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