本文整理汇总了Python中sage.combinat.root_system.root_system.RootSystem.algebra方法的典型用法代码示例。如果您正苦于以下问题：Python RootSystem.algebra方法的具体用法？Python RootSystem.algebra怎么用？Python RootSystem.algebra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.algebra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: one_dimensional_configuration_sum
# 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 algebra [as 别名]
def one_dimensional_configuration_sum(self, q = None, group_components = True):
r"""
Compute the one-dimensional configuration sum.
INPUT:
- ``q`` -- (default: ``None``) a variable or ``None``; if ``None``,
a variable ``q`` is set in the code
- ``group_components`` -- (default: ``True``) boolean; if ``True``,
then the terms are grouped by classical component
The one-dimensional configuration sum is the sum of the weights of all elements in the crystal
weighted by the energy function. For untwisted types it uses the parabolic quantum Bruhat graph, see [LNSSS2013]_.
In the dual-of-untwisted case, the parabolic quantum Bruhat graph is defined by
exchanging the roles of roots and coroots (which is still conjectural at this point).
EXAMPLES::
sage: R = RootSystem(['A',2,1])
sage: La = R.weight_space().basis()
sage: LS = crystals.ProjectedLevelZeroLSPaths(2*La[1])
sage: LS.one_dimensional_configuration_sum() # long time
B[-2*Lambda[1] + 2*Lambda[2]] + (q+1)*B[-Lambda[1]]
+ (q+1)*B[Lambda[1] - Lambda[2]] + B[2*Lambda[1]] + B[-2*Lambda[2]] + (q+1)*B[Lambda[2]]
sage: R.<t> = ZZ[]
sage: LS.one_dimensional_configuration_sum(t, False) # long time
B[-2*Lambda[1] + 2*Lambda[2]] + (t+1)*B[-Lambda[1]] + (t+1)*B[Lambda[1] - Lambda[2]]
+ B[2*Lambda[1]] + B[-2*Lambda[2]] + (t+1)*B[Lambda[2]]
TESTS::
sage: R = RootSystem(['B',3,1])
sage: La = R.weight_space().basis()
sage: LS = crystals.ProjectedLevelZeroLSPaths(La[1]+La[2])
sage: LS.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum(group_components=False) # long time
True
sage: K1 = crystals.KirillovReshetikhin(['B',3,1],1,1)
sage: K2 = crystals.KirillovReshetikhin(['B',3,1],2,1)
sage: T = crystals.TensorProduct(K2,K1)
sage: T.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum() # long time
True
sage: R = RootSystem(['D',4,2])
sage: La = R.weight_space().basis()
sage: LS = crystals.ProjectedLevelZeroLSPaths(La[1]+La[2])
sage: K1 = crystals.KirillovReshetikhin(['D',4,2],1,1)
sage: K2 = crystals.KirillovReshetikhin(['D',4,2],2,1)
sage: T = crystals.TensorProduct(K2,K1)
sage: T.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum() # long time
True
sage: R = RootSystem(['A',5,2])
sage: La = R.weight_space().basis()
sage: LS = crystals.ProjectedLevelZeroLSPaths(3*La[1])
sage: K1 = crystals.KirillovReshetikhin(['A',5,2],1,1)
sage: T = crystals.TensorProduct(K1,K1,K1)
sage: T.one_dimensional_configuration_sum() == LS.one_dimensional_configuration_sum() # long time
True
"""
if q is None:
from sage.rings.all import QQ
q = QQ['q'].gens()[0]
#P0 = self.weight_lattice_realization().classical()
P0 = RootSystem(self.cartan_type().classical()).weight_lattice()
B = P0.algebra(q.parent())
def weight(x):
w = x.weight()
return P0.sum(int(c)*P0.basis()[i] for i,c in w if i in P0.index_set())
if group_components:
G = self.digraph(index_set = self.cartan_type().classical().index_set())
C = G.connected_components()
return sum(q**(c[0].energy_function())*B.sum(B(weight(b)) for b in c) for c in C)
return B.sum(q**(b.energy_function())*B(weight(b)) for b in self)