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| from sympy.testing.pytest import raises | |
| from sympy.polys.polymatrix import PolyMatrix | |
| from sympy.polys import Poly | |
| from sympy.core.singleton import S | |
| from sympy.matrices.dense import Matrix | |
| from sympy.polys.domains.integerring import ZZ | |
| from sympy.polys.domains.rationalfield import QQ | |
| from sympy.abc import x, y | |
| def _test_polymatrix(): | |
| pm1 = PolyMatrix([[Poly(x**2, x), Poly(-x, x)], [Poly(x**3, x), Poly(-1 + x, x)]]) | |
| v1 = PolyMatrix([[1, 0], [-1, 0]], ring='ZZ[x]') | |
| m1 = PolyMatrix([[1, 0], [-1, 0]], ring='ZZ[x]') | |
| A = PolyMatrix([[Poly(x**2 + x, x), Poly(0, x)], \ | |
| [Poly(x**3 - x + 1, x), Poly(0, x)]]) | |
| B = PolyMatrix([[Poly(x**2, x), Poly(-x, x)], [Poly(-x**2, x), Poly(x, x)]]) | |
| assert A.ring == ZZ[x] | |
| assert isinstance(pm1*v1, PolyMatrix) | |
| assert pm1*v1 == A | |
| assert pm1*m1 == A | |
| assert v1*pm1 == B | |
| pm2 = PolyMatrix([[Poly(x**2, x, domain='QQ'), Poly(0, x, domain='QQ'), Poly(-x**2, x, domain='QQ'), \ | |
| Poly(x**3, x, domain='QQ'), Poly(0, x, domain='QQ'), Poly(-x**3, x, domain='QQ')]]) | |
| assert pm2.ring == QQ[x] | |
| v2 = PolyMatrix([1, 0, 0, 0, 0, 0], ring='ZZ[x]') | |
| m2 = PolyMatrix([1, 0, 0, 0, 0, 0], ring='ZZ[x]') | |
| C = PolyMatrix([[Poly(x**2, x, domain='QQ')]]) | |
| assert pm2*v2 == C | |
| assert pm2*m2 == C | |
| pm3 = PolyMatrix([[Poly(x**2, x), S.One]], ring='ZZ[x]') | |
| v3 = S.Half*pm3 | |
| assert v3 == PolyMatrix([[Poly(S.Half*x**2, x, domain='QQ'), S.Half]], ring='QQ[x]') | |
| assert pm3*S.Half == v3 | |
| assert v3.ring == QQ[x] | |
| pm4 = PolyMatrix([[Poly(x**2, x, domain='ZZ'), Poly(-x**2, x, domain='ZZ')]]) | |
| v4 = PolyMatrix([1, -1], ring='ZZ[x]') | |
| assert pm4*v4 == PolyMatrix([[Poly(2*x**2, x, domain='ZZ')]]) | |
| assert len(PolyMatrix(ring=ZZ[x])) == 0 | |
| assert PolyMatrix([1, 0, 0, 1], x)/(-1) == PolyMatrix([-1, 0, 0, -1], x) | |
| def test_polymatrix_constructor(): | |
| M1 = PolyMatrix([[x, y]], ring=QQ[x,y]) | |
| assert M1.ring == QQ[x,y] | |
| assert M1.domain == QQ | |
| assert M1.gens == (x, y) | |
| assert M1.shape == (1, 2) | |
| assert M1.rows == 1 | |
| assert M1.cols == 2 | |
| assert len(M1) == 2 | |
| assert list(M1) == [Poly(x, (x, y), domain=QQ), Poly(y, (x, y), domain=QQ)] | |
| M2 = PolyMatrix([[x, y]], ring=QQ[x][y]) | |
| assert M2.ring == QQ[x][y] | |
| assert M2.domain == QQ[x] | |
| assert M2.gens == (y,) | |
| assert M2.shape == (1, 2) | |
| assert M2.rows == 1 | |
| assert M2.cols == 2 | |
| assert len(M2) == 2 | |
| assert list(M2) == [Poly(x, (y,), domain=QQ[x]), Poly(y, (y,), domain=QQ[x])] | |
| assert PolyMatrix([[x, y]], y) == PolyMatrix([[x, y]], ring=ZZ.frac_field(x)[y]) | |
| assert PolyMatrix([[x, y]], ring='ZZ[x,y]') == PolyMatrix([[x, y]], ring=ZZ[x,y]) | |
| assert PolyMatrix([[x, y]], (x, y)) == PolyMatrix([[x, y]], ring=QQ[x,y]) | |
| assert PolyMatrix([[x, y]], x, y) == PolyMatrix([[x, y]], ring=QQ[x,y]) | |
| assert PolyMatrix([x, y]) == PolyMatrix([[x], [y]], ring=QQ[x,y]) | |
| assert PolyMatrix(1, 2, [x, y]) == PolyMatrix([[x, y]], ring=QQ[x,y]) | |
| assert PolyMatrix(1, 2, lambda i,j: [x,y][j]) == PolyMatrix([[x, y]], ring=QQ[x,y]) | |
| assert PolyMatrix(0, 2, [], x, y).shape == (0, 2) | |
| assert PolyMatrix(2, 0, [], x, y).shape == (2, 0) | |
| assert PolyMatrix([[], []], x, y).shape == (2, 0) | |
| assert PolyMatrix(ring=QQ[x,y]) == PolyMatrix(0, 0, [], ring=QQ[x,y]) == PolyMatrix([], ring=QQ[x,y]) | |
| raises(TypeError, lambda: PolyMatrix()) | |
| raises(TypeError, lambda: PolyMatrix(1)) | |
| assert PolyMatrix([Poly(x), Poly(y)]) == PolyMatrix([[x], [y]], ring=ZZ[x,y]) | |
| # XXX: Maybe a bug in parallel_poly_from_expr (x lost from gens and domain): | |
| assert PolyMatrix([Poly(y, x), 1]) == PolyMatrix([[y], [1]], ring=QQ[y]) | |
| def test_polymatrix_eq(): | |
| assert (PolyMatrix([x]) == PolyMatrix([x])) is True | |
| assert (PolyMatrix([y]) == PolyMatrix([x])) is False | |
| assert (PolyMatrix([x]) != PolyMatrix([x])) is False | |
| assert (PolyMatrix([y]) != PolyMatrix([x])) is True | |
| assert PolyMatrix([[x, y]]) != PolyMatrix([x, y]) == PolyMatrix([[x], [y]]) | |
| assert PolyMatrix([x], ring=QQ[x]) != PolyMatrix([x], ring=ZZ[x]) | |
| assert PolyMatrix([x]) != Matrix([x]) | |
| assert PolyMatrix([x]).to_Matrix() == Matrix([x]) | |
| assert PolyMatrix([1], x) == PolyMatrix([1], x) | |
| assert PolyMatrix([1], x) != PolyMatrix([1], y) | |
| def test_polymatrix_from_Matrix(): | |
| assert PolyMatrix.from_Matrix(Matrix([1, 2]), x) == PolyMatrix([1, 2], x, ring=QQ[x]) | |
| assert PolyMatrix.from_Matrix(Matrix([1]), ring=QQ[x]) == PolyMatrix([1], x) | |
| pmx = PolyMatrix([1, 2], x) | |
| pmy = PolyMatrix([1, 2], y) | |
| assert pmx != pmy | |
| assert pmx.set_gens(y) == pmy | |
| def test_polymatrix_repr(): | |
| assert repr(PolyMatrix([[1, 2]], x)) == 'PolyMatrix([[1, 2]], ring=QQ[x])' | |
| assert repr(PolyMatrix(0, 2, [], x)) == 'PolyMatrix(0, 2, [], ring=QQ[x])' | |
| def test_polymatrix_getitem(): | |
| M = PolyMatrix([[1, 2], [3, 4]], x) | |
| assert M[:, :] == M | |
| assert M[0, :] == PolyMatrix([[1, 2]], x) | |
| assert M[:, 0] == PolyMatrix([1, 3], x) | |
| assert M[0, 0] == Poly(1, x, domain=QQ) | |
| assert M[0] == Poly(1, x, domain=QQ) | |
| assert M[:2] == [Poly(1, x, domain=QQ), Poly(2, x, domain=QQ)] | |
| def test_polymatrix_arithmetic(): | |
| M = PolyMatrix([[1, 2], [3, 4]], x) | |
| assert M + M == PolyMatrix([[2, 4], [6, 8]], x) | |
| assert M - M == PolyMatrix([[0, 0], [0, 0]], x) | |
| assert -M == PolyMatrix([[-1, -2], [-3, -4]], x) | |
| raises(TypeError, lambda: M + 1) | |
| raises(TypeError, lambda: M - 1) | |
| raises(TypeError, lambda: 1 + M) | |
| raises(TypeError, lambda: 1 - M) | |
| assert M * M == PolyMatrix([[7, 10], [15, 22]], x) | |
| assert 2 * M == PolyMatrix([[2, 4], [6, 8]], x) | |
| assert M * 2 == PolyMatrix([[2, 4], [6, 8]], x) | |
| assert S(2) * M == PolyMatrix([[2, 4], [6, 8]], x) | |
| assert M * S(2) == PolyMatrix([[2, 4], [6, 8]], x) | |
| raises(TypeError, lambda: [] * M) | |
| raises(TypeError, lambda: M * []) | |
| M2 = PolyMatrix([[1, 2]], ring=ZZ[x]) | |
| assert S.Half * M2 == PolyMatrix([[S.Half, 1]], ring=QQ[x]) | |
| assert M2 * S.Half == PolyMatrix([[S.Half, 1]], ring=QQ[x]) | |
| assert M / 2 == PolyMatrix([[S(1)/2, 1], [S(3)/2, 2]], x) | |
| assert M / Poly(2, x) == PolyMatrix([[S(1)/2, 1], [S(3)/2, 2]], x) | |
| raises(TypeError, lambda: M / []) | |
| def test_polymatrix_manipulations(): | |
| M1 = PolyMatrix([[1, 2], [3, 4]], x) | |
| assert M1.transpose() == PolyMatrix([[1, 3], [2, 4]], x) | |
| M2 = PolyMatrix([[5, 6], [7, 8]], x) | |
| assert M1.row_join(M2) == PolyMatrix([[1, 2, 5, 6], [3, 4, 7, 8]], x) | |
| assert M1.col_join(M2) == PolyMatrix([[1, 2], [3, 4], [5, 6], [7, 8]], x) | |
| assert M1.applyfunc(lambda e: 2*e) == PolyMatrix([[2, 4], [6, 8]], x) | |
| def test_polymatrix_ones_zeros(): | |
| assert PolyMatrix.zeros(1, 2, x) == PolyMatrix([[0, 0]], x) | |
| assert PolyMatrix.eye(2, x) == PolyMatrix([[1, 0], [0, 1]], x) | |
| def test_polymatrix_rref(): | |
| M = PolyMatrix([[1, 2], [3, 4]], x) | |
| assert M.rref() == (PolyMatrix.eye(2, x), (0, 1)) | |
| raises(ValueError, lambda: PolyMatrix([1, 2], ring=ZZ[x]).rref()) | |
| raises(ValueError, lambda: PolyMatrix([1, x], ring=QQ[x]).rref()) | |
| def test_polymatrix_nullspace(): | |
| M = PolyMatrix([[1, 2], [3, 6]], x) | |
| assert M.nullspace() == [PolyMatrix([-2, 1], x)] | |
| raises(ValueError, lambda: PolyMatrix([1, 2], ring=ZZ[x]).nullspace()) | |
| raises(ValueError, lambda: PolyMatrix([1, x], ring=QQ[x]).nullspace()) | |
| assert M.rank() == 1 | |