def test_cofactor_and_minors():
x = Symbol('x')
e = DeterminantOnlyMatrix(
4, 4, [x, 1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 14])
m = Matrix([[x, 1, 3], [2, 9, 11], [12, 13, 14]])
cm = Matrix([[4, 76, -122, 48],
[-8, -14 * x - 68, 17 * x + 142, -4 * x - 72],
[4, 14 * x - 8, -21 * x + 4, 8 * x],
[0, -4 * x + 24, 8 * x - 48, -4 * x + 24]])
sub = Matrix([[x, 1, 2], [4, 5, 6], [2, 9, 10]])
assert e.minor_submatrix(1, 2) == m
assert e.minor_submatrix(-1, -1) == sub
assert e.minor(1, 2) == -17 * x - 142
assert e.cofactor(1, 2) == 17 * x + 142
assert e.cofactor_matrix() == cm
assert e.cofactor_matrix(method="bareiss") == cm
assert e.cofactor_matrix(method="berkowitz") == cm
raises(ValueError, lambda: e.cofactor(4, 5))
raises(ValueError, lambda: e.minor(4, 5))
raises(ValueError, lambda: e.minor_submatrix(4, 5))
a = DeterminantOnlyMatrix(2, 3, [1, 2, 3, 4, 5, 6])
assert a.minor_submatrix(0, 0) == Matrix([[5, 6]])
raises(ValueError,
lambda: DeterminantOnlyMatrix(0, 0, []).minor_submatrix(0, 0))
raises(NonSquareMatrixError, lambda: a.cofactor(0, 0))
raises(NonSquareMatrixError, lambda: a.minor(0, 0))
raises(NonSquareMatrixError, lambda: a.cofactor_matrix())
def test_cofactor_and_minors():
x = Symbol('x')
e = DeterminantOnlyMatrix(4,4,[x,1,2,3,4,5,6,7,2,9,10,11,12,13,14,14])
m = Matrix([
[ x, 1, 3],
[ 2, 9, 11],
[12, 13, 14]])
cm = Matrix([
[ 4, 76, -122, 48],
[-8, -14*x - 68, 17*x + 142, -4*x - 72],
[ 4, 14*x - 8, -21*x + 4, 8*x],
[ 0, -4*x + 24, 8*x - 48, -4*x + 24]])
sub = Matrix([
[x, 1, 2],
[4, 5, 6],
[2, 9, 10]])
assert e.minor_submatrix(1,2) == m
assert e.minor_submatrix(-1,-1) == sub
assert e.minor(1,2) == -17*x - 142
assert e.cofactor(1,2) == 17*x + 142
assert e.cofactor_matrix() == cm
assert e.cofactor_matrix(method="bareiss") == cm
assert e.cofactor_matrix(method="berkowitz") == cm
raises(ValueError, lambda: e.cofactor(4,5))
raises(ValueError, lambda: e.minor(4,5))
raises(ValueError, lambda: e.minor_submatrix(4,5))
a = DeterminantOnlyMatrix(2,3,[1,2,3,4,5,6])
assert a.minor_submatrix(0,0) == Matrix([[5, 6]])
raises(ValueError, lambda: DeterminantOnlyMatrix(0,0,[]).minor_submatrix(0,0))
raises(NonSquareMatrixError, lambda: a.cofactor(0,0))
raises(NonSquareMatrixError, lambda: a.minor(0,0))
raises(NonSquareMatrixError, lambda: a.cofactor_matrix())