def points_modulo_primes(X, primes):
r"""
Return a list of rational points modulo all p in primes
parallel implementation
"""
normalized_input = []
for p in primes:
normalized_input.append(((
X,
p,
), {}))
p_iter = p_iter_fork(ncpus())
points_pair = list(p_iter(parallel_function, normalized_input))
points_pair.sort()
modulo_points = []
for pair in points_pair:
modulo_points.append(pair[1])
return modulo_points
def lift_all_points():
r"""
Return list of all rational points lifted parallelly.
"""
normalized_input = []
points = modulo_points.pop(
) # remove the list of points corresponding to largest prime
len_modulo_points.pop()
for point in points:
normalized_input.append(((point, ), {}))
p_iter = p_iter_fork(ncpus())
points_satisfying = list(
p_iter(parallel_function_combination, normalized_input))
lifted_points = set()
for pair in points_satisfying:
L = pair[1]
for point in L:
lifted_points.add(X(tuple(point)))
return list(lifted_points)
def func(Z, p):
Xp = Z.change_ring(GF(p))
L = Xp.rational_points()
return [list(t) for t in L]
%time
from sage.parallel.ncpus import ncpus
from sage.parallel.use_fork import p_iter_fork
P.<x,y,z,q>=ProjectiveSpace(QQ,3)
Y=P.subscheme([x^2-3^2*y^2+z*q,x+z+4*q])
normalized_input = []
for q in primes(1,30):
normalized_input.append(((Y, q, ), {}))
# LL = func(Y,q)
p_iter = p_iter_fork(ncpus())
points_pair = list(p_iter(func, normalized_input))
points_pair.sort()
#print points_pair
modulo_points = []
for pair in points_pair:
modulo_points.append(pair[1])
#print modulo_points