Conversion for residue fields of number fields does not use lift map

[davidac897]

When I do

ZZp = Zp(p=2,prec=10, type = 'fixed-mod')
PRZZp.<x> = ZZp[]
R.<pi> = ZZp.extension(x^2+x+1)
Fp = R.residue_field()
a = Fp(pi)
b = R(a); b

I get pi. Without 'fixed-mod', I get pi+O(2).

But when I do

PRZZ.<x> = ZZ[]
R.<pi> = ZZ.extension(x^2+x+1)
Fp = ResidueField(R.ideal(2))
a = Fp(pi)
b = R(a)

I get an error.

This can be solved with lift_map, but I feel like that should be in the conversion.

Furthermore, it would be nice to be able to lift polynomials with coefficients in the residue field. I made my own implementation of that as follows:

def polynomiallift(g,PR,PFp): #PFp is the ring of polynomials over the residue field, PR is the ring of polynomials over the integer ring, L is the lift map, and g is an element of PFp
    if g.parent() != PFp:
        raise Exception('first argument must be an element of the last argument')
    Fp = PFp.base_ring()
    L = Fp.lift_map()
    if L.codomain() != PR.base_ring():
        raise Exception('codomain of lift map must be base ring of PR')
    f = PR(0)
    var_str = PR.variable_name()
    exec('vari = ' + var_str)
    coeffs = g.coefficients(sparse=False)
    for i in range(g.degree()+1):
        f += L(coeffs[i])*vari^i
    return f

Component: number fields

Keywords: residue_field, lift_map

Issue created by migration from https://trac.sagemath.org/ticket/30100

[mkoeppe]

comment:4

Moving to 9.4, as 9.3 has been released.