You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
186 lines
7.2 KiB
186 lines
7.2 KiB
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
|