| | 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]) |
| |
|
| | |
| | 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 |
| |
|
