def rank(self,curves,output_filename="rank_output.txt",\
problems_filename="rank_problems.txt",\
return_data=True,use_database=True,use_only_mwrank=False,\
print_timing=True):
r"""
Compute the algebraic rank for a list of curves ordered by height.
INPUT:
- ``curves`` -- A list of height/a-invariant tuples of
curves, as returned by the coefficients_over_height_range() method
Each tuple is of the form
(H, [a1,a2,a3,a4,a6]) where
H is the height of the curve, and
[a1,...,a6] the curve's a-invariants
- ``output_filename`` -- String, the name of the file to which the
output will be saved. Each line of the save file describes a
single curve, and consists of seven tab-separated integers:
the first is the height of the curve; the following five are
the curve's a-invariants, and the final integer is the curve's rank.
- ``problems_filename`` -- String: the file name to which problem
curves will be written. These are curves for which rank could not
be computed. Write format is the same as above, except rank is
omitted at the end.
- ``return_data`` -- (Default True): If set to False, the data
is not returned at the end of computation; only written to file.
- ``use_database`` -- (Default True): If set to False, the
Cremona database is not used to look up curve ranks.
- ``use_only_mwrank`` -- (Default False): If set to True, will not
try to use analytic methods to compute rank before consulting the
Cremona database
- ``print_timing`` -- (Default True): If set to False, wall time
of total computation will not be printed.
OUTPUT:
- Writes data to file. Each line of the written file consists of seven
tab separated entries of the form
H, a1, a2, a3, a4, a6, d
H: The curve's height
a1,...,a6: The curve's a-invariants
d: The computed datum for that curve
- (only if return_data==True) A list consisting of two lists:
The first is a list of triples of the form
(H, (a1,a2,a3,a4,a6), d)
where the entries are as above.
The second is a list of curve for which the datum could not be provably
computed; each entry of this list is just a pair consisting of height
and a-invariants.
EXAMPLES::
sage: from sage.schemes.elliptic_curves.curve_enumerator import *
sage: C = CurveEnumerator(family="short_weierstrass")
sage: L = C.coefficients_over_height_range(0,4)
sage: R = C.rank(L,return_data=True,print_timing=False)
sage: R[1]
[]
sage: for r in R[0]: print(r)
....:
(1, [0, 0, 0, -1, 0], 0)
(1, [0, 0, 0, 1, 0], 0)
(1, [0, 0, 0, 0, -1], 0)
(1, [0, 0, 0, 0, 1], 0)
(1, [0, 0, 0, -1, -1], 0)
(1, [0, 0, 0, -1, 1], 1)
(1, [0, 0, 0, 1, -1], 1)
(1, [0, 0, 0, 1, 1], 1)
(4, [0, 0, 0, -1, -2], 1)
(4, [0, 0, 0, -1, 2], 0)
(4, [0, 0, 0, 0, -2], 1)
(4, [0, 0, 0, 0, 2], 1)
(4, [0, 0, 0, 1, -2], 0)
(4, [0, 0, 0, 1, 2], 0)
"""
if print_timing:
t = time.time()
out_file = open(output_filename, "w")
prob_file = open(problems_filename, "w")
if return_data:
output = []
problems = []
for C in curves:
# Attempt to compute rank and write curve+rank to file
try:
E = EllipticCurve(C[1])
d = E.rank(use_database=use_database,
only_use_mwrank=use_only_mwrank)
out_file.write(str(C[0]) + "\t")
for a in C[1]:
out_file.write(str(a) + "\t")
out_file.write(str(d) + "\n")
out_file.flush()
if return_data:
output.append((C[0], C[1], d))
# Write to problem file if fail
except:
prob_file.write(str(C[0]) + "\t")
for a in C[1]:
prob_file.write(str(a) + "\t")
prob_file.write("\n")
prob_file.flush()
if return_data:
problems.append(C)
out_file.close()
prob_file.close()
if print_timing:
print(time.time() - t)
if return_data:
return output, problems
def rank(self,curves,output_filename="rank_output.txt",\
problems_filename="rank_problems.txt",\
return_data=True,use_database=True,use_only_mwrank=False,\
print_timing=True):
r"""
Compute the algebraic rank for a list of curves ordered by height.
INPUT:
- ``curves`` -- A list of height/a-invariant tuples of
curves, as returned by the coefficients_over_height_range() method
Each tuple is of the form
(H, [a1,a2,a3,a4,a6]) where
H is the height of the curve, and
[a1,...,a6] the curve's a-invariants
- ``output_filename`` -- String, the name of the file to which the
output will be saved. Each line of the save file describes a
single curve, and consists of seven tab-separated integers:
the first is the height of the curve; the following five are
the curve's a-invariants, and the final integer is the curve's rank.
- ``problems_filename`` -- String: the file name to which problem
curves will be written. These are curves for which rank could not
be computed. Write format is the same as above, except rank is
omitted at the end.
- ``return_data`` -- (Default True): If set to False, the data
is not returned at the end of computation; only written to file.
- ``use_database`` -- (Default True): If set to False, the
Cremona database is not used to look up curve ranks.
- ``use_only_mwrank`` -- (Default False): If set to True, will not
try to use analytic methods to compute rank before consulting the
Cremona database
- ``print_timing`` -- (Default True): If set to False, wall time
of total computation will not be printed.
OUTPUT:
- Writes data to file. Each line of the written file consists of seven
tab separated entries of the form
H, a1, a2, a3, a4, a6, d
H: The curve's height
a1,...,a6: The curve's a-invariants
d: The computed datum for that curve
- (only if return_data==True) A list consisting of two lists:
The first is a list of triples of the form
(H, (a1,a2,a3,a4,a6), d)
where the entries are as above.
The second is a list of curve for which the datum could not be provably
computed; each entry of this list is just a pair consisting of height
and a-invariants.
EXAMPLES::
sage: from sage.schemes.elliptic_curves.curve_enumerator import *
sage: C = CurveEnumerator(family="short_weierstrass")
sage: L = C.coefficients_over_height_range(0,4)
sage: R = C.rank(L,return_data=True,print_timing=False)
sage: R[1]
[]
sage: for r in R[0]: print(r)
....:
(1, [0, 0, 0, -1, 0], 0)
(1, [0, 0, 0, 1, 0], 0)
(1, [0, 0, 0, 0, -1], 0)
(1, [0, 0, 0, 0, 1], 0)
(1, [0, 0, 0, -1, -1], 0)
(1, [0, 0, 0, -1, 1], 1)
(1, [0, 0, 0, 1, -1], 1)
(1, [0, 0, 0, 1, 1], 1)
(4, [0, 0, 0, -1, -2], 1)
(4, [0, 0, 0, -1, 2], 0)
(4, [0, 0, 0, 0, -2], 1)
(4, [0, 0, 0, 0, 2], 1)
(4, [0, 0, 0, 1, -2], 0)
(4, [0, 0, 0, 1, 2], 0)
"""
if print_timing:
t = time.time()
out_file = open(output_filename,"w")
prob_file = open(problems_filename,"w")
if return_data:
output = []
problems = []
for C in curves:
# Attempt to compute rank and write curve+rank to file
try:
E = EllipticCurve(C[1])
d = E.rank(use_database=use_database,only_use_mwrank=use_only_mwrank)
out_file.write(str(C[0])+"\t")
for a in C[1]:
out_file.write(str(a)+"\t")
out_file.write(str(d)+"\n")
out_file.flush()
if return_data:
output.append((C[0],C[1],d))
# Write to problem file if fail
except:
prob_file.write(str(C[0])+"\t")
for a in C[1]:
prob_file.write(str(a)+"\t")
prob_file.write("\n")
prob_file.flush()
if return_data:
problems.append(C)
out_file.close()
prob_file.close()
if print_timing:
print(time.time()-t)
if return_data:
return output,problems
