solve_mod_mathematica

solve_mod_mathematica.sage

from wolframclient.evaluation import WolframLanguageSession
from wolframclient.language import wl

def solve_mma(eqn, modulus):
    if eqn.number_of_arguments() != 1:
        raise NotImplementedError('Not univariate')
    if eqn.is_polynomial(eqn.args()[0]):
        poly = eqn
    elif eqn.is_relational() and eqn.operator() is operator.eq:
        poly = eqn.lhs() - eqn.rhs()
    else:
        raise NotImplementedError('Not polynomial or equation')

    p = int(0)
    for c, e in poly.coefficients():
        p = wl.Plus(p, wl.Times(int(c), wl.Power(wl.x, int(e))))
    
    session = WolframLanguageSession()
    r = session.evaluate(wl.Quiet(wl.Solve(wl.Equal(p, int(0)), wl.x, Modulus=int(modulus))))
    ans = []
    for i in r:
        ans.append(session.evaluate(wl.Quiet(wl.ReplaceAll(*i)(wl.x))))
    session.terminate()
    
    return ans

# Usage:
# var('x')
# solve_mma(x ^ 2 == 1, 15)