def test_DomainMatrix_charpoly():
A = DomainMatrix([], (0, 0), ZZ)
assert A.charpoly() == [ZZ(1)]
A = DomainMatrix([[1]], (1, 1), ZZ)
assert A.charpoly() == [ZZ(1), ZZ(-1)]
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.charpoly() == [ZZ(1), ZZ(-5), ZZ(-2)]
A = DomainMatrix(
[[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)],
[ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ)
assert A.charpoly() == [ZZ(1), ZZ(-15), ZZ(-18), ZZ(0)]
Ans = DomainMatrix([[QQ(1), QQ(2)]], (1, 2), QQ)
raises(NonSquareMatrixError, lambda: Ans.charpoly())
def test_FiniteExtension_sincos_jacobian():
# Use FiniteExtensino to compute the Jacobian of a matrix involving sin
# and cos of different symbols.
r, p, t = symbols('rho, phi, theta')
elements = [
[sin(p)*cos(t), r*cos(p)*cos(t), -r*sin(p)*sin(t)],
[sin(p)*sin(t), r*cos(p)*sin(t), r*sin(p)*cos(t)],
[ cos(p), -r*sin(p), 0],
]
def make_extension(K):
K = FiniteExtension(Poly(sin(p)**2+cos(p)**2-1, sin(p), domain=K[cos(p)]))
K = FiniteExtension(Poly(sin(t)**2+cos(t)**2-1, sin(t), domain=K[cos(t)]))
return K
Ksc1 = make_extension(ZZ[r])
Ksc2 = make_extension(ZZ)[r]
for K in [Ksc1, Ksc2]:
elements_K = [[K.convert(e) for e in row] for row in elements]
J = DomainMatrix(elements_K, (3, 3), K)
det = J.charpoly()[-1] * (-K.one)**3
assert det == K.convert(r**2*sin(p))