def test_inversion():
R, x = ring('x', QQ)
p = 2 + x + 2*x**2
n = 5
p1 = rs_series_inversion(p, x, n)
assert rs_trunc(p*p1, x, n) == 1
R, x, y = ring('x, y', QQ)
p = 2 + x + 2*x**2 + y*x + x**2*y
p1 = rs_series_inversion(p, x, n)
assert rs_trunc(p*p1, x, n) == 1
R, x, y = ring('x, y', QQ)
p = 1 + x + y
def test2(p):
p1 = rs_series_inversion(p, x, 4)
raises(NotImplementedError, lambda: test2(p))
def test_series_from_list():
R, x = ring('x', QQ)
p = 1 + 2*x + x**2 + 3*x**3
c = [1, 2, 0, 4, 4]
r = rs_series_from_list(p, c, x, 5)
pc = R.from_list(list(reversed(c)))
r1 = rs_trunc(pc.compose(x, p), x, 5)
assert r == r1
R, x, y = ring('x, y', QQ)
c = [1, 3, 5, 7]
p1 = rs_series_from_list(x + y, c, x, 3, concur=0)
p2 = rs_trunc((1 + 3*(x+y) + 5*(x+y)**2 + 7*(x+y)**3), x, 3)
assert p1 == p2
R, x = ring('x', QQ)
h = 25
p = rs_exp(x, x, h) - 1
p1 = rs_series_from_list(p, c, x, h)
p2 = 0
for i, cx in enumerate(c):
p2 += cx*rs_pow(p, i, x, h)
assert p1 == p2
def test_pow_trunc():
R, x, y, z = ring('x, y, z', QQ)
p0 = y + x*z
p = p0**16
for xx in (x, y, z):
p1 = rs_trunc(p, xx, 8)
p2 = rs_pow(p0, 16, xx, 8)
assert p1 == p2
p = 1 + x
p1 = rs_pow(p, 3, x, 2)
assert p1 == 1 + 3*x
assert rs_pow(p, 0, x, 2) == 1
assert rs_pow(p, -2, x, 2) == 1 - 2*x
p = x + y
assert rs_pow(p, 3, y, 3) == x**3 + 3*x**2*y + 3*x*y**2
def test_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = (y + t*x)**4
p1 = rs_trunc(p, x, 3)
assert p1 == y**4 + 4*y**3*t*x + 6*y**2*t**2*x**2
def test_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = (y + t*x)**4
p1 = rs_trunc(p, x, 3)
assert p1 == y**4 + 4*y**3*t*x + 6*y**2*t**2*x**2
