本文整理匯總了Python中sage.combinat.sf.sf.SymmetricFunctions.homogeneous方法的典型用法代碼示例。如果您正苦於以下問題：Python SymmetricFunctions.homogeneous方法的具體用法？Python SymmetricFunctions.homogeneous怎麽用？Python SymmetricFunctions.homogeneous使用的例子？那麽, 這裏精選的方法代碼示例或許可以為您提供幫助。您也可以進一步了解該方法所在類sage.combinat.sf.sf.SymmetricFunctions的用法示例。
在下文中一共展示了SymmetricFunctions.homogeneous方法的1個代碼示例，這些例子默認根據受歡迎程度排序。您可以為喜歡或者感覺有用的代碼點讚，您的評價將有助於係統推薦出更棒的Python代碼示例。
示例1: k_schur_noncommutative_variables
# 需要導入模塊: from sage.combinat.sf.sf import SymmetricFunctions [as 別名]
# 或者: from sage.combinat.sf.sf.SymmetricFunctions import homogeneous [as 別名]
def k_schur_noncommutative_variables(self, la):
r"""
In type `A^{(1)}` this is the `k`-Schur function in noncommutative variables defined by Thomas Lam.
REFERENCES:
.. [Lam2005] T. Lam, Affine Stanley symmetric functions, Amer. J. Math. 128 (2006), no. 6, 1553--1586.
This function is currently only defined in type `A^{(1)}`.
INPUT:
- ``la`` -- a partition with first part bounded by the rank of the Weyl group
EXAMPLES::
sage: A = NilCoxeterAlgebra(WeylGroup(['A',3,1]))
sage: A.k_schur_noncommutative_variables([2,2])
u[0,3,1,0] + u[3,1,2,0] + u[1,2,0,1] + u[3,2,0,3] + u[2,0,3,1] + u[2,3,1,2]
TESTS::
sage: A = NilCoxeterAlgebra(WeylGroup(['A',3,1]))
sage: A.k_schur_noncommutative_variables([])
1
sage: A.k_schur_noncommutative_variables([1,2])
Traceback (most recent call last):
...
AssertionError: [1, 2] is not a partition.
sage: A.k_schur_noncommutative_variables([4,2])
Traceback (most recent call last):
...
AssertionError: [4, 2] is not a 3-bounded partition.
sage: C = NilCoxeterAlgebra(WeylGroup(['C',3,1]))
sage: C.k_schur_noncommutative_variables([2,2])
Traceback (most recent call last):
...
AssertionError: Weyl Group of type ['C', 3, 1] (as a matrix group acting on the root space) is not affine type A.
"""
assert self._cartan_type[0] == 'A' and len(self._cartan_type) == 3 and self._cartan_type[2] == 1, "%s is not affine type A."%(self._W)
assert la in Partitions(), "%s is not a partition."%(la)
assert (len(la) == 0 or la[0] < self._W.n), "%s is not a %s-bounded partition."%(la, self._W.n-1)
Sym = SymmetricFunctions(self._base_ring)
h = Sym.homogeneous()
ks = Sym.kschur(self._n-1,1)
f = h(ks[la])
return sum(f.coefficient(x)*self.homogeneous_noncommutative_variables(x) for x in f.support())