def __init__(self, filename, verbose=VLog.DEBUG):
if __debug__:
assert filename is None or is_str(filename), filename
logger.level = verbose
import dig_inv, dig_refine, dig_arrays, dig_polynomials
for f in [dig_miscs, dig_inv, dig_refine, dig_arrays, dig_polynomials]:
f.logger.set_level(logger.level)
from platform import node, system, release, machine
margs = [
get_cur_time(time_only=False),
version(), ' '.join([node(),
system(),
release(),
machine()])
]
logger.info("DIG (Dynamic Invariant Generator)\n"
"{}, {}, {}".format(*margs))
if filename is not None:
self._setup(filename)
else:
logger.warn('No filename given, manual setup')
def compute_atkin_lehner(N, k, i):
filename = filenames.ambient(N, k, i)
if not os.path.exists(filename):
print "Ambient (%s,%s,%s) space not computed."%(N,k,i)
return
#compute_ambient_space(N, k, i)
print "computing atkin-lehner for (%s,%s,%s)"%(N,k,i)
m = filenames.number_of_known_factors(N, k, i)
M = load_ambient_space(N, k, i)
for d in range(m):
atkin_lehner_file = filenames.factor_atkin_lehner(N, k, i, d, False)
if os.path.exists(atkin_lehner_file):
print "skipping computing atkin_lehner for (%s,%s,%s,%s) since it already exists"%(N,k,i,d)
# already done
continue
# compute atkin_lehner
print "computing atkin_lehner for (%s,%s,%s,%s)"%(N,k,i,d)
t = cputime()
A = load_factor(N, k, i, d, M)
al = ' '.join(['+' if a > 0 else '-' for a in atkin_lehner_signs(A)])
print al
open(atkin_lehner_file, 'w').write(al)
tm = cputime(t)
meta = {'cputime':tm, 'version':version()}
save(meta, filenames.meta(atkin_lehner_file))
def compute_ambient_space(N, k, i):
if i == 'all':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn:
compute_ambient_space(N,k,j)
return
if i == 'quadratic':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn and g[0].order()==2:
compute_ambient_space(N,k,j)
return
filename = filenames.ambient(N, k, i)
if os.path.exists(filename):
return
eps = character(N, i)
t = cputime()
M = ModularSymbols(eps, weight=k, sign=1)
tm = cputime(t)
save(M, filename)
meta = {'cputime':tm, 'dim':M.dimension(), 'M':str(M), 'version':version()}
save(meta, filenames.meta(filename))
def compute_aplists(N, k, i, *args):
if i == 'all':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn:
compute_aplists(N,k,j,*args)
return
if i == 'quadratic':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn and g[0].order()==2:
compute_aplists(N,k,j,*args)
return
if len(args) == 0:
args = (100, )
filename = filenames.ambient(N, k, i)
if not os.path.exists(filename):
print "Ambient (%s,%s,%s) space not computed."%(N,k,i)
return
#compute_ambient_space(N, k, i)
print "computing aplists for (%s,%s,%s)"%(N,k,i)
m = filenames.number_of_known_factors(N, k, i)
if m == 0:
# nothing to do
return
M = load_ambient_space(N, k, i)
for d in range(m):
aplist_file = filenames.factor_aplist(N, k, i, d, False, *args)
if os.path.exists(aplist_file):
print "skipping computing aplist(%s) for (%s,%s,%s,%s) since it already exists"%(args, N,k,i,d)
# already done
continue
# compute aplist
print "computing aplist(%s) for (%s,%s,%s,%s)"%(args, N,k,i,d)
t = cputime()
A = load_factor(N, k, i, d, M)
aplist, _ = A.compact_system_of_eigenvalues(prime_range(*args), 'a')
print aplist, aplist_file
save(aplist, aplist_file)
tm = cputime(t)
meta = {'cputime':tm, 'version':version()}
save(meta, filenames.meta(aplist_file))
def render_web_newform(level, weight, character, label, **kwds):
r"""
Renders the webpage for one elliptic modular form.
"""
citation = ['Sage:' + version()]
info = set_info_for_web_newform(level, weight, character, label, **kwds)
emf_logger.debug("info={0}".format(info.keys()))
err = info.get('error', '')
## Check if we want to download either file of the function or Fourier coefficients
if 'download' in info and 'error' not in info:
return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
return render_template("emf_web_newform.html", **info)
def render_web_newform(level, weight, character, label, **kwds):
r"""
Renders the webpage for one elliptic modular form.
"""
citation = ['Sage:' + version()]
info = set_info_for_web_newform(level, weight, character, label, **kwds)
emf_logger.debug("info={0}".format(info.keys()))
err = info.get('error', '')
## Check if we want to download either file of the function or Fourier coefficients
if 'download' in info and 'error' not in info:
return send_file(info['tempfile'], as_attachment=True, attachment_filename=info['filename'])
return render_template("emf_web_newform.html", **info)
def compute_decompositions(N, k, i):
if i == 'all':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn:
compute_decompositions(N,k,j)
return
if i == 'quadratic':
G = DirichletGroup(N).galois_orbits()
sgn = (-1)**k
for j, g in enumerate(G):
if g[0](-1) == sgn and g[0].order()==2:
compute_decompositions(N,k,j)
return
filename = filenames.ambient(N, k, i)
if not os.path.exists(filename):
print "Ambient space (%s,%s,%s) not computed."%(N,k,i)
return
#compute_ambient_space(N, k, i)
if not os.path.exists(filename):
return
eps = DirichletGroup(N).galois_orbits()[i][0]
if os.path.exists(filenames.factor(N, k, i, 0, makedir=False)):
return
t = cputime()
M = load_ambient_space(N, k, i)
D = M.cuspidal_subspace().new_subspace().decomposition()
for d in range(len(D)):
f = filenames.factor_basis_matrix(N, k, i, d)
if os.path.exists(f):
continue
A = D[d]
B = A.free_module().basis_matrix()
Bd = A.dual_free_module().basis_matrix()
v = A.dual_eigenvector(names='a', lift=False) # vector over number field
nz = A._eigen_nonzero()
save(B, filenames.factor_basis_matrix(N, k, i, d))
save(Bd, filenames.factor_dual_basis_matrix(N, k, i, d))
save(v, filenames.factor_dual_eigenvector(N, k, i, d))
save(nz, filenames.factor_eigen_nonzero(N, k, i, d))
tm = cputime(t)
meta = {'cputime':tm, 'number':len(D), 'version':version()}
save(meta, filenames.decomp_meta(N, k, i))
def run_criterion(result_table,iterator,congruence_type,algorithm="default",verbose=False):
"""
The iterator should spit out things of the form (torsion_order,degree,t1n,t1mod,t2q)
"""
insert_point=result_table.insert()
old_torsion=None
for torsion_order,degree,t1n,t1mod,t2q in iterator:
if not old_torsion==torsion_order:
old_torsion=torsion_order
C=KamiennyCriterion(torsion_order,congruence_type=congruence_type,algorithm=algorithm,verbose=verbose)
verified,message=C.verify_criterion(degree,n=t1n,p=t1mod,q=t2q,verbose=verbose)
insert_point.execute(torsion_order=int(torsion_order), extension_degree=int(degree),
t1n=int(t1n), t1mod=int(t1mod), t2q=int(t2q),
congruence_type=int(congruence_type), result=verified,
kamienny_version=Kamienny_Version,sage_version=version())
def run_criterion(result_table,iterator,congruence_type,algorithm="default",verbose=False):
"""
The iterator should spit out things of the form (torsion_order,degree,t1n,t1mod,t2q)
"""
insert_point=result_table.insert()
old_torsion=None
for torsion_order,degree,t1n,t1mod,t2q in iterator:
if not old_torsion==torsion_order:
old_torsion=torsion_order
C=KamiennyCriterion(torsion_order,congruence_type=congruence_type,algorithm=algorithm,verbose=verbose)
verified,message=C.verify_criterion(degree,n=t1n,p=t1mod,q=t2q,verbose=verbose)
insert_point.execute(torsion_order=int(torsion_order), extension_degree=int(degree),
t1n=int(t1n), t1mod=int(t1mod), t2q=int(t2q),
congruence_type=int(congruence_type), result=verified,
kamienny_version=Kamienny_Version,sage_version=version())
def __init__(self,filename,verbose=VLog.DEBUG):
if __debug__:
assert filename is None or is_str(filename), filename
logger.level = verbose
import dig_inv, refine, dig_arrays, dig_polynomials
for f in [dig_inv, refine, dig_arrays, dig_polynomials, dig_miscs]:
f.logger.set_level(logger.level)
from platform import node, system, release, machine
margs = [get_cur_time(time_only=False),version(),
' '.join([node(),system(),release(),machine()])]
logger.info("{}, {}, {}".format(*margs))
if filename is not None:
self._setup(filename)
else:
logger.warn('No filename given, manual setup')
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
modules = []
try:
from sage import all as sage
from mathics.optional import calculus, numerical_optimization
modules += [calculus, numerical_optimization]
sage_version = sage.version()
except ImportError:
# silently ignore when Sage cannot be imported
sage_version = None
from mathics.builtin import add_builtins, builtins_by_module, is_builtin
from mathics.builtin.base import Builtin
optional_builtins = []
optional_builtins_by_module = {}
for module in modules:
optional_builtins_by_module[module.__name__] = []
vars = dir(module)
for name in vars:
var = getattr(module, name)
def verify_criterion(self, d, t=None, n=5, p=65521, q=3, v=None, use_rand_vec=False, verbose=False):
"""
Attempt to verify the criterion at p using the input t. If t is not
given compute it using n, p and q
INPUT:
- `t` -- hecke operator (optional default=None)
- `n` -- integer (optional default=5), used in computing t1
- `p` -- prime (optional default=46337), used in computing t1
- `q` -- prime (optional default=3), used in computing t2
- `verbose` -- bool (default: True); if true, print to
stdout as the computation is performed.
OUTPUT:
- bool -- True if criterion satisfied; otherwise, False
- string -- message about what happened or went wrong
EXAMPLES:
We can't get p=29 to work no matter what I try, which nicely illustrates
the various ways the criterion can fail::
sage: from mdsage import *
sage: C = KamiennyCriterion(29)
sage: C.verify_criterion(4,n=5)
dependency dimension to large to search through
(False,
'There is a dependency of weigt 2 in dependencies(3,1)',
[Vector space of degree 4 and dimension 0 over Finite Field of size 2
Basis matrix:
[], Vector space of degree 16 and dimension 8 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0]
[0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0], Vector space of degree 28 and dimension 19 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
[0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]])
With p=43 the criterion is satisfied for d=4, thus proving that 43 is
not the order of a torsion point on any elliptic curve over
a quartic field::
sage: C = KamiennyCriterion(43); C
Kamienny's Criterion for p=43
sage: C.verify_criterion(4)
(True,
'All conditions are satified for Gamma1 d=4 p=43. Using n=5, modp=65521, q=3 in Kamienny Version 1.5 and SageMath version ...',
[Vector space of degree 4 and dimension 0 over Finite Field of size 2
Basis matrix:
[], Vector space of degree 23 and dimension 2 over Finite Field of size 2
Basis matrix:
[1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0]
[0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0], Vector space of degree 42 and dimension 11 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1]
[0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0]])
"""
if self.verbose: tm = cputime(); mem = get_memory_usage(); print "verif start"
if self.p < (1 + 2 ** (d / 2)) ** 2 and self.verbose:
print "WARNING: p must be at least (1+2^(d/2))^2 for the criterion to work."
if t == None:
t = self.t(n, p, q)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "t"
if v==None:
if use_rand_vec:
v=self.v
else:
v=t.parent()(1)
if self.congruence_type==0:
verified,message,dependencies=self.verify_gamma0(d,t,v)
else:
verified,message,dependencies=self.verify_gamma1(d,t,v)
if self.verbose: print "time and mem", cputime(tm), get_memory_usage(mem), "total verif time"
if not verified:
return verified,message,dependencies
return True, "All conditions are satified for Gamma%s d=%s p=%s. Using n=%s, modp=%s, q=%s in Kamienny Version %s and %s" % (self.congruence_type,d, self.p, n, p, q, Kamienny_Version, version()),dependencies
def verify_criterion(self, d, t=None, n=5, p=65521, q=3, v=None, use_rand_vec=False, verbose=False):
"""
Attempt to verify the criterion at p using the input t. If t is not
given compute it using n, p and q
INPUT:
- `t` -- hecke operator (optional default=None)
- `n` -- integer (optional default=5), used in computing t1
- `p` -- prime (optional default=46337), used in computing t1
- `q` -- prime (optional default=3), used in computing t2
- `verbose` -- bool (default: True); if true, print to
stdout as the computation is performed.
OUTPUT:
- bool -- True if criterion satisfied; otherwise, False
- string -- message about what happened or went wrong
EXAMPLES:
We can't get p=29 to work no matter what I try, which nicely illustrates
the various ways the criterion can fail::
sage: from mdsage import *
sage: C = KamiennyCriterion(29)
sage: C.verify_criterion(4,n=5)
dependency dimension to large to search through
(False,
'There is a dependency of weigt 2 in dependencies(3,1)',
[Vector space of degree 4 and dimension 0 over Finite Field of size 2
Basis matrix:
[], Vector space of degree 16 and dimension 8 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0]
[0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0], Vector space of degree 28 and dimension 19 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
[0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0]])
With p=43 the criterion is satisfied for d=4, thus proving that 43 is
not the order of a torsion point on any elliptic curve over
a quartic field::
sage: C = KamiennyCriterion(43); C
Kamienny's Criterion for p=43
sage: C.verify_criterion(4)
(True,
'All conditions are satified for Gamma1 d=4 p=43. Using n=5, modp=65521, q=3 in Kamienny Version 1.5 and SageMath version ...',
[Vector space of degree 4 and dimension 0 over Finite Field of size 2
Basis matrix:
[], Vector space of degree 23 and dimension 2 over Finite Field of size 2
Basis matrix:
[1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0]
[0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0], Vector space of degree 42 and dimension 11 over Finite Field of size 2
Basis matrix:
[1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1]
[0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0]
[0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0]
[0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0]])
"""
if self.verbose: tm = cputime(); mem = get_memory_usage(); print("verif start")
if self.p < (1 + 2 ** (d / 2)) ** 2 and self.verbose:
print("WARNING: p must be at least (1+2^(d/2))^2 for the criterion to work.")
if t == None:
t = self.t(n, p, q)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "t")
if v==None:
if use_rand_vec:
v=self.v
else:
v=t.parent()(1)
if self.congruence_type==0:
verified,message,dependencies=self.verify_gamma0(d,t,v)
else:
verified,message,dependencies=self.verify_gamma1(d,t,v)
if self.verbose: print("time and mem", cputime(tm), get_memory_usage(mem), "total verif time")
if not verified:
return verified,message,dependencies
return True, "All conditions are satified for Gamma%s d=%s p=%s. Using n=%s, modp=%s, q=%s in Kamienny Version %s and %s" % (self.congruence_type,d, self.p, n, p, q, Kamienny_Version, version()),dependencies