def test_fmpz_mat():
M = flint.fmpz_mat
a = M(2, 3, [1, 2, 3, 4, 5, 6])
b = M(2, 3, [4, 5, 6, 7, 8, 9])
assert a == a
assert a == M(a)
assert a != b
assert a.nrows() == 2
assert a.ncols() == 3
assert a.entries() == [1, 2, 3, 4, 5, 6]
assert a.table() == [[1, 2, 3], [4, 5, 6]]
assert (a + b).entries() == [5, 7, 9, 11, 13, 15]
assert raises(a.det, ValueError)
assert +a == a
assert -a == M(2, 3, [-1, -2, -3, -4, -5, -6])
c = M(2, 2, [1, 2, 3, 4])
assert c.det() == -2
assert raises(lambda: a + c, ValueError)
assert (a * 3).entries() == [3, 6, 9, 12, 15, 18]
assert (3 * a).entries() == [3, 6, 9, 12, 15, 18]
assert (a * long(3)).entries() == [3, 6, 9, 12, 15, 18]
assert (long(3) * a).entries() == [3, 6, 9, 12, 15, 18]
assert (a * flint.fmpz(3)).entries() == [3, 6, 9, 12, 15, 18]
assert (flint.fmpz(3) * a).entries() == [3, 6, 9, 12, 15, 18]
assert M.randrank(5, 7, 3, 10).rank() == 3
A = M.randbits(5, 3, 2)
B = M.randtest(3, 7, 3)
C = M.randtest(7, 2, 4)
assert A * (B * C) == (A * B) * C
assert bool(M(2, 2, [0, 0, 0, 0])) == False
assert bool(M(2, 2, [0, 0, 0, 1])) == True
ctx.pretty = False
assert repr(M(2, 2, [1, 2, 3, 4])) == 'fmpz_mat(2, 2, [1, 2, 3, 4])'
ctx.pretty = True
assert str(M(2, 2, [1, 2, 3, 4])) == '[1, 2]\n[3, 4]'
assert M(1, 2, [3, 4]) * flint.fmpq(1, 3) == flint.fmpq_mat(
1, 2, [1, flint.fmpq(4, 3)])
assert flint.fmpq(1, 3) * M(1, 2, [3, 4]) == flint.fmpq_mat(
1, 2, [1, flint.fmpq(4, 3)])
assert M(1, 2, [3, 4]) / 3 == flint.fmpq_mat(1, 2, [1, flint.fmpq(4, 3)])
assert M(2, 2,
[1, 2, 3, 4
]).inv().det() == flint.fmpq(1) / M(2, 2, [1, 2, 3, 4]).det()
assert M(2, 2, [1, 2, 3, 4]).inv().inv() == M(2, 2, [1, 2, 3, 4])
assert raises(lambda: M.randrank(4, 3, 4, 1), ValueError)
assert raises(lambda: M.randrank(3, 4, 4, 1), ValueError)
assert M(1, 1, [3])**5 == M(1, 1, [3**5])
assert raises(lambda: M(1, 2)**3, ValueError)
assert raises(lambda: M(1, 1)**M(1, 1), TypeError)
assert raises(lambda: 1**M(1, 1), TypeError)
assert raises(lambda: M([1]), TypeError)
assert raises(lambda: M([[1], [2, 3]]), ValueError)
assert M([[1, 2, 3], [4, 5, 6]]) == M(2, 3, [1, 2, 3, 4, 5, 6])
def inverse(M, A, indices_from, indices_to):
m = fmpq_mat(M, M)
d, (r, c) = A
for j in range(len(d)):
a = guessrational(d[j])
#print("guessed", d[j], "=", a)
m[r[j], c[j]] = guessrational(d[j])
t = fmpq_mat(len(indices_from), len(indices_to))
for j in range(len(indices_to)):
z = fmpq_mat(M, 1)
z[indices_to[j], 0] = 1
o = m.solve(z)
for i in range(len(indices_from)):
t[i, j] = o[indices_from[i], 0]
return t
def test_fmpz_mat():
M = flint.fmpz_mat
a = M(2,3,[1,2,3,4,5,6])
b = M(2,3,[4,5,6,7,8,9])
assert a == a
assert a == M(a)
assert a != b
assert a.nrows() == 2
assert a.ncols() == 3
assert a.entries() == [1,2,3,4,5,6]
assert a.table() == [[1,2,3],[4,5,6]]
assert (a + b).entries() == [5,7,9,11,13,15]
assert raises(a.det, ValueError)
assert +a == a
assert -a == M(2,3,[-1,-2,-3,-4,-5,-6])
c = M(2,2,[1,2,3,4])
assert c.det() == -2
assert raises(lambda: a + c, ValueError)
assert (a * 3).entries() == [3,6,9,12,15,18]
assert (3 * a).entries() == [3,6,9,12,15,18]
assert (a * 3L).entries() == [3,6,9,12,15,18]
assert (3L * a).entries() == [3,6,9,12,15,18]
assert (a * flint.fmpz(3)).entries() == [3,6,9,12,15,18]
assert (flint.fmpz(3) * a).entries() == [3,6,9,12,15,18]
assert M.randrank(5,7,3,10).rank() == 3
A = M.randbits(5,3,2)
B = M.randtest(3,7,3)
C = M.randtest(7,2,4)
assert A*(B*C) == (A*B)*C
assert bool(M(2,2,[0,0,0,0])) == False
assert bool(M(2,2,[0,0,0,1])) == True
assert repr(M(2,2,[1,2,3,4])) == 'fmpz_mat(2, 2, [1, 2, 3, 4])'
assert str(M(2,2,[1,2,3,4])) == '[1, 2]\n[3, 4]'
assert M(1,2,[3,4]) * flint.fmpq(1,3) == flint.fmpq_mat(1, 2, [1, flint.fmpq(4,3)])
assert flint.fmpq(1,3) * M(1,2,[3,4]) == flint.fmpq_mat(1, 2, [1, flint.fmpq(4,3)])
assert M(1,2,[3,4]) / 3 == flint.fmpq_mat(1, 2, [1, flint.fmpq(4,3)])
assert (~M(2,2,[1,2,3,4])).det() == flint.fmpq(1) / M(2,2,[1,2,3,4]).det()
assert ~~M(2,2,[1,2,3,4]) == M(2,2,[1,2,3,4])
assert raises(lambda: M.randrank(4,3,4,1), ValueError)
assert raises(lambda: M.randrank(3,4,4,1), ValueError)
assert M(1,1,[3]) ** 5 == M(1,1,[3**5])
assert raises(lambda: M(1,2) ** 3, ValueError)
assert raises(lambda: M(1,1) ** M(1,1), TypeError)
assert raises(lambda: 1 ** M(1,1), TypeError)
def matrix_eigenvalues(mat):
mat = fmpq_mat(mat)
return alg.polynomial_roots(mat.charpoly())