build_Lfunction_db.py

import sys

from sage.all import DirichletGroup
from sage.all import CC, EllipticCurve, sqrt

import sage.libs.lcalc.lcalc_Lfunction as lc

from lmfdb import base
C = base.getDBConnection()

Lfunctions = C.test.Lfunctions_test2


def remove_all():
    Lfunctions.drop()


def insert_dirichlet_L_functions(start, end):
    print("Putting Dirichlet L-functions into database.")
    start = max(3, start)
    for q in range(start, end):
        print("Working on modulus", q)
        sys.stdout.flush()
        G = DirichletGroup(q)
        for n in range(len(G)):
            chi = G[n]
            if chi.is_primitive():
                L = lc.Lfunction_from_character(chi)
                z = L.find_zeros_via_N(1)[0]
                Lfunction_data = {}
                Lfunction_data['first_zero'] = float(z)
                Lfunction_data['description'] = "Dirichlet L-function for character number " + \
                    str(n) + " modulo " + str(q)
                Lfunction_data['degree'] = 1
                Lfunction_data['signature'] = (1, 0)
                if chi.is_odd():
                    Lfunction_data['mu'] = [(1.0, 0.0), ]
                else:
                    Lfunction_data['mu'] = [(0.0, 0.0), ]

                Lfunction_data['level'] = q

                coeffs = []

                for k in range(0, 10):
                    coeffs.append(CC(chi(k)))

                Lfunction_data['coeffs'] = [(float(x.real()), float(x.imag())) for x in coeffs]
                Lfunction_data['special'] = {'type': 'dirichlet', 'modulus': q, 'number': n}

                Lfunctions.insert(Lfunction_data)


def update_entries():
    # one time function to run to update everything in the database with an extra tag
    everything = Lfunctions.find()
    for L in everything:
        if L['description'].startswith("Dirichlet"):
            n, q = L['description'][42:].split(" modulo ")
            # print n, q
            n = int(n)
            q = int(q)
            L['special'] = {'type': 'dirichlet', 'modulus': q, 'number': n}
            Lfunctions.save(L)
        elif L['description'].startswith("Elliptic"):
            label = L['description'][36:]
            L['special'] = {'type': 'elliptic', 'label': label}
            Lfunctions.save(L)


def insert_EC_L_functions(start=1, end=100):
    curves = C.ellcurves.curves
    for N in range(start, end):
        print("Processing conductor", N)
        sys.stdout.flush()
        query = curves.find({'conductor': N, 'number': 1})
        for curve in query:
            E = EllipticCurve([int(x) for x in curve['ainvs']])
            L = lc.Lfunction_from_elliptic_curve(E)
            first_zeros = L.find_zeros_via_N(curve['rank'] + 1)
            if len(first_zeros) > 1:
                if not first_zeros[-2] == 0:
                    print("problem")

            z = float(first_zeros[-1])

            Lfunction_data = {}
            Lfunction_data['first_zero'] = z
            Lfunction_data['description'] = 'Elliptic curve L-function for curve ' + str(curve['label'][:-1])
            Lfunction_data['degree'] = 2
            Lfunction_data['signature'] = [0, 1]
            Lfunction_data['eta'] = [(1.0, 0), ]

            Lfunction_data['level'] = N
            Lfunction_data['special'] = {'type': 'elliptic', 'label': curve['label'][:-1]}

            coeffs = []

            for k in range(1, 11):
                coeffs.append(CC(E.an(k) / sqrt(k)))

            Lfunction_data['coeffs'] = [(float(x.real()), float(x.imag())) for x in coeffs]

            Lfunctions.insert(Lfunction_data)


def build_indices():
    Lfunctions.create_index("first_zero")
    Lfunctions.create_index("level")
    Lfunctions.create_index("degree")


if __name__ == "__main__":
    # build_indices()
    # remove_all()
    for n in range(1, 10):
        insert_EC_L_functions(n * 100, (n + 1) * 100)
        # insert_dirichlet_L_functions(n * 100, (n+1)*100)
    # insert_dirichlet_L_functions(50)