def computation_roots(self):
# Write these as p-adic series. Start with helper
def help_padic(n, p, prec):
"""
Take an integer n, prime p, and precision prec, and return a
prec-tuple of the p-adic coefficients of j
"""
n = int(n)
res = [0 for j in range(prec)]
while n < 0:
n += p**prec
for k in range(prec):
res[k] = n % p
n = (n - res[k]) / p
return res
# Second helper, in case some arrays are not extended by 0
def getel(li, j):
if j < len(li):
return li[j]
return 0
myroots = self._data["QpRts"]
p = self._data['QpRts-p']
myroots = [[help_padic(z, p, self._data['QpRts-prec']) for z in t]
for t in myroots]
myroots = [[[
getel(root[j], r)
for j in range(len(self._data['QpRts-minpoly']) - 1)
] for r in range(self._data['QpRts-prec'])] for root in myroots]
myroots = [[coeff_to_poly(x, var='a') for x in root]
for root in myroots]
# Use power series so degrees increase
# Use formal p so we can make a power series
PR = PowerSeriesRing(PolynomialRing(QQ, 'a'), 'p')
myroots = [web_latex(PR(x), enclose=False) for x in myroots]
# change p into its value
myroots = [
re.sub(r'([a)\d]) *p', r'\1\cdot ' + str(p), z) for z in myroots
]
return [z.replace('p', str(p)) for z in myroots]
def computation_minimal_polynomial_latex(self):
pol = coeff_to_poly(self._data["QpRts-minpoly"])
return web_latex(pol, enclose=False)
def polynomial_latex(self):
return web_latex(coeff_to_poly(self.polynomial()), enclose=False)