本文整理汇总了Python中sage.matrix.constructor.Matrix.stack方法的典型用法代码示例。如果您正苦于以下问题：Python Matrix.stack方法的具体用法？Python Matrix.stack怎么用？Python Matrix.stack使用的例子？那么恭喜您, 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.matrix.constructor.Matrix的用法示例。
在下文中一共展示了Matrix.stack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: primary_decomposition
# 需要导入模块: from sage.matrix.constructor import Matrix [as 别名]
# 或者: from sage.matrix.constructor.Matrix import stack [as 别名]
def primary_decomposition(self):
"""
Return the primary decomposition of ``self``.
.. NOTE::
``self`` must be unitary, commutative and associative.
OUTPUT:
- a list consisting of the quotient maps ``self`` -> `A`,
with `A` running through the primary factors of ``self``
EXAMPLES::
sage: A = FiniteDimensionalAlgebra(GF(3), [Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])])
sage: A.primary_decomposition()
[Morphism from Finite-dimensional algebra of degree 2 over Finite Field of size 3 to Finite-dimensional algebra of degree 2 over Finite Field of size 3 given by matrix [1 0]
[0 1]]
sage: B = FiniteDimensionalAlgebra(QQ, [Matrix([[1,0,0], [0,1,0], [0,0,0]]), Matrix([[0,1,0], [0,0,0], [0,0,0]]), Matrix([[0,0,0], [0,0,0], [0,0,1]])])
sage: B.primary_decomposition()
[Morphism from Finite-dimensional algebra of degree 3 over Rational Field to Finite-dimensional algebra of degree 1 over Rational Field given by matrix [0]
[0]
[1], Morphism from Finite-dimensional algebra of degree 3 over Rational Field to Finite-dimensional algebra of degree 2 over Rational Field given by matrix [1 0]
[0 1]
[0 0]]
"""
k = self.base_ring()
n = self.degree()
if n == 0:
return []
if not (self.is_unitary() and self.is_commutative()
and (self._assume_associative or self.is_associative())):
raise TypeError("algebra must be unitary, commutative and associative")
# Start with the trivial decomposition of self.
components = [Matrix.identity(k, n)]
for b in self.table():
# Use the action of the basis element b to refine our
# decomposition of self.
components_new = []
for c in components:
# Compute the matrix of b on the component c, find its
# characteristic polynomial, and factor it.
b_c = c.solve_left(c * b)
fact = b_c.characteristic_polynomial().factor()
if len(fact) == 1:
components_new.append(c)
else:
for f in fact:
h, a = f
e = h(b_c) ** a
ker_e = e.kernel().basis_matrix()
components_new.append(ker_e * c)
components = components_new
quotients = []
for i in range(len(components)):
I = Matrix(k, 0, n)
for j,c in enumerate(components):
if j != i:
I = I.stack(c)
quotients.append(self.quotient_map(self.ideal(I, given_by_matrix=True)))
return quotients