def test_Domain_field():
assert EX.field == EX
assert ZZ.field == QQ
assert QQ.field == QQ
assert RR.field == RR
assert ALG.field == ALG
assert ZZ.inject(x).field == ZZ.frac_field(x)
assert QQ.inject(x).field == QQ.frac_field(x)
assert ZZ.inject(x, y).field == ZZ.frac_field(x, y)
assert QQ.inject(x, y).field == QQ.frac_field(x, y)
def test_sturm():
R, x = ring('x', QQ)
assert R(5).sturm() == [1]
assert x.sturm() == [x, 1]
f = x**3 - 2 * x**2 + 3 * x - 5
assert f.sturm() == [
f, 3 * x**2 - 4 * x + 3, -10 * x / 9 + QQ(13, 3), -QQ(3303, 100)
]
f = x**3 - 2 * x**2 + x - 3
assert f.sturm() == [
f, 3 * x**2 - 4 * x + 1, 2 * x / 9 + QQ(25, 9),
QQ(-2079, 4)
]
pytest.raises(DomainError, lambda: x.set_domain(ZZ).sturm())
F = ZZ.frac_field('pi')
pi = F.pi
R, x = ring('x', F)
f = (1024 / (15625 * pi**8) * x**5 - 4096 / (625 * pi**8) * x**4 + 32 /
(15625 * pi**4) * x**3 - 128 / (625 * pi**4) * x**2 + x / 62500 - F(
(1, 625)))
assert f.sturm() == [
x**3 - 100 * x**2 + pi**4 / 64 * x - 25 * pi**4 / 16,
3 * x**2 - 200 * x + pi**4 / 64, (F(
(20000, 9)) - pi**4 / 96) * x + 25 * pi**4 / 18,
(-3686400000000 * pi**4 - 11520000 * pi**8 - 9 * pi**12) /
(26214400000000 - 245760000 * pi**4 + 576 * pi**8)
]