本文整理汇总了Python中sage.combinat.root_system.root_system.RootSystem.fundamental_weights方法的典型用法代码示例。如果您正苦于以下问题：Python RootSystem.fundamental_weights方法的具体用法？Python RootSystem.fundamental_weights怎么用？Python RootSystem.fundamental_weights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.fundamental_weights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: maximal_elements
# 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 fundamental_weights [as 别名]
def maximal_elements(self):
r"""
Return the maximal elements of ``self`` with respect to Bruhat order.
The current implementation is via a conjectural type-free
formula. Use maximal_elements_combinatorial() for proven
type-specific implementations. To compare type-free and
type-specific (combinatorial) implementations, use method
:meth:`_test_maximal_elements`.
EXAMPLES::
sage: W = WeylGroup(['A',4,1])
sage: PF = W.pieri_factors()
sage: sorted([w.reduced_word() for w in PF.maximal_elements()], key=str)
[[0, 4, 3, 2], [1, 0, 4, 3], [2, 1, 0, 4], [3, 2, 1, 0], [4, 3, 2, 1]]
sage: W = WeylGroup(RootSystem(["C",3,1]).weight_space())
sage: PF = W.pieri_factors()
sage: sorted([w.reduced_word() for w in PF.maximal_elements()], key=str)
[[0, 1, 2, 3, 2, 1], [1, 0, 1, 2, 3, 2], [1, 2, 3, 2, 1, 0],
[2, 1, 0, 1, 2, 3], [2, 3, 2, 1, 0, 1], [3, 2, 1, 0, 1, 2]]
sage: W = WeylGroup(RootSystem(["B",3,1]).weight_space())
sage: PF = W.pieri_factors()
sage: sorted([w.reduced_word() for w in PF.maximal_elements()], key=str)
[[0, 2, 3, 2, 0], [1, 0, 2, 3, 2], [1, 2, 3, 2, 1],
[2, 1, 0, 2, 3], [2, 3, 2, 1, 0], [3, 2, 1, 0, 2]]
sage: W = WeylGroup(['D',4,1])
sage: PF = W.pieri_factors()
sage: sorted([w.reduced_word() for w in PF.maximal_elements()], key=str)
[[0, 2, 4, 3, 2, 0], [1, 0, 2, 4, 3, 2], [1, 2, 4, 3, 2, 1],
[2, 1, 0, 2, 4, 3], [2, 4, 3, 2, 1, 0], [3, 2, 1, 0, 2, 3],
[4, 2, 1, 0, 2, 4], [4, 3, 2, 1, 0, 2]]
"""
ct = self.W.cartan_type()
s = ct.translation_factors()[1]
R = RootSystem(ct).weight_space()
Lambda = R.fundamental_weights()
orbit = [R.reduced_word_of_translation(x)
for x in (s*(Lambda[1]-Lambda[1].level()*Lambda[0]))._orbit_iter()]
return [self.W.from_reduced_word(x) for x in orbit]