def test_DomainMatrix_from_Matrix():
ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]]))
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
K = QQ.algebraic_field(sqrt(2))
ddm = DDM([[
K.convert(1 + sqrt(2)), K.convert(2 + sqrt(2))
], [K.convert(3 + sqrt(2)), K.convert(4 + sqrt(2))]], (2, 2), K)
A = DomainMatrix.from_Matrix(Matrix([[1 + sqrt(2), 2 + sqrt(2)],
[3 + sqrt(2), 4 + sqrt(2)]]),
extension=True)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == K
def _eigenvects_DOM(M, **kwargs):
DOM = DomainMatrix.from_Matrix(M, field=True, extension=True)
if DOM.domain != EX:
rational, algebraic = dom_eigenvects(DOM)
eigenvects = dom_eigenvects_to_sympy(rational, algebraic, M.__class__,
**kwargs)
eigenvects = sorted(eigenvects, key=lambda x: default_sort_key(x[0]))
return eigenvects
return None