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from sympy.testing.pytest import raises |
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from sympy.matrices.exceptions import NonSquareMatrixError, NonInvertibleMatrixError |
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from sympy import Matrix, Rational |
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def test_lll(): |
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A = Matrix([[1, 0, 0, 0, -20160], |
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[0, 1, 0, 0, 33768], |
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[0, 0, 1, 0, 39578], |
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[0, 0, 0, 1, 47757]]) |
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L = Matrix([[ 10, -3, -2, 8, -4], |
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[ 3, -9, 8, 1, -11], |
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[ -3, 13, -9, -3, -9], |
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[-12, -7, -11, 9, -1]]) |
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T = Matrix([[ 10, -3, -2, 8], |
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[ 3, -9, 8, 1], |
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[ -3, 13, -9, -3], |
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[-12, -7, -11, 9]]) |
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assert A.lll() == L |
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assert A.lll_transform() == (L, T) |
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assert T * A == L |
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def test_matrix_inv_mod(): |
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A = Matrix(2, 1, [1, 0]) |
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raises(NonSquareMatrixError, lambda: A.inv_mod(2)) |
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A = Matrix(2, 2, [1, 0, 0, 0]) |
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raises(NonInvertibleMatrixError, lambda: A.inv_mod(2)) |
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A = Matrix(2, 2, [1, 2, 3, 4]) |
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Ai = Matrix(2, 2, [1, 1, 0, 1]) |
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assert A.inv_mod(3) == Ai |
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A = Matrix(2, 2, [1, 0, 0, 1]) |
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assert A.inv_mod(2) == A |
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A = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9]) |
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raises(NonInvertibleMatrixError, lambda: A.inv_mod(5)) |
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A = Matrix(3, 3, [5, 1, 3, 2, 6, 0, 2, 1, 1]) |
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Ai = Matrix(3, 3, [6, 8, 0, 1, 5, 6, 5, 6, 4]) |
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assert A.inv_mod(9) == Ai |
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A = Matrix(3, 3, [1, 6, -3, 4, 1, -5, 3, -5, 5]) |
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Ai = Matrix(3, 3, [4, 3, 3, 1, 2, 5, 1, 5, 1]) |
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assert A.inv_mod(6) == Ai |
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A = Matrix(3, 3, [1, 6, 1, 4, 1, 5, 3, 2, 5]) |
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Ai = Matrix(3, 3, [6, 0, 3, 6, 6, 4, 1, 6, 1]) |
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assert A.inv_mod(7) == Ai |
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A = Matrix([[1, 2], [3, Rational(3,4)]]) |
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raises(ValueError, lambda: A.inv_mod(2)) |
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A = Matrix([[1, 2], [3, 4]]) |
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raises(TypeError, lambda: A.inv_mod(Rational(1, 2))) |
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M = Matrix([ |
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[2, 3, 1, 4], |
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[1, 5, 3, 2], |
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[3, 2, 4, 1], |
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[4, 1, 2, 5], |
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]) |
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assert M.inv_mod(26) == Matrix([ |
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[7, 21, 10, 10], |
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[1, 7, 19, 3], |
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[14, 1, 15, 1], |
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[25, 23, 3, 12], |
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]) |
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