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######################################################################
#
# Functions to check Minkowksi-reduction of generators, and compare
#
######################################################################
import os
from sage.all import EllipticCurve
from codec import split, parse_int_list, proj_to_point, point_to_proj
from red_gens import reduce_gens, check_minkowski
HOME = os.getenv("HOME")
ECDATA_DIR = os.path.join(HOME, "ecdata")
BASE_DIR = ECDATA_DIR
def check_mink(filename, base_dir=BASE_DIR):
infilename = os.path.join(base_dir, filename)
with open(infilename) as infile:
n = 0
nbad = 0
for line in infile:
n += 1
data = split(line)
label = "".join(data[:3])
ainvs = parse_int_list(data[3])
E = EllipticCurve(ainvs)
rank = int(data[4])
gens = [proj_to_point(gen, E) for gen in data[6:6 + rank]]
if not check_minkowski(gens):
nbad += 1
print("{}: gens {} are not Minkowski-reduced".format(label, gens))
print("heights: {}".format([P.height() for P in gens]))
print("Out of {} curves, {} were reduced and {} not".format(n, n-nbad, nbad))
def rewrite_gens(filename, base_dir=BASE_DIR):
oldfile = os.path.join(base_dir, filename)
newfile = ".".join([oldfile, 'new'])
with open(oldfile) as infile, open(newfile, 'w') as outfile:
n = 0
for line in infile:
n += 1
data = split(line)
label = "".join(data[:3])
ainvs = parse_int_list(data[3])
E = EllipticCurve(ainvs)
rank = int(data[4])
gens = [proj_to_point(gen, E) for gen in data[6:6 + rank]]
tgens = [proj_to_point(gen, E) for gen in data[6 + rank:]]
if len(tgens) == 2 and tgens[0].order() > tgens[1].order():
print("torsion gens for {} in wrong order".format(label))
newgens, tgens = reduce_gens(gens, tgens)
newgens = [point_to_proj(P) for P in newgens]
tgens = [point_to_proj(P) for P in tgens]
data[6:6+rank] = newgens
data[6+rank:] = tgens
outfile.write(" ".join(data) + "\n")
if n%1000 == 0:
print("{} lines output...".format(n))
print("Done. {} lines output".format(n))
def compare_gens(filename1, filename2, base_dir=BASE_DIR):
file1 = os.path.join(base_dir, filename1)
file2 = os.path.join(base_dir, filename2)
Egens = {}
with open(file1) as infile1, open(file2) as infile2:
for infile, infilename in zip([infile1, infile2], [file1, file2]):
for line in infile:
data = split(line)
label = "".join(data[:3])
ainvs = parse_int_list(data[3])
E = EllipticCurve(ainvs)
rank = int(data[4])
gens = [proj_to_point(gen, E) for gen in data[6:6 + rank]]
if label not in Egens:
Egens[label] = {}
Egens[label][infilename] = gens
print("Finished reading {}".format(infilename))
nsame = 0
ndiff = 0
nsame_uptosign = 0
nsame_uptotorsion = 0
ndiff_really = 0
with open(file1 + '.uptosign.txt', 'w') as logfile2, open(file1 + '.uptotorsion.txt', 'w') as logfile3:
for label in Egens:
bothgens = Egens[label]
gens1 = bothgens[file1]
gens2 = bothgens[file2]
if gens1 == gens2:
nsame += 1
else:
ndiff += 1
if all([(P == Q) or (P == -Q) for P, Q in zip(gens1, gens2)]):
nsame_uptosign += 1
logfile2.write("{} gens1: {}\n{} gens2: {}\n".format(label, gens1, label, gens2))
else:
if all([(P - Q).has_finite_order() or (P + Q).has_finite_order() for P, Q in zip(gens1, gens2)]):
nsame_uptotorsion += 1
logfile3.write("{} gens1: {}\n{} gens2: {}\n".format(label, gens1, label, gens2))
else:
ndiff_really += 1
print("gens equal in {} cases, different in {} cases".format(nsame, ndiff))
print("gens equal up to sign in {} more cases".format(nsame_uptosign))
print("gens equal up to torsion in {} more cases".format(nsame_uptotorsion))
if ndiff_really:
print("gens different, even up to sign and torsion in {} cases".format(ndiff_really))
else:
print("In all cases the gens are the same up to sign and torsion")
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