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))