"""
Queries
This file contains code that carries out interesting queries
regarding the database of elliptic curves.
"""
def counts_collection(address='localhost:29000'):
from psage.lmfdb.auth import userpass
user, password = userpass()
from pymongo import Connection
from pymongo.connection import DuplicateKeyError
C = Connection(address).research
C.authenticate(user, password)
return C.ellcurves
def create_counts_table(levels, address, verbose=0):
"""
QUESTION: What proportion of curves in the database have
squarefree conductor, as a function of the conductor?
To answer, make another table ellcurves.counts with documents:
{'_id':N, 'c':number_of_isogeny_classes_of_curves_of_conductor_N, 'ss':True}
where 'ss':True is set only if N is squarefree.
Once we have this table, the rest should be relatively easy.
"""
db_counts = get_ellcurves(address).counts
from sage.all import is_squarefree
i = 0
for N in levels:
N = int(N)
c = ellcurves.find({'level':N, 'number':1}).count()
doc = {'_id':N, 'c':c}
if is_squarefree(N):
doc['ss'] = True
try:
db_counts.insert(doc, safe=True)
except DuplicateKeyError:
if verbose and i%verbose == 0:
print '[%s]'%N,
else:
if verbose and i%verbose == 0:
print N,
i += 1
import sys; sys.stdout.flush()
def counts_intlist(Nmax):
"""
Return an Intlist v such that for N<=Nmax, we have v[N] = # of
isogeny classes of curves of conductor N in the database.
"""
Nmax = int(Nmax)
db_counts = get_ellcurves(address).counts
from sage.all import stats
v = stats.IntList(Nmax + 1)
query = {'_id':{'$lte':Nmax}, 'c':{'$exists':True}}
for c in db_counts.find(query):
v[c['_id']] = c['c']
return v
def create_disc_counts_table(levels, address, verbose=0):
"""
QUESTION: What proportion of curves in the database have
squarefree conductor, as a function of the conductor?
To answer, make another table ellcurves.counts with documents:
{'_id':N, 'c':number_of_isogeny_classes_of_curves_of_conductor_N, 'ss':True}
where 'ss':True is set only if N is squarefree.
Once we have this table, the rest should be relatively easy.
"""
db_counts = get_ellcurves(address).disc_counts
