msfast11.py

from time import time

pari.init()


def pari_eval(s):
    return eval(pari.exec(s))


def prime_range(start, stop):
    return pari_eval(f'primes([{start},{stop}-1])')


def next_prime(n):
    return pari_eval(f'nextprime({n+1})')


def primitive_root(m):
    return pari_eval(f'lift(znprimroot({m}))')


#ms = P.fastModularSymbolMap_11a


def goSlow(numCoeffs, d=3, p=32749):
    M = 11
    MS = ManinSymbols(M)
    P = MS.presentation(p)
    v = []
    m = 100
    while True:
        m = next_prime(m)
        while m % d != 1:
            m = next_prime(m)
        print(f'd={d}: {len(v)} < {numCoeffs}')
        g = primitive_root(m)
        special = pari_eval(f'lift(Mod(-1/{M},{m})^(({d}+1)/2))')
        scale = pari_eval(f'1/sqrt(({m}-1)*log({m}))')
        #print(m, g, special, scale)
        ww = (d - 1) / 2
        for k in range(1, ww + 1):
            s = 0
            zz = (m - 1) / (2 * d)
            for j in range(zz):
                numer = pari_eval(
                    f'lift({special}*Mod({g},{m})^({j}*{d}+{k}))')
                #print("ms ", numer, m, ZZ(P.fastModularSymbolMap_11a(numer, m))/10)
                s += P.fastModularSymbolMap_11a(numer, m)
            v.append(scale * s / 10)
            if len(v) >= numCoeffs: return v


# NOTE: p better be less than 2^15.  Biggest option is the default.
def go(numCoeffs, d=3, p=32749):
    t0 = time()
    M = 11
    MS = ManinSymbols(M)
    P = MS.presentation(p)
    v = []
    m = 100
    while True:
        m = next_prime(m)
        while m % d != 1:
            m = next_prime(m)
        if len(v) > 0:
            eta = int((int(time()-t0) / len(v)) * (numCoeffs - len(v)))
            print(f'd={d}:  numCoeffs={len(v)} < {numCoeffs},  time={int(time()-t0)}s,  ETA={eta}s')
        g = primitive_root(m)
        special = pari_eval(f'lift(Mod(-1/{M},{m})^(({d}+1)/2))')
        scale = pari_eval(f'1/sqrt(({m}-1)*log({m}))')
        #print(m, g, special, scale)
        ww = (d - 1) / 2
        for k in range(1, ww + 1):
            s = 0
            a = pari_eval(f'lift({special}*Mod({g}, {m})^{k})')
            gd = pari_eval(f'lift(Mod({g}, {m})^{d})')
            numer = a
            zz = (m - 1) / (2 * d)
            for j in range(zz):
                #print("ms ", numer, m,
                #      ZZ(P.fastModularSymbolMap_11a(numer, m)) / 10)
                s += P.fastModularSymbolMap_11a(numer, m)
                numer = (numer * gd) % m
            v.append(scale * s / 10)
            if len(v) >= numCoeffs:
                save(v, f'data/v-d{d}n{numCoeffs}p{p}.json')
                return v


def save(obj, name):
    require('fs').writeFileSync(name, JSON.stringify(obj))