check_ap2_amn_parallel.py

import sys, os, time
try:
    # Make lmfdb available
    sys.path.append(os.path.join(os.path.dirname(os.path.realpath(__file__)),"../.."))
except NameError:
    pass
from psycodict import db
from sage.all import CC, prime_range, gcd
from lmfdb.characters.TinyConrey import ConreyCharacter


def check_ap2_slow(rec):
    # Check a_{p^2} = a_p^2 - chi(p) for primes up to 31
    ls = rec['lfunction_label'].split('.')
    level, weight, chi = map(int, [ls[0], ls[1], ls[-2]])
    char = ConreyCharacter(level, chi)
    Z = rec['an_normalized[0:1000]']
    for p in prime_range(31+1):
        if level % p != 0:
            # a_{p^2} = a_p^2 - chi(p)
            charval = CC(2*char.conreyangle(int(p)) * CC.pi()*CC.gens()[0]).exp()
        else:
            charval = 0
        if  (CC(*Z[p**2 - 1]) - (CC(*Z[p-1])**2 - charval)).abs() > 1e-11:
            return False
    return True

pairs = [(m,n) for m in range(2,1000) for n in range(m, 1000) if gcd(m,n) == 1 and m*n <= 1000]

def check_amn_slow(rec):
    Z = [0] + [CC(*elt) for elt in rec['an_normalized[0:1000]']]
    for m, n in pairs:
        if (Z[m*n] - Z[m]*Z[n]).abs() > 1e-11:
            return False
    return True

import sys
if len(sys.argv) == 3:
    k = int(sys.argv[1])
    j = int(sys.argv[2])
    assert k > j
    assert j >= 0
    _min_id = db.mf_hecke_cc.min_id()
    _max_id = db.mf_hecke_cc.max_id()
    chunk_size = (_max_id - _min_id )/k + 1
    start_time = time.time()
    counter = 0
    minid = _min_id + j*chunk_size
    maxid = _min_id + (j+1)*chunk_size
    query = {'id':{'$gte': minid, '$lt': maxid}}
    total = db.mf_hecke_cc.count(query)
    print("%d: %d rows to check" % (j, total))
    if total > 0:
        with open(os.path.join(os.path.dirname(os.path.realpath(__file__)),'../../logs/check_ap2_amn.%d.log' % j), 'w') as F:
            while counter < total:
                for rec in db.mf_hecke_cc.search(query, ['id','lfunction_label', 'an_normalized[0:1000]'], sort = ['id'], limit = 1000):
                    counter += 1
                    if not check_amn_slow(rec):
                        F.write('%s:amn\n' % rec['lfunction_label'])
                        F.flush()
                    if not check_ap2_slow(rec):
                        F.write('%s:ap2\n' % rec['lfunction_label'])
                        F.flush()
                    if total > 100:
                        if counter % (total/100) == 0:
                            print("%d: %.2ff%% done -- avg %.3f s" % (j, counter*100./total, (time.time() - start_time)/counter))
                assert rec['id'] > minid
                minid = rec['id']
                query = {'id':{'$gt': minid, '$lt': maxid}}
        print("%d: DONE -- avg %.3f s" % (j, (time.time() - start_time)/counter))
    else:
        print("%d: DONE -- avg oo s" % j)


else:
    print(r"""Usage:
        You should run this on legendre as: (this will use 40 cores):
        # parallel -u -j 40 --halt 2 --progress sage -python %s 40 ::: {0..39}""" % sys.argv[0])