def _test(self):
from sage.all import QQ, PolynomialRing, GaussValuation, FunctionField
R = PolynomialRing(QQ, 'x')
x = R.gen()
v = GaussValuation(R, QQ.valuation(2))
K = FunctionField(QQ, 'x')
x = K.gen()
v = K.valuation(v)
K.valuation((v, K.hom(x/2), K.hom(2*x)))
def _test(self):
from sage.all import FunctionField, QQ, PolynomialRing
K = FunctionField(QQ, 'x')
x = K.gen()
R = PolynomialRing(K, 'y')
y = R.gen()
L = K.extension(y**3 - 1 / x**3 * y + 2 / x**4, 'y')
v = K.valuation(x)
v.extensions(L)
def _test(self):
from sage.all import PolynomialRing, QQ, NumberField, GaussValuation, FunctionField
R = PolynomialRing(QQ, 'x')
x = R.gen()
K = NumberField(x**6 + 126 * x**3 + 126, 'pi')
v = K.valuation(2)
R = PolynomialRing(K, 'x')
x = R.gen()
v = GaussValuation(R, v).augmentation(x, QQ(2) / 3)
F = FunctionField(K, 'x')
x = F.gen()
v = F.valuation(v)
S = PolynomialRing(F, 'y')
y = S.gen()
w0 = GaussValuation(S, v)
G = y**2 - x**3 - 3
w1 = w0.mac_lane_step(G)[0]
w1.mac_lane_step(G)