911 lines
32 KiB
Python
911 lines
32 KiB
Python
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from sympy.testing.pytest import raises
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from sympy.core.numbers import Integer, Rational
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from sympy.core.singleton import S
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from sympy.functions import sqrt
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from sympy.matrices.dense import Matrix
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from sympy.polys.domains import FF, ZZ, QQ, EXRAW
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from sympy.polys.matrices.domainmatrix import DomainMatrix, DomainScalar, DM
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from sympy.polys.matrices.exceptions import (
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DMBadInputError, DMDomainError, DMShapeError, DMFormatError, DMNotAField,
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DMNonSquareMatrixError, DMNonInvertibleMatrixError,
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)
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from sympy.polys.matrices.ddm import DDM
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from sympy.polys.matrices.sdm import SDM
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def test_DM():
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ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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A = DM([[1, 2], [3, 4]], ZZ)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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def test_DomainMatrix_init():
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lol = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
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dod = {0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}
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ddm = DDM(lol, (2, 2), ZZ)
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sdm = SDM(dod, (2, 2), ZZ)
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A = DomainMatrix(lol, (2, 2), ZZ)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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A = DomainMatrix(dod, (2, 2), ZZ)
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assert A.rep == sdm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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raises(TypeError, lambda: DomainMatrix(ddm, (2, 2), ZZ))
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raises(TypeError, lambda: DomainMatrix(sdm, (2, 2), ZZ))
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raises(TypeError, lambda: DomainMatrix(Matrix([[1]]), (1, 1), ZZ))
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for fmt, rep in [('sparse', sdm), ('dense', ddm)]:
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A = DomainMatrix(lol, (2, 2), ZZ, fmt=fmt)
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assert A.rep == rep
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A = DomainMatrix(dod, (2, 2), ZZ, fmt=fmt)
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assert A.rep == rep
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raises(ValueError, lambda: DomainMatrix(lol, (2, 2), ZZ, fmt='invalid'))
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raises(DMBadInputError, lambda: DomainMatrix([[ZZ(1), ZZ(2)]], (2, 2), ZZ))
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def test_DomainMatrix_from_rep():
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ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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A = DomainMatrix.from_rep(ddm)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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sdm = SDM({0: {0: ZZ(1), 1:ZZ(2)}, 1: {0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
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A = DomainMatrix.from_rep(sdm)
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assert A.rep == sdm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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A = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
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raises(TypeError, lambda: DomainMatrix.from_rep(A))
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def test_DomainMatrix_from_list():
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ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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A = DomainMatrix.from_list([[1, 2], [3, 4]], ZZ)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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dom = FF(7)
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ddm = DDM([[dom(1), dom(2)], [dom(3), dom(4)]], (2, 2), dom)
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A = DomainMatrix.from_list([[1, 2], [3, 4]], dom)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == dom
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ddm = DDM([[QQ(1, 2), QQ(3, 1)], [QQ(1, 4), QQ(5, 1)]], (2, 2), QQ)
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A = DomainMatrix.from_list([[(1, 2), (3, 1)], [(1, 4), (5, 1)]], QQ)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == QQ
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def test_DomainMatrix_from_list_sympy():
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ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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A = DomainMatrix.from_list_sympy(2, 2, [[1, 2], [3, 4]])
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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K = QQ.algebraic_field(sqrt(2))
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ddm = DDM(
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[[K.convert(1 + sqrt(2)), K.convert(2 + sqrt(2))],
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[K.convert(3 + sqrt(2)), K.convert(4 + sqrt(2))]],
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(2, 2),
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K
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)
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A = DomainMatrix.from_list_sympy(
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2, 2, [[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]],
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extension=True)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == K
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def test_DomainMatrix_from_dict_sympy():
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sdm = SDM({0: {0: QQ(1, 2)}, 1: {1: QQ(2, 3)}}, (2, 2), QQ)
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sympy_dict = {0: {0: Rational(1, 2)}, 1: {1: Rational(2, 3)}}
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A = DomainMatrix.from_dict_sympy(2, 2, sympy_dict)
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assert A.rep == sdm
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assert A.shape == (2, 2)
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assert A.domain == QQ
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fds = DomainMatrix.from_dict_sympy
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raises(DMBadInputError, lambda: fds(2, 2, {3: {0: Rational(1, 2)}}))
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raises(DMBadInputError, lambda: fds(2, 2, {0: {3: Rational(1, 2)}}))
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def test_DomainMatrix_from_Matrix():
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sdm = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
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A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]]))
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assert A.rep == sdm
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assert A.shape == (2, 2)
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assert A.domain == ZZ
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K = QQ.algebraic_field(sqrt(2))
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sdm = SDM(
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{0: {0: K.convert(1 + sqrt(2)), 1: K.convert(2 + sqrt(2))},
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1: {0: K.convert(3 + sqrt(2)), 1: K.convert(4 + sqrt(2))}},
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(2, 2),
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K
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)
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A = DomainMatrix.from_Matrix(
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Matrix([[1 + sqrt(2), 2 + sqrt(2)], [3 + sqrt(2), 4 + sqrt(2)]]),
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extension=True)
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assert A.rep == sdm
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assert A.shape == (2, 2)
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assert A.domain == K
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A = DomainMatrix.from_Matrix(Matrix([[QQ(1, 2), QQ(3, 4)], [QQ(0, 1), QQ(0, 1)]]), fmt='dense')
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ddm = DDM([[QQ(1, 2), QQ(3, 4)], [QQ(0, 1), QQ(0, 1)]], (2, 2), QQ)
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assert A.rep == ddm
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assert A.shape == (2, 2)
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assert A.domain == QQ
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def test_DomainMatrix_eq():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A == A
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B = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(1)]], (2, 2), ZZ)
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assert A != B
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C = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
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assert A != C
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def test_DomainMatrix_unify_eq():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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B1 = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
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B2 = DomainMatrix([[QQ(1), QQ(3)], [QQ(3), QQ(4)]], (2, 2), QQ)
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B3 = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
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assert A.unify_eq(B1) is True
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assert A.unify_eq(B2) is False
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assert A.unify_eq(B3) is False
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def test_DomainMatrix_get_domain():
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K, items = DomainMatrix.get_domain([1, 2, 3, 4])
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assert items == [ZZ(1), ZZ(2), ZZ(3), ZZ(4)]
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assert K == ZZ
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K, items = DomainMatrix.get_domain([1, 2, 3, Rational(1, 2)])
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assert items == [QQ(1), QQ(2), QQ(3), QQ(1, 2)]
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assert K == QQ
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def test_DomainMatrix_convert_to():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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Aq = A.convert_to(QQ)
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assert Aq == DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
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Acopy = A.convert_to(None)
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assert Acopy == A and Acopy is not A
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def test_DomainMatrix_to_sympy():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.to_sympy() == A.convert_to(EXRAW)
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def test_DomainMatrix_to_field():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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Aq = A.to_field()
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assert Aq == DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
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def test_DomainMatrix_to_sparse():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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A_sparse = A.to_sparse()
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assert A_sparse.rep == {0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}
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def test_DomainMatrix_to_dense():
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A = DomainMatrix({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
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A_dense = A.to_dense()
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assert A_dense.rep == DDM([[1, 2], [3, 4]], (2, 2), ZZ)
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def test_DomainMatrix_unify():
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Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
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assert Az.unify(Az) == (Az, Az)
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assert Az.unify(Aq) == (Aq, Aq)
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assert Aq.unify(Az) == (Aq, Aq)
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assert Aq.unify(Aq) == (Aq, Aq)
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As = DomainMatrix({0: {1: ZZ(1)}, 1:{0:ZZ(2)}}, (2, 2), ZZ)
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Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert As.unify(As) == (As, As)
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assert Ad.unify(Ad) == (Ad, Ad)
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Bs, Bd = As.unify(Ad, fmt='dense')
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assert Bs.rep == DDM([[0, 1], [2, 0]], (2, 2), ZZ)
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assert Bd.rep == DDM([[1, 2],[3, 4]], (2, 2), ZZ)
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Bs, Bd = As.unify(Ad, fmt='sparse')
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assert Bs.rep == SDM({0: {1: 1}, 1: {0: 2}}, (2, 2), ZZ)
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assert Bd.rep == SDM({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
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raises(ValueError, lambda: As.unify(Ad, fmt='invalid'))
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def test_DomainMatrix_to_Matrix():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.to_Matrix() == Matrix([[1, 2], [3, 4]])
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def test_DomainMatrix_to_list():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.to_list() == [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
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def test_DomainMatrix_to_list_flat():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.to_list_flat() == [ZZ(1), ZZ(2), ZZ(3), ZZ(4)]
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def test_DomainMatrix_to_dok():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.to_dok() == {(0, 0):ZZ(1), (0, 1):ZZ(2), (1, 0):ZZ(3), (1, 1):ZZ(4)}
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def test_DomainMatrix_repr():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert repr(A) == 'DomainMatrix([[1, 2], [3, 4]], (2, 2), ZZ)'
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def test_DomainMatrix_transpose():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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AT = DomainMatrix([[ZZ(1), ZZ(3)], [ZZ(2), ZZ(4)]], (2, 2), ZZ)
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assert A.transpose() == AT
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def test_DomainMatrix_flat():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.flat() == [ZZ(1), ZZ(2), ZZ(3), ZZ(4)]
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def test_DomainMatrix_is_zero_matrix():
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A = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
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B = DomainMatrix([[ZZ(0)]], (1, 1), ZZ)
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assert A.is_zero_matrix is False
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assert B.is_zero_matrix is True
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def test_DomainMatrix_is_upper():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(0), ZZ(4)]], (2, 2), ZZ)
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B = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.is_upper is True
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assert B.is_upper is False
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def test_DomainMatrix_is_lower():
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A = DomainMatrix([[ZZ(1), ZZ(0)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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B = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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assert A.is_lower is True
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assert B.is_lower is False
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def test_DomainMatrix_is_square():
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A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
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B = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)], [ZZ(5), ZZ(6)]], (3, 2), ZZ)
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assert A.is_square is True
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assert B.is_square is False
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||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_rank():
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(6), QQ(8)]], (3, 2), QQ)
|
||
|
|
assert A.rank() == 2
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_add():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
assert A + A == A.add(A) == B
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
L = [[2, 3], [3, 4]]
|
||
|
|
raises(TypeError, lambda: A + L)
|
||
|
|
raises(TypeError, lambda: L + A)
|
||
|
|
|
||
|
|
A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
|
||
|
|
raises(DMShapeError, lambda: A1 + A2)
|
||
|
|
raises(DMShapeError, lambda: A2 + A1)
|
||
|
|
raises(DMShapeError, lambda: A1.add(A2))
|
||
|
|
raises(DMShapeError, lambda: A2.add(A1))
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Asum = DomainMatrix([[QQ(2), QQ(4)], [QQ(6), QQ(8)]], (2, 2), QQ)
|
||
|
|
assert Az + Aq == Asum
|
||
|
|
assert Aq + Az == Asum
|
||
|
|
raises(DMDomainError, lambda: Az.add(Aq))
|
||
|
|
raises(DMDomainError, lambda: Aq.add(Az))
|
||
|
|
|
||
|
|
As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
|
||
|
|
Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
Asd = As + Ad
|
||
|
|
Ads = Ad + As
|
||
|
|
assert Asd == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ)
|
||
|
|
assert Asd.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ)
|
||
|
|
assert Ads == DomainMatrix([[1, 3], [5, 4]], (2, 2), ZZ)
|
||
|
|
assert Ads.rep == DDM([[1, 3], [5, 4]], (2, 2), ZZ)
|
||
|
|
raises(DMFormatError, lambda: As.add(Ad))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_sub():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(0), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
|
||
|
|
assert A - A == A.sub(A) == B
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
L = [[2, 3], [3, 4]]
|
||
|
|
raises(TypeError, lambda: A - L)
|
||
|
|
raises(TypeError, lambda: L - A)
|
||
|
|
|
||
|
|
A1 = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
A2 = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
|
||
|
|
raises(DMShapeError, lambda: A1 - A2)
|
||
|
|
raises(DMShapeError, lambda: A2 - A1)
|
||
|
|
raises(DMShapeError, lambda: A1.sub(A2))
|
||
|
|
raises(DMShapeError, lambda: A2.sub(A1))
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Adiff = DomainMatrix([[QQ(0), QQ(0)], [QQ(0), QQ(0)]], (2, 2), QQ)
|
||
|
|
assert Az - Aq == Adiff
|
||
|
|
assert Aq - Az == Adiff
|
||
|
|
raises(DMDomainError, lambda: Az.sub(Aq))
|
||
|
|
raises(DMDomainError, lambda: Aq.sub(Az))
|
||
|
|
|
||
|
|
As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
|
||
|
|
Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
Asd = As - Ad
|
||
|
|
Ads = Ad - As
|
||
|
|
assert Asd == DomainMatrix([[-1, -1], [-1, -4]], (2, 2), ZZ)
|
||
|
|
assert Asd.rep == DDM([[-1, -1], [-1, -4]], (2, 2), ZZ)
|
||
|
|
assert Asd == -Ads
|
||
|
|
assert Asd.rep == -Ads.rep
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_neg():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
Aneg = DomainMatrix([[ZZ(-1), ZZ(-2)], [ZZ(-3), ZZ(-4)]], (2, 2), ZZ)
|
||
|
|
assert -A == A.neg() == Aneg
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_mul():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
A2 = DomainMatrix([[ZZ(7), ZZ(10)], [ZZ(15), ZZ(22)]], (2, 2), ZZ)
|
||
|
|
assert A*A == A.matmul(A) == A2
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
L = [[1, 2], [3, 4]]
|
||
|
|
raises(TypeError, lambda: A * L)
|
||
|
|
raises(TypeError, lambda: L * A)
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Aprod = DomainMatrix([[QQ(7), QQ(10)], [QQ(15), QQ(22)]], (2, 2), QQ)
|
||
|
|
assert Az * Aq == Aprod
|
||
|
|
assert Aq * Az == Aprod
|
||
|
|
raises(DMDomainError, lambda: Az.matmul(Aq))
|
||
|
|
raises(DMDomainError, lambda: Aq.matmul(Az))
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
AA = DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
x = ZZ(2)
|
||
|
|
assert A * x == x * A == A.mul(x) == AA
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
AA = DomainMatrix.zeros((2, 2), ZZ)
|
||
|
|
x = ZZ(0)
|
||
|
|
assert A * x == x * A == A.mul(x).to_sparse() == AA
|
||
|
|
|
||
|
|
As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
|
||
|
|
Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
Asd = As * Ad
|
||
|
|
Ads = Ad * As
|
||
|
|
assert Asd == DomainMatrix([[3, 4], [2, 4]], (2, 2), ZZ)
|
||
|
|
assert Asd.rep == DDM([[3, 4], [2, 4]], (2, 2), ZZ)
|
||
|
|
assert Ads == DomainMatrix([[4, 1], [8, 3]], (2, 2), ZZ)
|
||
|
|
assert Ads.rep == DDM([[4, 1], [8, 3]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_mul_elementwise():
|
||
|
|
A = DomainMatrix([[ZZ(2), ZZ(2)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(4), ZZ(0)], [ZZ(3), ZZ(0)]], (2, 2), ZZ)
|
||
|
|
C = DomainMatrix([[ZZ(8), ZZ(0)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
|
||
|
|
assert A.mul_elementwise(B) == C
|
||
|
|
assert B.mul_elementwise(A) == C
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_pow():
|
||
|
|
eye = DomainMatrix.eye(2, ZZ)
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
A2 = DomainMatrix([[ZZ(7), ZZ(10)], [ZZ(15), ZZ(22)]], (2, 2), ZZ)
|
||
|
|
A3 = DomainMatrix([[ZZ(37), ZZ(54)], [ZZ(81), ZZ(118)]], (2, 2), ZZ)
|
||
|
|
assert A**0 == A.pow(0) == eye
|
||
|
|
assert A**1 == A.pow(1) == A
|
||
|
|
assert A**2 == A.pow(2) == A2
|
||
|
|
assert A**3 == A.pow(3) == A3
|
||
|
|
|
||
|
|
raises(TypeError, lambda: A ** Rational(1, 2))
|
||
|
|
raises(NotImplementedError, lambda: A ** -1)
|
||
|
|
raises(NotImplementedError, lambda: A.pow(-1))
|
||
|
|
|
||
|
|
A = DomainMatrix.zeros((2, 1), ZZ)
|
||
|
|
raises(DMNonSquareMatrixError, lambda: A ** 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_scc():
|
||
|
|
Ad = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)],
|
||
|
|
[ZZ(0), ZZ(1), ZZ(0)],
|
||
|
|
[ZZ(2), ZZ(0), ZZ(4)]], (3, 3), ZZ)
|
||
|
|
As = Ad.to_sparse()
|
||
|
|
Addm = Ad.rep
|
||
|
|
Asdm = As.rep
|
||
|
|
for A in [Ad, As, Addm, Asdm]:
|
||
|
|
assert Ad.scc() == [[1], [0, 2]]
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_rref():
|
||
|
|
A = DomainMatrix([], (0, 1), QQ)
|
||
|
|
assert A.rref() == (A, ())
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1)]], (1, 1), QQ)
|
||
|
|
assert A.rref() == (A, (0,))
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(0)]], (1, 1), QQ)
|
||
|
|
assert A.rref() == (A, ())
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Ar, pivots = A.rref()
|
||
|
|
assert Ar == DomainMatrix([[QQ(1), QQ(0)], [QQ(0), QQ(1)]], (2, 2), QQ)
|
||
|
|
assert pivots == (0, 1)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(0), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Ar, pivots = A.rref()
|
||
|
|
assert Ar == DomainMatrix([[QQ(1), QQ(0)], [QQ(0), QQ(1)]], (2, 2), QQ)
|
||
|
|
assert pivots == (0, 1)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(0), QQ(2)], [QQ(0), QQ(4)]], (2, 2), QQ)
|
||
|
|
Ar, pivots = A.rref()
|
||
|
|
assert Ar == DomainMatrix([[QQ(0), QQ(1)], [QQ(0), QQ(0)]], (2, 2), QQ)
|
||
|
|
assert pivots == (1,)
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
raises(DMNotAField, lambda: Az.rref())
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_columnspace():
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(-1), QQ(1)], [QQ(2), QQ(-2), QQ(3)]], (2, 3), QQ)
|
||
|
|
Acol = DomainMatrix([[QQ(1), QQ(1)], [QQ(2), QQ(3)]], (2, 2), QQ)
|
||
|
|
assert A.columnspace() == Acol
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(-1), ZZ(1)], [ZZ(2), ZZ(-2), ZZ(3)]], (2, 3), ZZ)
|
||
|
|
raises(DMNotAField, lambda: Az.columnspace())
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(-1), QQ(1)], [QQ(2), QQ(-2), QQ(3)]], (2, 3), QQ, fmt='sparse')
|
||
|
|
Acol = DomainMatrix({0: {0: QQ(1), 1: QQ(1)}, 1: {0: QQ(2), 1: QQ(3)}}, (2, 2), QQ)
|
||
|
|
assert A.columnspace() == Acol
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_rowspace():
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(-1), QQ(1)], [QQ(2), QQ(-2), QQ(3)]], (2, 3), QQ)
|
||
|
|
assert A.rowspace() == A
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(-1), ZZ(1)], [ZZ(2), ZZ(-2), ZZ(3)]], (2, 3), ZZ)
|
||
|
|
raises(DMNotAField, lambda: Az.rowspace())
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(-1), QQ(1)], [QQ(2), QQ(-2), QQ(3)]], (2, 3), QQ, fmt='sparse')
|
||
|
|
assert A.rowspace() == A
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_nullspace():
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(1)], [QQ(1), QQ(1)]], (2, 2), QQ)
|
||
|
|
Anull = DomainMatrix([[QQ(-1), QQ(1)]], (1, 2), QQ)
|
||
|
|
assert A.nullspace() == Anull
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(1)], [ZZ(1), ZZ(1)]], (2, 2), ZZ)
|
||
|
|
raises(DMNotAField, lambda: Az.nullspace())
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_solve():
|
||
|
|
# XXX: Maybe the _solve method should be changed...
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(2), QQ(4)]], (2, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)]], (2, 1), QQ)
|
||
|
|
particular = DomainMatrix([[1, 0]], (1, 2), QQ)
|
||
|
|
nullspace = DomainMatrix([[-2, 1]], (1, 2), QQ)
|
||
|
|
assert A._solve(b) == (particular, nullspace)
|
||
|
|
|
||
|
|
b3 = DomainMatrix([[QQ(1)], [QQ(1)], [QQ(1)]], (3, 1), QQ)
|
||
|
|
raises(DMShapeError, lambda: A._solve(b3))
|
||
|
|
|
||
|
|
bz = DomainMatrix([[ZZ(1)], [ZZ(1)]], (2, 1), ZZ)
|
||
|
|
raises(DMNotAField, lambda: A._solve(bz))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_inv():
|
||
|
|
A = DomainMatrix([], (0, 0), QQ)
|
||
|
|
assert A.inv() == A
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
Ainv = DomainMatrix([[QQ(-2), QQ(1)], [QQ(3, 2), QQ(-1, 2)]], (2, 2), QQ)
|
||
|
|
assert A.inv() == Ainv
|
||
|
|
|
||
|
|
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
raises(DMNotAField, lambda: Az.inv())
|
||
|
|
|
||
|
|
Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
|
||
|
|
raises(DMNonSquareMatrixError, lambda: Ans.inv())
|
||
|
|
|
||
|
|
Aninv = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(6)]], (2, 2), QQ)
|
||
|
|
raises(DMNonInvertibleMatrixError, lambda: Aninv.inv())
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_det():
|
||
|
|
A = DomainMatrix([], (0, 0), ZZ)
|
||
|
|
assert A.det() == 1
|
||
|
|
|
||
|
|
A = DomainMatrix([[1]], (1, 1), ZZ)
|
||
|
|
assert A.det() == 1
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
assert A.det() == ZZ(-2)
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(3), ZZ(5)]], (3, 3), ZZ)
|
||
|
|
assert A.det() == ZZ(-1)
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(2), ZZ(5)]], (3, 3), ZZ)
|
||
|
|
assert A.det() == ZZ(0)
|
||
|
|
|
||
|
|
Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
|
||
|
|
raises(DMNonSquareMatrixError, lambda: Ans.det())
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
assert A.det() == QQ(-2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_lu():
|
||
|
|
A = DomainMatrix([], (0, 0), QQ)
|
||
|
|
assert A.lu() == (A, A, [])
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
L = DomainMatrix([[QQ(1), QQ(0)], [QQ(3), QQ(1)]], (2, 2), QQ)
|
||
|
|
U = DomainMatrix([[QQ(1), QQ(2)], [QQ(0), QQ(-2)]], (2, 2), QQ)
|
||
|
|
swaps = []
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(0), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
L = DomainMatrix([[QQ(1), QQ(0)], [QQ(0), QQ(1)]], (2, 2), QQ)
|
||
|
|
U = DomainMatrix([[QQ(3), QQ(4)], [QQ(0), QQ(2)]], (2, 2), QQ)
|
||
|
|
swaps = [(0, 1)]
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(2), QQ(4)]], (2, 2), QQ)
|
||
|
|
L = DomainMatrix([[QQ(1), QQ(0)], [QQ(2), QQ(1)]], (2, 2), QQ)
|
||
|
|
U = DomainMatrix([[QQ(1), QQ(2)], [QQ(0), QQ(0)]], (2, 2), QQ)
|
||
|
|
swaps = []
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(0), QQ(2)], [QQ(0), QQ(4)]], (2, 2), QQ)
|
||
|
|
L = DomainMatrix([[QQ(1), QQ(0)], [QQ(0), QQ(1)]], (2, 2), QQ)
|
||
|
|
U = DomainMatrix([[QQ(0), QQ(2)], [QQ(0), QQ(4)]], (2, 2), QQ)
|
||
|
|
swaps = []
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2), QQ(3)], [QQ(4), QQ(5), QQ(6)]], (2, 3), QQ)
|
||
|
|
L = DomainMatrix([[QQ(1), QQ(0)], [QQ(4), QQ(1)]], (2, 2), QQ)
|
||
|
|
U = DomainMatrix([[QQ(1), QQ(2), QQ(3)], [QQ(0), QQ(-3), QQ(-6)]], (2, 3), QQ)
|
||
|
|
swaps = []
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ)
|
||
|
|
L = DomainMatrix([
|
||
|
|
[QQ(1), QQ(0), QQ(0)],
|
||
|
|
[QQ(3), QQ(1), QQ(0)],
|
||
|
|
[QQ(5), QQ(2), QQ(1)]], (3, 3), QQ)
|
||
|
|
U = DomainMatrix([[QQ(1), QQ(2)], [QQ(0), QQ(-2)], [QQ(0), QQ(0)]], (3, 2), QQ)
|
||
|
|
swaps = []
|
||
|
|
assert A.lu() == (L, U, swaps)
|
||
|
|
|
||
|
|
A = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [0, 0, 1, 2]]
|
||
|
|
L = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 1, 1]]
|
||
|
|
U = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [0, 0, 0, 1]]
|
||
|
|
to_dom = lambda rows, dom: [[dom(e) for e in row] for row in rows]
|
||
|
|
A = DomainMatrix(to_dom(A, QQ), (4, 4), QQ)
|
||
|
|
L = DomainMatrix(to_dom(L, QQ), (4, 4), QQ)
|
||
|
|
U = DomainMatrix(to_dom(U, QQ), (4, 4), QQ)
|
||
|
|
assert A.lu() == (L, U, [])
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
raises(DMNotAField, lambda: A.lu())
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_lu_solve():
|
||
|
|
# Base case
|
||
|
|
A = b = x = DomainMatrix([], (0, 0), QQ)
|
||
|
|
assert A.lu_solve(b) == x
|
||
|
|
|
||
|
|
# Basic example
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)]], (2, 1), QQ)
|
||
|
|
x = DomainMatrix([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ)
|
||
|
|
assert A.lu_solve(b) == x
|
||
|
|
|
||
|
|
# Example with swaps
|
||
|
|
A = DomainMatrix([[QQ(0), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)]], (2, 1), QQ)
|
||
|
|
x = DomainMatrix([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ)
|
||
|
|
assert A.lu_solve(b) == x
|
||
|
|
|
||
|
|
# Non-invertible
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(2), QQ(4)]], (2, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)]], (2, 1), QQ)
|
||
|
|
raises(DMNonInvertibleMatrixError, lambda: A.lu_solve(b))
|
||
|
|
|
||
|
|
# Overdetermined, consistent
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)], [QQ(3)]], (3, 1), QQ)
|
||
|
|
x = DomainMatrix([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ)
|
||
|
|
assert A.lu_solve(b) == x
|
||
|
|
|
||
|
|
# Overdetermined, inconsistent
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)], [QQ(2)], [QQ(4)]], (3, 1), QQ)
|
||
|
|
raises(DMNonInvertibleMatrixError, lambda: A.lu_solve(b))
|
||
|
|
|
||
|
|
# Underdetermined
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1)]], (1, 1), QQ)
|
||
|
|
raises(NotImplementedError, lambda: A.lu_solve(b))
|
||
|
|
|
||
|
|
# Non-field
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
b = DomainMatrix([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ)
|
||
|
|
raises(DMNotAField, lambda: A.lu_solve(b))
|
||
|
|
|
||
|
|
# Shape mismatch
|
||
|
|
A = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
|
||
|
|
b = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
|
||
|
|
raises(DMShapeError, lambda: A.lu_solve(b))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_charpoly():
|
||
|
|
A = DomainMatrix([], (0, 0), ZZ)
|
||
|
|
assert A.charpoly() == [ZZ(1)]
|
||
|
|
|
||
|
|
A = DomainMatrix([[1]], (1, 1), ZZ)
|
||
|
|
assert A.charpoly() == [ZZ(1), ZZ(-1)]
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
assert A.charpoly() == [ZZ(1), ZZ(-5), ZZ(-2)]
|
||
|
|
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)], [ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
|
||
|
|
assert A.charpoly() == [ZZ(1), ZZ(-15), ZZ(-18), ZZ(0)]
|
||
|
|
|
||
|
|
Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
|
||
|
|
raises(DMNonSquareMatrixError, lambda: Ans.charpoly())
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_eye():
|
||
|
|
A = DomainMatrix.eye(3, QQ)
|
||
|
|
assert A.rep == SDM.eye((3, 3), QQ)
|
||
|
|
assert A.shape == (3, 3)
|
||
|
|
assert A.domain == QQ
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_zeros():
|
||
|
|
A = DomainMatrix.zeros((1, 2), QQ)
|
||
|
|
assert A.rep == SDM.zeros((1, 2), QQ)
|
||
|
|
assert A.shape == (1, 2)
|
||
|
|
assert A.domain == QQ
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_ones():
|
||
|
|
A = DomainMatrix.ones((2, 3), QQ)
|
||
|
|
assert A.rep == DDM.ones((2, 3), QQ)
|
||
|
|
assert A.shape == (2, 3)
|
||
|
|
assert A.domain == QQ
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_diag():
|
||
|
|
A = DomainMatrix({0:{0:ZZ(2)}, 1:{1:ZZ(3)}}, (2, 2), ZZ)
|
||
|
|
assert DomainMatrix.diag([ZZ(2), ZZ(3)], ZZ) == A
|
||
|
|
|
||
|
|
A = DomainMatrix({0:{0:ZZ(2)}, 1:{1:ZZ(3)}}, (3, 4), ZZ)
|
||
|
|
assert DomainMatrix.diag([ZZ(2), ZZ(3)], ZZ, (3, 4)) == A
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_hstack():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(5), ZZ(6)], [ZZ(7), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
C = DomainMatrix([[ZZ(9), ZZ(10)], [ZZ(11), ZZ(12)]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
AB = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2), ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(3), ZZ(4), ZZ(7), ZZ(8)]], (2, 4), ZZ)
|
||
|
|
ABC = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2), ZZ(5), ZZ(6), ZZ(9), ZZ(10)],
|
||
|
|
[ZZ(3), ZZ(4), ZZ(7), ZZ(8), ZZ(11), ZZ(12)]], (2, 6), ZZ)
|
||
|
|
assert A.hstack(B) == AB
|
||
|
|
assert A.hstack(B, C) == ABC
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_vstack():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(5), ZZ(6)], [ZZ(7), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
C = DomainMatrix([[ZZ(9), ZZ(10)], [ZZ(11), ZZ(12)]], (2, 2), ZZ)
|
||
|
|
|
||
|
|
AB = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2)],
|
||
|
|
[ZZ(3), ZZ(4)],
|
||
|
|
[ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(7), ZZ(8)]], (4, 2), ZZ)
|
||
|
|
ABC = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2)],
|
||
|
|
[ZZ(3), ZZ(4)],
|
||
|
|
[ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(7), ZZ(8)],
|
||
|
|
[ZZ(9), ZZ(10)],
|
||
|
|
[ZZ(11), ZZ(12)]], (6, 2), ZZ)
|
||
|
|
assert A.vstack(B) == AB
|
||
|
|
assert A.vstack(B, C) == ABC
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_applyfunc():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)]], (1, 2), ZZ)
|
||
|
|
B = DomainMatrix([[ZZ(2), ZZ(4)]], (1, 2), ZZ)
|
||
|
|
assert A.applyfunc(lambda x: 2*x) == B
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_scalarmul():
|
||
|
|
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
lamda = DomainScalar(QQ(3)/QQ(2), QQ)
|
||
|
|
assert A * lamda == DomainMatrix([[QQ(3, 2), QQ(3)], [QQ(9, 2), QQ(6)]], (2, 2), QQ)
|
||
|
|
assert A * 2 == DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
assert 2 * A == DomainMatrix([[ZZ(2), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ)
|
||
|
|
assert A * DomainScalar(ZZ(0), ZZ) == DomainMatrix({}, (2, 2), ZZ)
|
||
|
|
assert A * DomainScalar(ZZ(1), ZZ) == A
|
||
|
|
|
||
|
|
raises(TypeError, lambda: A * 1.5)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_truediv():
|
||
|
|
A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]]))
|
||
|
|
lamda = DomainScalar(QQ(3)/QQ(2), QQ)
|
||
|
|
assert A / lamda == DomainMatrix({0: {0: QQ(2, 3), 1: QQ(4, 3)}, 1: {0: QQ(2), 1: QQ(8, 3)}}, (2, 2), QQ)
|
||
|
|
b = DomainScalar(ZZ(1), ZZ)
|
||
|
|
assert A / b == DomainMatrix({0: {0: QQ(1), 1: QQ(2)}, 1: {0: QQ(3), 1: QQ(4)}}, (2, 2), QQ)
|
||
|
|
|
||
|
|
assert A / 1 == DomainMatrix({0: {0: QQ(1), 1: QQ(2)}, 1: {0: QQ(3), 1: QQ(4)}}, (2, 2), QQ)
|
||
|
|
assert A / 2 == DomainMatrix({0: {0: QQ(1, 2), 1: QQ(1)}, 1: {0: QQ(3, 2), 1: QQ(2)}}, (2, 2), QQ)
|
||
|
|
|
||
|
|
raises(ZeroDivisionError, lambda: A / 0)
|
||
|
|
raises(TypeError, lambda: A / 1.5)
|
||
|
|
raises(ZeroDivisionError, lambda: A / DomainScalar(ZZ(0), ZZ))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_getitem():
|
||
|
|
dM = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2), ZZ(3)],
|
||
|
|
[ZZ(4), ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
|
||
|
|
|
||
|
|
assert dM[1:,:-2] == DomainMatrix([[ZZ(4)], [ZZ(7)]], (2, 1), ZZ)
|
||
|
|
assert dM[2,:-2] == DomainMatrix([[ZZ(7)]], (1, 1), ZZ)
|
||
|
|
assert dM[:-2,:-2] == DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
|
||
|
|
assert dM[:-1,0:2] == DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(4), ZZ(5)]], (2, 2), ZZ)
|
||
|
|
assert dM[:, -1] == DomainMatrix([[ZZ(3)], [ZZ(6)], [ZZ(9)]], (3, 1), ZZ)
|
||
|
|
assert dM[-1, :] == DomainMatrix([[ZZ(7), ZZ(8), ZZ(9)]], (1, 3), ZZ)
|
||
|
|
assert dM[::-1, :] == DomainMatrix([
|
||
|
|
[ZZ(7), ZZ(8), ZZ(9)],
|
||
|
|
[ZZ(4), ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(1), ZZ(2), ZZ(3)]], (3, 3), ZZ)
|
||
|
|
|
||
|
|
raises(IndexError, lambda: dM[4, :-2])
|
||
|
|
raises(IndexError, lambda: dM[:-2, 4])
|
||
|
|
|
||
|
|
assert dM[1, 2] == DomainScalar(ZZ(6), ZZ)
|
||
|
|
assert dM[-2, 2] == DomainScalar(ZZ(6), ZZ)
|
||
|
|
assert dM[1, -2] == DomainScalar(ZZ(5), ZZ)
|
||
|
|
assert dM[-1, -3] == DomainScalar(ZZ(7), ZZ)
|
||
|
|
|
||
|
|
raises(IndexError, lambda: dM[3, 3])
|
||
|
|
raises(IndexError, lambda: dM[1, 4])
|
||
|
|
raises(IndexError, lambda: dM[-1, -4])
|
||
|
|
|
||
|
|
dM = DomainMatrix({0: {0: ZZ(1)}}, (10, 10), ZZ)
|
||
|
|
assert dM[5, 5] == DomainScalar(ZZ(0), ZZ)
|
||
|
|
assert dM[0, 0] == DomainScalar(ZZ(1), ZZ)
|
||
|
|
|
||
|
|
dM = DomainMatrix({1: {0: 1}}, (2,1), ZZ)
|
||
|
|
assert dM[0:, 0] == DomainMatrix({1: {0: 1}}, (2, 1), ZZ)
|
||
|
|
raises(IndexError, lambda: dM[3, 0])
|
||
|
|
|
||
|
|
dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
|
||
|
|
assert dM[:2,:2] == DomainMatrix({}, (2, 2), ZZ)
|
||
|
|
assert dM[2:,2:] == DomainMatrix({0: {0: 1}, 2: {2: 1}}, (3, 3), ZZ)
|
||
|
|
assert dM[3:,3:] == DomainMatrix({1: {1: 1}}, (2, 2), ZZ)
|
||
|
|
assert dM[2:, 6:] == DomainMatrix({}, (3, 0), ZZ)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_getitem_sympy():
|
||
|
|
dM = DomainMatrix({2: {2: ZZ(2)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
|
||
|
|
val1 = dM.getitem_sympy(0, 0)
|
||
|
|
assert val1 is S.Zero
|
||
|
|
val2 = dM.getitem_sympy(2, 2)
|
||
|
|
assert val2 == 2 and isinstance(val2, Integer)
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_extract():
|
||
|
|
dM1 = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2), ZZ(3)],
|
||
|
|
[ZZ(4), ZZ(5), ZZ(6)],
|
||
|
|
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
|
||
|
|
dM2 = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(3)],
|
||
|
|
[ZZ(7), ZZ(9)]], (2, 2), ZZ)
|
||
|
|
assert dM1.extract([0, 2], [0, 2]) == dM2
|
||
|
|
assert dM1.to_sparse().extract([0, 2], [0, 2]) == dM2.to_sparse()
|
||
|
|
assert dM1.extract([0, -1], [0, -1]) == dM2
|
||
|
|
assert dM1.to_sparse().extract([0, -1], [0, -1]) == dM2.to_sparse()
|
||
|
|
|
||
|
|
dM3 = DomainMatrix([
|
||
|
|
[ZZ(1), ZZ(2), ZZ(2)],
|
||
|
|
[ZZ(4), ZZ(5), ZZ(5)],
|
||
|
|
[ZZ(4), ZZ(5), ZZ(5)]], (3, 3), ZZ)
|
||
|
|
assert dM1.extract([0, 1, 1], [0, 1, 1]) == dM3
|
||
|
|
assert dM1.to_sparse().extract([0, 1, 1], [0, 1, 1]) == dM3.to_sparse()
|
||
|
|
|
||
|
|
empty = [
|
||
|
|
([], [], (0, 0)),
|
||
|
|
([1], [], (1, 0)),
|
||
|
|
([], [1], (0, 1)),
|
||
|
|
]
|
||
|
|
for rows, cols, size in empty:
|
||
|
|
assert dM1.extract(rows, cols) == DomainMatrix.zeros(size, ZZ).to_dense()
|
||
|
|
assert dM1.to_sparse().extract(rows, cols) == DomainMatrix.zeros(size, ZZ)
|
||
|
|
|
||
|
|
dM = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
bad_indices = [([2], [0]), ([0], [2]), ([-3], [0]), ([0], [-3])]
|
||
|
|
for rows, cols in bad_indices:
|
||
|
|
raises(IndexError, lambda: dM.extract(rows, cols))
|
||
|
|
raises(IndexError, lambda: dM.to_sparse().extract(rows, cols))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_setitem():
|
||
|
|
dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
|
||
|
|
dM[2, 2] = ZZ(2)
|
||
|
|
assert dM == DomainMatrix({2: {2: ZZ(2)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
|
||
|
|
def setitem(i, j, val):
|
||
|
|
dM[i, j] = val
|
||
|
|
raises(TypeError, lambda: setitem(2, 2, QQ(1, 2)))
|
||
|
|
raises(NotImplementedError, lambda: setitem(slice(1, 2), 2, ZZ(1)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_DomainMatrix_pickling():
|
||
|
|
import pickle
|
||
|
|
dM = DomainMatrix({2: {2: ZZ(1)}, 4: {4: ZZ(1)}}, (5, 5), ZZ)
|
||
|
|
assert pickle.loads(pickle.dumps(dM)) == dM
|
||
|
|
dM = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
|
||
|
|
assert pickle.loads(pickle.dumps(dM)) == dM
|