def test_PQ_f7(self):
S = QQ['t']
t = S.gen()
r0, r1, r2 = (t**3 - t**2 + 1).roots(QQbar, multiplicities=False)
series = self.get_PQ(self.f7)
x, y = self.f7.parent().gens()
x = QQbar['x,y'](x)
y = QQbar['x,y'](y)
self.assertItemsEqual(series, [(x, y + r0), (x, y + r1), (x, y + r2)])
def test_PQ_f27(self):
S = QQ['t']
t = S.gen()
sqrt2 = (t**2 - 2).roots(QQbar, multiplicities=False)[0]
series = self.get_PQ(self.f27)
x, y = self.f27.parent().gens()
x = QQbar['x,y'](x)
y = QQbar['x,y'](y)
self.assertItemsEqual(series, [(x, x * (y + sqrt2)),
(x, x * (y - sqrt2)),
(x**2 / 2, x**3 * (y + 1) / 2),
(x**3 / 2, x * (y + 1))])
def test_PQ_f7(self):
S = QQ['t']
t = S.gen()
r0,r1,r2 = (t**3 - t**2 + 1).roots(QQbar, multiplicities=False)
series = self.get_PQ(self.f7)
x,y = self.f7.parent().gens()
x = QQbar['x,y'](x)
y = QQbar['x,y'](y)
self.assertItemsEqual(
series,
[(x, y + r0),
(x, y + r1),
(x, y + r2)])
def test_PQ_f27(self):
S = QQ['t']
t = S.gen()
sqrt2 = (t**2 - 2).roots(QQbar, multiplicities=False)[0]
series = self.get_PQ(self.f27)
x,y = self.f27.parent().gens()
x = QQbar['x,y'](x)
y = QQbar['x,y'](y)
self.assertItemsEqual(
series,
[(x, x*(y + sqrt2)),
(x, x*(y - sqrt2)),
(x**2/2, x**3*(y + 1)/2),
(x**3/2, x*(y + 1))])
