omega = RootSystem(cartan_type_classical).weight_lattice().fundamental_weights()
W = Q.weyl_group(prefix="s")
for i in self._special_nodes:
if i == special_node:
continue
antidominant_weight, reduced_word = omega[i].to_dominant_chamber(reduced_word=True, positive=False)
reduced_words_dict[i] = tuple(reduced_word)
w0i = W.from_reduced_word(reduced_word)
idual = leading_support(-antidominant_weight)
inverse_dict[i] = idual
auto_dict[i,special_node] = i
for j in I:
if j == idual:
auto_dict[i,j] = special_node
else:
auto_dict[i,j] = leading_support(w0i.action(alpha[j]))
self._action = Family(self._special_nodes, lambda i: Family(cartan_type.index_set(), lambda j: auto_dict[i,j]))
self._dual_node = Family(self._special_nodes, inverse_dict.__getitem__)
self._reduced_words = Family(self._special_nodes, reduced_words_dict.__getitem__)
if finite:
cat = Category.join((Groups().Commutative().Finite(),EnumeratedSets()))
else:
cat = Groups().Commutative().Infinite()
Parent.__init__(self, category = cat)