def build(name, data_tgz, largest_conductor=0, mini=False, decompress=True):
"""
Build the CremonaDatabase with given name from scratch
using the data_tgz tarball.
... note::
For data up to level 170000, this function takes about 5
minutes on a 2.9Ghz Nehalem Core i3. The resulting database
occupies 216MB disk space.
To create the large Cremona database from Cremona's data_tgz tarball,
run the following command::
sage: d = sage.databases.cremona.build('cremona','ecdata.tgz') # not tested
"""
t = name.replace(' ', '_')
if os.path.exists("%s/cremona/%s.db" % (SAGE_DATA, t)):
raise RuntimeError("Please (re)move %s/cremona/%s.db" %
(SAGE_DATA, t) + " before rebuilding database.")
if not os.path.exists(data_tgz):
raise IOError, "The data file is not at %s" % data_tgz
t = walltime()
if decompress:
cmd = "tar zxvf %s" % data_tgz
n = os.system(cmd)
if n:
raise RuntimeError, "Error extracting tarball."
if mini:
c = MiniCremonaDatabase(name, False, True)
else:
c = LargeCremonaDatabase(name, False, True)
c._init_from_ftpdata('ecdata', largest_conductor)
print "Total time: ", walltime(t)
def build(name, data_tgz, largest_conductor=0, mini=False, decompress=True):
"""
Build the CremonaDatabase with given name from scratch
using the data_tgz tarball.
... note::
For data up to level 170000, this function takes about 5
minutes on a 2.9Ghz Nehalem Core i3. The resulting database
occupies 216MB disk space.
To create the large Cremona database from Cremona's data_tgz tarball,
run the following command::
sage: d = sage.databases.cremona.build('cremona','ecdata.tgz') # not tested
"""
t = name.replace(' ','_')
if os.path.exists("%s/cremona/%s.db"%(SAGE_DATA, t)):
raise RuntimeError("Please (re)move %s/cremona/%s.db"%(SAGE_DATA, t)
+ " before rebuilding database.")
if not os.path.exists(data_tgz):
raise IOError, "The data file is not at %s"%data_tgz
t = walltime()
if decompress:
cmd = "tar zxvf %s"%data_tgz
n = os.system(cmd)
if n:
raise RuntimeError, "Error extracting tarball."
if mini:
c = MiniCremonaDatabase(name,False,True)
else:
c = LargeCremonaDatabase(name,False,True)
c._init_from_ftpdata('ecdata', largest_conductor)
print "Total time: ", walltime(t)
def manyvars(s, num=70000, inlen=1, step=2000):
"""
Test that > 65,000 variable names works in each system.
"""
print "Testing -- %s"%s
t = '"%s"'%('9'*int(inlen))
try:
t = cputime()
w = walltime()
v = []
for i in range(num):
if i%step==0:
sys.stdout.write('%s '%i)
sys.stdout.flush()
v.append(s(t))
print '\nsuccess -- time = cpu: %s, wall: %s'%(cputime(t), walltime(w))
except Exception:
print "%s -- failed!"%s
def manyvars(s, num=70000, inlen=1, step=2000):
"""
Test that > 65,000 variable names works in each system.
"""
print "Testing -- %s"%s
t = '"%s"'%('9'*int(inlen))
try:
t = cputime()
w = walltime()
v = []
for i in range(num):
if i%step==0:
sys.stdout.write('%s '%i)
sys.stdout.flush()
v.append(s(t))
print '\nsuccess -- time = cpu: %s, wall: %s'%(cputime(t), walltime(w))
except:
print "%s -- failed!"%s
def test_gens_cyclotomic(p, n):
'''
Test routine for `find_gens_cyclotomic`. Constructs two random
extensions of F_p of degree n, then calls find_gens_cyclotomic and
tests that the returned elements have the same minimal polynomial
over F_p, and that the polynomial has degree n.
'''
c, w = cputime(), walltime()
k1 = GF(p**n, 'z1', modulus='random')
k2 = GF(p**n, 'z2', modulus='random')
print "Field creation: CPU %s, Wall %s" % (cputime(c), walltime(w))
c, w = cputime(), walltime()
a, b = find_gens_cyclotomic(k1, k2)
print "Rains' algorithm: CPU %s, Wall %s" % (cputime(c), walltime(w))
P = a.minpoly()
assert(P.degree() == n)
assert(P(b) == 0)
def test_gens(p, n, use_lucas=True, verbose=False):
'''
Test routine for `find_gens`. Constructs two random
extensions of F_p of degree n, then calls find_gens and
tests that the returned elements have the same minimal polynomial
over F_p, and that the polynomial has degree n.
'''
c, w = cputime(), walltime()
k1 = GF(p**n, 'z1', modulus='random')
k2 = GF(p**n, 'z2', modulus='random')
print "Field creation: CPU %s, Wall %s" % (cputime(c), walltime(w))
c, w = cputime(), walltime()
a, b = find_gens(k1, k2, use_lucas=use_lucas, verbose=verbose)
print "Rains' algorithm: CPU %s, Wall %s" % (cputime(c), walltime(w))
P = a.minpoly()
assert (P.degree() == n)
assert (P(b) == 0)
def __init__(self, input, starttime=None, failure=""):
r"""
See the class documentation for description of the inputs.
EXAMPLES::
sage: from sage.parallel.use_fork import WorkerData
sage: W = WorkerData(42)
"""
self.input = input
self.starttime = starttime or walltime()
self.failure = failure
def __init__(self, input, starttime=None, failure=""):
r"""
See the class documentation for description of the inputs.
EXAMPLES::
sage: from sage.parallel.use_fork import WorkerData
sage: W = WorkerData(42)
"""
self.input = input
self.starttime = starttime or walltime()
self.failure = failure
def start(self):
"""
Start the timer.
EXAMPLES::
sage: from sage.doctest.util import Timer
sage: Timer().start()
{'cputime': ..., 'walltime': ...}
"""
self.cputime = cputime()
self.walltime = walltime()
return self
def start(self):
"""
Start the timer.
EXAMPLES::
sage: from sage.doctest.util import Timer
sage: Timer().start()
{'cputime': ..., 'walltime': ...}
"""
self.cputime = cputime()
self.walltime = walltime()
return self
def stop(self):
"""
Stops the timer, recording the time that has passed since it
was started.
EXAMPLES::
sage: from sage.doctest.util import Timer
sage: import time
sage: timer = Timer().start()
sage: time.sleep(0.5)
sage: timer.stop()
{'cputime': ..., 'walltime': ...}
"""
self.cputime = cputime(self.cputime)
self.walltime = walltime(self.walltime)
return self
def stop(self):
"""
Stops the timer, recording the time that has passed since it
was started.
EXAMPLES::
sage: from sage.doctest.util import Timer
sage: import time
sage: timer = Timer().start()
sage: time.sleep(0.5)
sage: timer.stop()
{'cputime': ..., 'walltime': ...}
"""
self.cputime = cputime(self.cputime)
self.walltime = walltime(self.walltime)
return self
def darmon_point(P, E, beta, prec, ramification_at_infinity = None, input_data = None, magma = None, working_prec = None, **kwargs):
r'''
EXAMPLES:
We first need to import the module::
sage: from darmonpoints.darmonpoints import darmon_point
A first example (Stark--Heegner point)::
sage: from darmonpoints.darmonpoints import darmon_point
sage: darmon_point(7,EllipticCurve('35a1'),41,20, cohomological=False, use_magma=False, use_ps_dists = True)
Starting computation of the Darmon point
...
(-70*alpha + 449 : 2100*alpha - 13444 : 1)
A quaternionic (Greenberg) point::
sage: darmon_point(13,EllipticCurve('78a1'),5,20) # long time # optional - magma
A Darmon point over a cubic (1,1) field::
sage: F.<r> = NumberField(x^3 - x^2 - x + 2)
sage: E = EllipticCurve([-r -1, -r, -r - 1,-r - 1, 0])
sage: N = E.conductor()
sage: P = F.ideal(r^2 - 2*r - 1)
sage: beta = -3*r^2 + 9*r - 6
sage: darmon_point(P,E,beta,20) # long time # optional - magma
'''
# global G, Coh, phiE, Phi, dK, J, J1, cycleGn, nn, Jlist
config = ConfigParser.ConfigParser()
config.read('config.ini')
param_dict = config_section_map(config, 'General')
param_dict.update(config_section_map(config, 'DarmonPoint'))
param_dict.update(kwargs)
param = Bunch(**param_dict)
# Get general parameters
outfile = param.get('outfile')
use_ps_dists = param.get('use_ps_dists',False)
use_shapiro = param.get('use_shapiro',True)
use_sage_db = param.get('use_sage_db',False)
magma_seed = param.get('magma_seed',1515316)
parallelize = param.get('parallelize',False)
Up_method = param.get('up_method','naive')
use_magma = param.get('use_magma',True)
progress_bar = param.get('progress_bar',True)
sign_at_infinity = param.get('sign_at_infinity',ZZ(1))
# Get darmon_point specific parameters
idx_orientation = param.get('idx_orientation')
idx_embedding = param.get('idx_embedding',0)
algorithm = param.get('algorithm')
quaternionic = param.get('quaternionic')
cohomological = param.get('cohomological',True)
if Up_method == "bigmatrix" and use_shapiro == True:
import warnings
warnings.warn('Use of "bigmatrix" for Up iteration is incompatible with Shapiro Lemma trick. Using "naive" method for Up.')
Up_method = 'naive'
if working_prec is None:
working_prec = max([2 * prec + 10, 30])
if use_magma:
page_path = os.path.dirname(__file__) + '/KleinianGroups-1.0/klngpspec'
if magma is None:
from sage.interfaces.magma import Magma
magma = Magma()
quit_when_done = True
else:
quit_when_done = False
magma.attach_spec(page_path)
else:
quit_when_done = False
sys.setrecursionlimit(10**6)
F = E.base_ring()
beta = F(beta)
DB,Np,Ncartan = get_heegner_params(P,E,beta)
if quaternionic is None:
quaternionic = ( DB != 1 )
if cohomological is None:
cohomological = quaternionic
if quaternionic and not cohomological:
raise ValueError("Need cohomological algorithm when dealing with quaternions")
if use_ps_dists is None:
use_ps_dists = False if cohomological else True
try:
p = ZZ(P)
except TypeError:
p = ZZ(P.norm())
if not p.is_prime():
raise ValueError,'P (= %s) should be a prime, of inertia degree 1'%P
if F == QQ:
dK = ZZ(beta)
extra_conductor_sq = dK/fundamental_discriminant(dK)
assert ZZ(extra_conductor_sq).is_square()
extra_conductor = extra_conductor_sq.sqrt()
dK = dK / extra_conductor_sq
assert dK == fundamental_discriminant(dK)
if dK % 4 == 0:
dK = ZZ(dK/4)
beta = dK
else:
dK = beta
# Compute the completion of K at p
x = QQ['x'].gen()
K = F.extension(x*x - dK,names = 'alpha')
if F == QQ:
dK = K.discriminant()
else:
dK = K.relative_discriminant()
hK = K.class_number()
sgninfty = 'plus' if sign_at_infinity == 1 else 'minus'
if hasattr(E,'cremona_label'):
Ename = E.cremona_label()
elif hasattr(E,'ainvs'):
Ename = E.ainvs()
else:
Ename = 'unknown'
fname = 'moments_%s_%s_%s_%s.sobj'%(P,Ename,sgninfty,prec)
if use_sage_db:
print("Moments will be stored in database as %s"%(fname))
if outfile == 'log':
outfile = '%s_%s_%s_%s_%s_%s.log'%(P,Ename,dK,sgninfty,prec,datetime.datetime.now().strftime("%Y%m%d-%H%M%S"))
outfile = outfile.replace('/','div')
outfile = '/tmp/darmonpoint_' + outfile
fwrite("Starting computation of the Darmon point",outfile)
fwrite('D_B = %s %s'%(DB,factor(DB)),outfile)
fwrite('Np = %s'%Np,outfile)
if Ncartan is not None:
fwrite('Ncartan = %s'%Ncartan,outfile)
fwrite('dK = %s (class number = %s)'%(dK,hK),outfile)
fwrite('Calculation with p = %s and prec = %s'%(P,prec),outfile)
fwrite('Elliptic curve %s: %s'%(Ename,E),outfile)
if outfile is not None:
print("Partial results will be saved in %s"%outfile)
if input_data is None:
if cohomological:
# Define the S-arithmetic group
if F != QQ and ramification_at_infinity is None:
if F.signature()[0] > 1:
if F.signature()[1] == 1:
ramification_at_infinity = F.real_places(prec = Infinity) # Totally 'definite'
else:
raise ValueError,'Please specify the ramification at infinity'
elif F.signature()[0] == 1:
if len(F.ideal(DB).factor()) % 2 == 0:
ramification_at_infinity = [] # Split at infinity
else:
ramification_at_infinity = F.real_places(prec = Infinity) # Ramified at infinity
else:
ramification_at_infinity = None
if F == QQ:
abtuple = QuaternionAlgebra(DB).invariants()
else:
abtuple = quaternion_algebra_invariants_from_ramification(F, DB, ramification_at_infinity)
G = BigArithGroup(P,abtuple,Np,base = F,outfile = outfile,seed = magma_seed,use_sage_db = use_sage_db,magma = magma, use_shapiro = use_shapiro, nscartan=Ncartan)
# Define the cycle ( in H_1(G,Div^0 Hp) )
Coh = ArithCoh(G)
while True:
try:
cycleGn,nn,ell = construct_homology_cycle(G,beta,working_prec,lambda q: Coh.hecke_matrix(q).minpoly(), outfile = outfile, elliptic_curve = E)
break
except PrecisionError:
working_prec *= 2
verbose('Encountered precision error, trying with higher precision (= %s)'%working_prec)
except ValueError:
fwrite('ValueError occurred when constructing homology cycle. Returning the S-arithmetic group.', outfile)
if quit_when_done:
magma.quit()
return G
except AssertionError as e:
fwrite('Assertion occurred when constructing homology cycle. Returning the S-arithmetic group.', outfile)
fwrite('%s'%str(e), outfile)
if quit_when_done:
magma.quit()
return G
eisenstein_constant = -ZZ(E.reduction(ell).count_points())
fwrite('r = %s, so a_r(E) - r - 1 = %s'%(ell,eisenstein_constant), outfile)
fwrite('exponent = %s'%nn, outfile)
phiE = Coh.get_cocycle_from_elliptic_curve(E, sign = sign_at_infinity)
if hasattr(E,'ap'):
sign_ap = E.ap(P)
else:
try:
sign_ap = ZZ(P.norm() + 1 - E.reduction(P).count_points())
except ValueError:
sign_ap = ZZ(P.norm() + 1 - Curve(E).change_ring(P.residue_field()).count_points(1)[0])
Phi = get_overconvergent_class_quaternionic(P,phiE,G,prec,sign_at_infinity,sign_ap,use_ps_dists = use_ps_dists,use_sage_db = use_sage_db,parallelize = parallelize,method = Up_method, progress_bar = progress_bar,Ename = Ename)
# Integration with moments
tot_time = walltime()
J = integrate_H1(G,cycleGn,Phi,1,method = 'moments',prec = working_prec,parallelize = parallelize,twist = True,progress_bar = progress_bar)
verbose('integration tot_time = %s'%walltime(tot_time))
if use_sage_db:
G.save_to_db()
else: # not cohomological
nn = 1
eisenstein_constant = 1
if algorithm is None:
if Np == 1:
algorithm = 'darmon_pollack'
else:
algorithm = 'guitart_masdeu'
w = K.maximal_order().ring_generators()[0]
r0,r1 = w.coordinates_in_terms_of_powers()(K.gen())
QQp = Qp(p,working_prec)
Cp = QQp.extension(w.minpoly().change_ring(QQp),names = 'g')
v0 = K.hom([r0 + r1 * Cp.gen()])
# Optimal embeddings of level one
fwrite("Computing optimal embeddings of level one...", outfile)
Wlist = find_optimal_embeddings(K,use_magma = use_magma, extra_conductor = extra_conductor)
fwrite("Found %s such embeddings."%len(Wlist), outfile)
if idx_embedding is not None:
if idx_embedding >= len(Wlist):
fwrite('There are not enough embeddings. Taking the index modulo %s'%len(Wlist), outfile)
idx_embedding = idx_embedding % len(Wlist)
fwrite('Taking only embedding number %s'%(idx_embedding), outfile)
Wlist = [Wlist[idx_embedding]]
# Find the orientations
orients = K.maximal_order().ring_generators()[0].minpoly().roots(Zmod(Np),multiplicities = False)
fwrite("Possible orientations: %s"%orients, outfile)
if len(Wlist) == 1 or idx_orientation == -1:
fwrite("Using all orientations, since hK = 1", outfile)
chosen_orientation = None
else:
fwrite("Using orientation = %s"%orients[idx_orientation], outfile)
chosen_orientation = orients[idx_orientation]
emblist = []
for i,W in enumerate(Wlist):
tau, gtau,sign,limits = find_tau0_and_gtau(v0,Np,W,algorithm = algorithm,orientation = chosen_orientation,extra_conductor = extra_conductor)
fwrite('n_evals = %s'%sum((num_evals(t1,t2) for t1,t2 in limits)), outfile)
emblist.append((tau,gtau,sign,limits))
# Get the cohomology class from E
Phi = get_overconvergent_class_matrices(P,E,prec,sign_at_infinity,use_ps_dists = use_ps_dists,use_sage_db = use_sage_db,parallelize = parallelize,progress_bar = progress_bar)
J = 1
Jlist = []
for i,emb in enumerate(emblist):
fwrite("Computing %s-th period, attached to the embedding: %s"%(i,Wlist[i].list()), outfile)
tau, gtau,sign,limits = emb
n_evals = sum((num_evals(t1,t2) for t1,t2 in limits))
fwrite("Computing one period...(total of %s evaluations)"%n_evals, outfile)
newJ = prod((double_integral_zero_infty(Phi,t1,t2) for t1,t2 in limits))**ZZ(sign)
Jlist.append(newJ)
J *= newJ
else: # input_data is not None
Phi,J = input_data[1:3]
fwrite('Integral done. Now trying to recognize the point', outfile)
fwrite('J_psi = %s'%J,outfile)
fwrite('g belongs to %s'%J.parent(),outfile)
#Try to recognize a generator
if quaternionic:
local_embedding = G.base_ring_local_embedding(working_prec)
twopowlist = [4, 3, 2, 1, QQ(1)/2, QQ(3)/2, QQ(1)/3, QQ(2)/3, QQ(1)/4, QQ(3)/4, QQ(5)/2, QQ(4)/3]
else:
local_embedding = Qp(p,working_prec)
twopowlist = [4, 3, 2, 1, QQ(1)/2, QQ(3)/2, QQ(1)/3, QQ(2)/3, QQ(1)/4, QQ(3)/4, QQ(5)/2, QQ(4)/3]
known_multiple = QQ(nn * eisenstein_constant) # It seems that we are not getting it with present algorithm.
while known_multiple % p == 0:
known_multiple = ZZ(known_multiple / p)
candidate,twopow,J1 = recognize_J(E,J,K,local_embedding = local_embedding,known_multiple = known_multiple,twopowlist = twopowlist,prec = prec, outfile = outfile)
if candidate is not None:
HCF = K.hilbert_class_field(names = 'r1') if hK > 1 else K
if hK == 1:
try:
verbose('candidate = %s'%candidate)
Ptsmall = E.change_ring(HCF)(candidate)
fwrite('twopow = %s'%twopow,outfile)
fwrite('Computed point: %s * %s * %s'%(twopow,known_multiple,Ptsmall),outfile)
fwrite('(first factor is not understood, second factor is)',outfile)
fwrite('(r satisfies %s = 0)'%(Ptsmall[0].parent().gen().minpoly()),outfile)
fwrite('================================================',outfile)
if quit_when_done:
magma.quit()
return Ptsmall
except (TypeError,ValueError):
verbose("Could not recognize the point.")
else:
verbose('candidate = %s'%candidate)
fwrite('twopow = %s'%twopow,outfile)
fwrite('Computed point: %s * %s * (x,y)'%(twopow,known_multiple),outfile)
fwrite('(first factor is not understood, second factor is)',outfile)
try:
pols = [HCF(c).relative_minpoly() for c in candidate[:2]]
except AttributeError:
pols = [HCF(c).minpoly() for c in candidate[:2]]
fwrite('Where x satisfies %s'%pols[0],outfile)
fwrite('and y satisfies %s'%pols[1],outfile)
fwrite('================================================',outfile)
if quit_when_done:
magma.quit()
return candidate
else:
fwrite('================================================',outfile)
if quit_when_done:
magma.quit()
return []
def darmon_point(P,
E,
beta,
prec,
ramification_at_infinity=None,
input_data=None,
magma=None,
working_prec=None,
recognize_point=True,
**kwargs):
r'''
EXAMPLES:
We first need to import the module::
sage: from darmonpoints.darmonpoints import darmon_point
A first example (Stark--Heegner point)::
sage: from darmonpoints.darmonpoints import darmon_point
sage: darmon_point(7,EllipticCurve('35a1'),41,20, cohomological=False, use_magma=False, use_ps_dists = True)
Starting computation of the Darmon point
...
(-70*alpha + 449 : 2100*alpha - 13444 : 1)
A quaternionic (Greenberg) point::
sage: darmon_point(13,EllipticCurve('78a1'),5,20) # long time # optional - magma
A Darmon point over a cubic (1,1) field::
sage: F.<r> = NumberField(x^3 - x^2 - x + 2)
sage: E = EllipticCurve([-r -1, -r, -r - 1,-r - 1, 0])
sage: N = E.conductor()
sage: P = F.ideal(r^2 - 2*r - 1)
sage: beta = -3*r^2 + 9*r - 6
sage: darmon_point(P,E,beta,20) # long time # optional - magma
'''
# global G, Coh, phiE, Phi, dK, J, J1, cycleGn, nn, Jlist
config = ConfigParser.ConfigParser()
config.read('config.ini')
param_dict = config_section_map(config, 'General')
param_dict.update(config_section_map(config, 'DarmonPoint'))
param_dict.update(kwargs)
param = Bunch(**param_dict)
# Get general parameters
outfile = param.get('outfile')
use_ps_dists = param.get('use_ps_dists', False)
use_shapiro = param.get('use_shapiro', False)
use_sage_db = param.get('use_sage_db', False)
magma_seed = param.get('magma_seed', 1515316)
parallelize = param.get('parallelize', False)
Up_method = param.get('up_method', 'naive')
use_magma = param.get('use_magma', True)
progress_bar = param.get('progress_bar', True)
sign_at_infinity = param.get('sign_at_infinity', ZZ(1))
# Get darmon_point specific parameters
idx_orientation = param.get('idx_orientation')
idx_embedding = param.get('idx_embedding', 0)
algorithm = param.get('algorithm')
quaternionic = param.get('quaternionic')
cohomological = param.get('cohomological', True)
if Up_method == "bigmatrix" and use_shapiro == True:
import warnings
warnings.warn(
'Use of "bigmatrix" for Up iteration is incompatible with Shapiro Lemma trick. Using "naive" method for Up.'
)
Up_method = 'naive'
if working_prec is None:
working_prec = max([2 * prec + 10, 30])
if use_magma:
page_path = os.path.dirname(__file__) + '/KleinianGroups-1.0/klngpspec'
if magma is None:
from sage.interfaces.magma import Magma
magma = Magma()
quit_when_done = True
else:
quit_when_done = False
magma.attach_spec(page_path)
else:
quit_when_done = False
sys.setrecursionlimit(10**6)
F = E.base_ring()
beta = F(beta)
DB, Np, Ncartan = get_heegner_params(P, E, beta)
if quaternionic is None:
quaternionic = (DB != 1)
if cohomological is None:
cohomological = quaternionic
if quaternionic and not cohomological:
raise ValueError(
"Need cohomological algorithm when dealing with quaternions")
if use_ps_dists is None:
use_ps_dists = False if cohomological else True
try:
p = ZZ(P)
except TypeError:
p = ZZ(P.norm())
if not p.is_prime():
raise ValueError('P (= %s) should be a prime, of inertia degree 1' % P)
if F == QQ:
dK = ZZ(beta)
extra_conductor_sq = dK / fundamental_discriminant(dK)
assert ZZ(extra_conductor_sq).is_square()
extra_conductor = extra_conductor_sq.sqrt()
dK = dK / extra_conductor_sq
assert dK == fundamental_discriminant(dK)
if dK % 4 == 0:
dK = ZZ(dK / 4)
beta = dK
else:
dK = beta
# Compute the completion of K at p
x = QQ['x'].gen()
K = F.extension(x * x - dK, names='alpha')
if F == QQ:
dK = K.discriminant()
else:
dK = K.relative_discriminant()
hK = K.class_number()
sgninfty = 'plus' if sign_at_infinity == 1 else 'minus'
if hasattr(E, 'cremona_label'):
Ename = E.cremona_label()
elif hasattr(E, 'ainvs'):
Ename = E.ainvs()
else:
Ename = 'unknown'
fname = 'moments_%s_%s_%s_%s.sobj' % (P, Ename, sgninfty, prec)
if use_sage_db:
print("Moments will be stored in database as %s" % (fname))
if outfile == 'log':
outfile = '%s_%s_%s_%s_%s_%s.log' % (
P, Ename, dK, sgninfty, prec,
datetime.datetime.now().strftime("%Y%m%d-%H%M%S"))
outfile = outfile.replace('/', 'div')
outfile = '/tmp/darmonpoint_' + outfile
fwrite("Starting computation of the Darmon point", outfile)
fwrite('D_B = %s %s' % (DB, factor(DB)), outfile)
fwrite('Np = %s' % Np, outfile)
if Ncartan is not None:
fwrite('Ncartan = %s' % Ncartan, outfile)
fwrite('dK = %s (class number = %s)' % (dK, hK), outfile)
fwrite('Calculation with p = %s and prec = %s' % (P, prec), outfile)
fwrite('Elliptic curve %s: %s' % (Ename, E), outfile)
if outfile is not None:
print("Partial results will be saved in %s" % outfile)
if input_data is None:
if cohomological:
# Define the S-arithmetic group
if F != QQ and ramification_at_infinity is None:
if F.signature()[0] > 1:
if F.signature()[1] == 1:
ramification_at_infinity = F.real_places(
prec=Infinity) # Totally 'definite'
else:
raise ValueError(
'Please specify the ramification at infinity')
elif F.signature()[0] == 1:
if len(F.ideal(DB).factor()) % 2 == 0:
ramification_at_infinity = [] # Split at infinity
else:
ramification_at_infinity = F.real_places(
prec=Infinity) # Ramified at infinity
else:
ramification_at_infinity = None
if F == QQ:
abtuple = QuaternionAlgebra(DB).invariants()
else:
abtuple = quaternion_algebra_invariants_from_ramification(
F, DB, ramification_at_infinity, magma=magma)
G = BigArithGroup(P,
abtuple,
Np,
base=F,
outfile=outfile,
seed=magma_seed,
use_sage_db=use_sage_db,
magma=magma,
use_shapiro=use_shapiro,
nscartan=Ncartan)
# Define the cycle ( in H_1(G,Div^0 Hp) )
Coh = ArithCoh(G)
while True:
try:
cycleGn, nn, ell = construct_homology_cycle(
p,
G.Gn,
beta,
working_prec,
lambda q: Coh.hecke_matrix(q).minpoly(),
outfile=outfile,
elliptic_curve=E)
break
except PrecisionError:
working_prec *= 2
verbose(
'Encountered precision error, trying with higher precision (= %s)'
% working_prec)
except ValueError:
fwrite(
'ValueError occurred when constructing homology cycle. Returning the S-arithmetic group.',
outfile)
if quit_when_done:
magma.quit()
return G
except AssertionError as e:
fwrite(
'Assertion occurred when constructing homology cycle. Returning the S-arithmetic group.',
outfile)
fwrite('%s' % str(e), outfile)
if quit_when_done:
magma.quit()
return G
eisenstein_constant = -ZZ(E.reduction(ell).count_points())
fwrite(
'r = %s, so a_r(E) - r - 1 = %s' % (ell, eisenstein_constant),
outfile)
fwrite('exponent = %s' % nn, outfile)
phiE = Coh.get_cocycle_from_elliptic_curve(E,
sign=sign_at_infinity)
if hasattr(E, 'ap'):
sign_ap = E.ap(P)
else:
try:
sign_ap = ZZ(P.norm() + 1 - E.reduction(P).count_points())
except ValueError:
sign_ap = ZZ(P.norm() + 1 - Curve(E).change_ring(
P.residue_field()).count_points(1)[0])
Phi = get_overconvergent_class_quaternionic(
P,
phiE,
G,
prec,
sign_at_infinity,
sign_ap,
use_ps_dists=use_ps_dists,
use_sage_db=use_sage_db,
parallelize=parallelize,
method=Up_method,
progress_bar=progress_bar,
Ename=Ename)
# Integration with moments
tot_time = walltime()
J = integrate_H1(G,
cycleGn,
Phi,
1,
method='moments',
prec=working_prec,
parallelize=parallelize,
twist=True,
progress_bar=progress_bar)
verbose('integration tot_time = %s' % walltime(tot_time))
if use_sage_db:
G.save_to_db()
else: # not cohomological
nn = 1
eisenstein_constant = 1
if algorithm is None:
if Np == 1:
algorithm = 'darmon_pollack'
else:
algorithm = 'guitart_masdeu'
w = K.maximal_order().ring_generators()[0]
r0, r1 = w.coordinates_in_terms_of_powers()(K.gen())
QQp = Qp(p, working_prec)
Cp = QQp.extension(w.minpoly().change_ring(QQp), names='g')
v0 = K.hom([r0 + r1 * Cp.gen()])
# Optimal embeddings of level one
fwrite("Computing optimal embeddings of level one...", outfile)
Wlist = find_optimal_embeddings(K,
use_magma=use_magma,
extra_conductor=extra_conductor)
fwrite("Found %s such embeddings." % len(Wlist), outfile)
if idx_embedding is not None:
if idx_embedding >= len(Wlist):
fwrite(
'There are not enough embeddings. Taking the index modulo %s'
% len(Wlist), outfile)
idx_embedding = idx_embedding % len(Wlist)
fwrite('Taking only embedding number %s' % (idx_embedding),
outfile)
Wlist = [Wlist[idx_embedding]]
# Find the orientations
orients = K.maximal_order().ring_generators()[0].minpoly().roots(
Zmod(Np), multiplicities=False)
fwrite("Possible orientations: %s" % orients, outfile)
if len(Wlist) == 1 or idx_orientation == -1:
fwrite("Using all orientations, since hK = 1", outfile)
chosen_orientation = None
else:
fwrite("Using orientation = %s" % orients[idx_orientation],
outfile)
chosen_orientation = orients[idx_orientation]
emblist = []
for i, W in enumerate(Wlist):
tau, gtau, sign, limits = find_tau0_and_gtau(
v0,
Np,
W,
algorithm=algorithm,
orientation=chosen_orientation,
extra_conductor=extra_conductor)
fwrite(
'n_evals = %s' % sum(
(num_evals(t1, t2) for t1, t2 in limits)), outfile)
emblist.append((tau, gtau, sign, limits))
# Get the cohomology class from E
Phi = get_overconvergent_class_matrices(P,
E,
prec,
sign_at_infinity,
use_ps_dists=use_ps_dists,
use_sage_db=use_sage_db,
parallelize=parallelize,
progress_bar=progress_bar)
J = 1
Jlist = []
for i, emb in enumerate(emblist):
fwrite(
"Computing %s-th period, attached to the embedding: %s" %
(i, Wlist[i].list()), outfile)
tau, gtau, sign, limits = emb
n_evals = sum((num_evals(t1, t2) for t1, t2 in limits))
fwrite(
"Computing one period...(total of %s evaluations)" %
n_evals, outfile)
newJ = prod((double_integral_zero_infty(Phi, t1, t2)
for t1, t2 in limits))**ZZ(sign)
Jlist.append(newJ)
J *= newJ
else: # input_data is not None
Phi, J = input_data[1:3]
fwrite('Integral done. Now trying to recognize the point', outfile)
fwrite('J_psi = %s' % J, outfile)
fwrite('g belongs to %s' % J.parent(), outfile)
#Try to recognize a generator
if quaternionic:
local_embedding = G.base_ring_local_embedding(working_prec)
twopowlist = [
4, 3, 2, 1,
QQ(1) / 2,
QQ(3) / 2,
QQ(1) / 3,
QQ(2) / 3,
QQ(1) / 4,
QQ(3) / 4,
QQ(5) / 2,
QQ(4) / 3
]
else:
local_embedding = Qp(p, working_prec)
twopowlist = [
4, 3, 2, 1,
QQ(1) / 2,
QQ(3) / 2,
QQ(1) / 3,
QQ(2) / 3,
QQ(1) / 4,
QQ(3) / 4,
QQ(5) / 2,
QQ(4) / 3
]
known_multiple = QQ(
nn * eisenstein_constant
) # It seems that we are not getting it with present algorithm.
while known_multiple % p == 0:
known_multiple = ZZ(known_multiple / p)
if not recognize_point:
fwrite('known_multiple = %s' % known_multiple, outfile)
if quit_when_done:
magma.quit()
return J, Jlist
candidate, twopow, J1 = recognize_J(E,
J,
K,
local_embedding=local_embedding,
known_multiple=known_multiple,
twopowlist=twopowlist,
prec=prec,
outfile=outfile)
if candidate is not None:
HCF = K.hilbert_class_field(names='r1') if hK > 1 else K
if hK == 1:
try:
verbose('candidate = %s' % candidate)
Ptsmall = E.change_ring(HCF)(candidate)
fwrite('twopow = %s' % twopow, outfile)
fwrite(
'Computed point: %s * %s * %s' %
(twopow, known_multiple, Ptsmall), outfile)
fwrite('(first factor is not understood, second factor is)',
outfile)
fwrite(
'(r satisfies %s = 0)' %
(Ptsmall[0].parent().gen().minpoly()), outfile)
fwrite('================================================',
outfile)
if quit_when_done:
magma.quit()
return Ptsmall
except (TypeError, ValueError):
verbose("Could not recognize the point.")
else:
verbose('candidate = %s' % candidate)
fwrite('twopow = %s' % twopow, outfile)
fwrite(
'Computed point: %s * %s * (x,y)' % (twopow, known_multiple),
outfile)
fwrite('(first factor is not understood, second factor is)',
outfile)
try:
pols = [HCF(c).relative_minpoly() for c in candidate[:2]]
except AttributeError:
pols = [HCF(c).minpoly() for c in candidate[:2]]
fwrite('Where x satisfies %s' % pols[0], outfile)
fwrite('and y satisfies %s' % pols[1], outfile)
fwrite('================================================', outfile)
if quit_when_done:
magma.quit()
return candidate
else:
fwrite('================================================', outfile)
if quit_when_done:
magma.quit()
return []
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a function (or more general, any callable)
- ``inputs`` -- a list of pairs ``(args, kwds)`` to be used as
arguments to ``f``, where ``args`` is a tuple and ``kwds`` is
a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
TESTS:
The output of functions decorated with :func:`parallel` is read
as a pickle by the parent process. We intentionally break the
unpickling and demonstrate that this failure is handled
gracefully (the exception is put in the list instead of the
answer)::
sage: Polygen = parallel(polygen)
sage: list(Polygen([QQ]))
[(((Rational Field,), {}), x)]
sage: from sage.misc.persist import unpickle_override, register_unpickle_override
sage: register_unpickle_override('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint', Integer)
sage: L = list(Polygen([QQ]))
sage: L
[(((Rational Field,), {}),
'INVALID DATA __init__() takes at most 2 positional arguments (4 given)')]
Fix the unpickling::
sage: del unpickle_override[('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint')]
sage: list(Polygen([QQ,QQ]))
[(((Rational Field,), {}), x), (((Rational Field,), {}), x)]
"""
n = self.ncpus
v = list(inputs)
import os
import sys
import signal
from sage.misc.persist import loads
from sage.misc.temporary_file import tmp_dir
dir = tmp_dir()
timeout = self.timeout
workers = {}
try:
while v or workers:
# Spawn up to n subprocesses
while v and len(workers) < n:
v0 = v.pop(0) # Input value for the next subprocess
with ContainChildren():
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if not pid:
# This is the subprocess.
self._subprocess(f, dir, *v0)
workers[pid] = WorkerData(v0)
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
T = walltime()
if timeout:
oldest = min(W.starttime for W in workers.values())
alarm(max(timeout - (T - oldest), 0.1))
try:
pid = os.wait()[0]
cancel_alarm()
W = workers.pop(pid)
except AlarmInterrupt:
# Kill workers that are too old
for pid, W in workers.items():
if T - W.starttime > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, W.input))
os.kill(pid, signal.SIGKILL)
W.failure = " (timed out)"
except KeyError:
# Some other process exited, not our problem...
pass
else:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj' % pid)
try:
with open(sobj, "rb") as file:
data = file.read()
except IOError:
answer = "NO DATA" + W.failure
else:
os.unlink(sobj)
try:
answer = loads(data, compress=False)
except Exception as E:
answer = "INVALID DATA {}".format(E)
out = os.path.join(dir, '%s.out' % pid)
try:
with open(out) as file:
sys.stdout.write(file.read())
os.unlink(out)
except IOError:
pass
yield (W.input, answer)
finally:
# Send SIGKILL signal to workers that are left.
if workers:
if self.verbose:
print("Killing any remaining workers...")
sys.stdout.flush()
for pid in workers:
try:
os.kill(pid, signal.SIGKILL)
except OSError:
# If kill() failed, it is most likely because
# the process already exited.
pass
else:
try:
os.waitpid(pid, 0)
except OSError as msg:
if self.verbose:
print(msg)
# Clean up all temporary files.
rmtree(dir)
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a Python function that need not be pickleable or anything else!
- ``inputs`` -- a list of pickleable pairs ``(args, kwds)``, where
``args`` is a tuple and ``kwds`` is a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
"""
n = self.ncpus
v = list(inputs)
import os, sys, signal
from sage.structure.sage_object import load
from sage.misc.misc import tmp_dir, walltime
dir = tmp_dir()
timeout = self.timeout
# Subprocesses shouldn't inherit unflushed buffers (cf. #11778):
sys.stdout.flush()
sys.stderr.flush()
workers = {}
try:
while len(v) > 0 or len(workers) > 0:
# Spawn up to n subprocesses
while len(v) > 0 and len(workers) < n:
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if pid:
# This is the parent master process.
workers[pid] = [v[0], walltime(), '']
del v[0]
else:
# This is the subprocess.
self._subprocess(f, dir, v[0])
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
if timeout:
def mysig(a, b):
raise RuntimeError, "SIGALRM"
oldest = min([X[1] for X in workers.values()])
signal.signal(signal.SIGALRM, mysig)
signal.alarm(
max(int(timeout - (walltime() - oldest)), 1))
try:
pid = os.wait()[0]
signal.signal(signal.SIGALRM, signal.SIG_IGN)
except RuntimeError:
signal.signal(signal.SIGALRM, signal.SIG_IGN)
# Kill workers that are too old
for pid, X in workers.iteritems():
if walltime() - X[1] > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, X[0]))
sys.stdout.flush()
os.kill(pid, 9)
X[-1] = ' (timed out)'
else:
# If the computation was interrupted the pid
# might not be in the workers list, in which
# case we skip this.
if pid in workers:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj' % pid)
if not os.path.exists(sobj):
X = "NO DATA" + workers[pid][
-1] # the message field
else:
X = load(sobj, compress=False)
os.unlink(sobj)
out = os.path.join(dir, '%s.out' % pid)
if not os.path.exists(out):
output = "NO OUTPUT"
else:
output = open(out).read()
os.unlink(out)
if output.strip():
print output,
sys.stdout.flush()
yield (workers[pid][0], X)
del workers[pid]
except Exception, msg:
print msg
sys.stdout.flush()
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a Python function that need not be pickleable or anything else!
- ``inputs`` -- a list of pickleable pairs ``(args, kwds)``, where
``args`` is a tuple and ``kwds`` is a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
"""
n = self.ncpus
v = list(inputs)
import os, sys, signal
from sage.structure.sage_object import load
from sage.misc.misc import tmp_dir, walltime
dir = tmp_dir()
timeout = self.timeout
# Subprocesses shouldn't inherit unflushed buffers (cf. #11778):
sys.stdout.flush()
sys.stderr.flush()
workers = {}
try:
while len(v) > 0 or len(workers) > 0:
# Spawn up to n subprocesses
while len(v) > 0 and len(workers) < n:
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if pid:
# This is the parent master process.
workers[pid] = [v[0], walltime(), '']
del v[0]
else:
# This is the subprocess.
self._subprocess(f, dir, v[0])
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
if timeout:
def mysig(a,b):
raise RuntimeError, "SIGALRM"
oldest = min([X[1] for X in workers.values()])
signal.signal(signal.SIGALRM, mysig)
signal.alarm(max(int(timeout - (walltime()-oldest)), 1))
try:
pid = os.wait()[0]
signal.signal(signal.SIGALRM, signal.SIG_IGN)
except RuntimeError:
signal.signal(signal.SIGALRM, signal.SIG_IGN)
# Kill workers that are too old
for pid, X in workers.iteritems():
if walltime() - X[1] > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, X[0]) )
sys.stdout.flush()
os.kill(pid,9)
X[-1] = ' (timed out)'
else:
# If the computation was interrupted the pid
# might not be in the workers list, in which
# case we skip this.
if pid in workers:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj'%pid)
if not os.path.exists(sobj):
X = "NO DATA" + workers[pid][-1] # the message field
else:
X = load(sobj, compress=False)
os.unlink(sobj)
out = os.path.join(dir, '%s.out'%pid)
if not os.path.exists(out):
output = "NO OUTPUT"
else:
output = open(out).read()
os.unlink(out)
if output.strip():
print output,
sys.stdout.flush()
yield (workers[pid][0], X)
del workers[pid]
except Exception, msg:
print msg
sys.stdout.flush()
def __call__(self, f, inputs):
"""
Parallel iterator using ``fork()``.
INPUT:
- ``f`` -- a function (or more general, any callable)
- ``inputs`` -- a list of pairs ``(args, kwds)`` to be used as
arguments to ``f``, where ``args`` is a tuple and ``kwds`` is
a dictionary.
OUTPUT:
EXAMPLES::
sage: F = sage.parallel.use_fork.p_iter_fork(2,3)
sage: sorted(list( F( (lambda x: x^2), [([10],{}), ([20],{})])))
[(([10], {}), 100), (([20], {}), 400)]
sage: sorted(list( F( (lambda x, y: x^2+y), [([10],{'y':1}), ([20],{'y':2})])))
[(([10], {'y': 1}), 101), (([20], {'y': 2}), 402)]
TESTS:
The output of functions decorated with :func:`parallel` is read
as a pickle by the parent process. We intentionally break the
unpickling and demonstrate that this failure is handled
gracefully (the exception is put in the list instead of the
answer)::
sage: Polygen = parallel(polygen)
sage: list(Polygen([QQ]))
[(((Rational Field,), {}), x)]
sage: from sage.structure.sage_object import unpickle_override, register_unpickle_override
sage: register_unpickle_override('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint', Integer)
sage: L = list(Polygen([QQ]))
sage: L
[(((Rational Field,), {}),
'INVALID DATA __init__() takes at most 2 positional arguments (4 given)')]
Fix the unpickling::
sage: del unpickle_override[('sage.rings.polynomial.polynomial_rational_flint', 'Polynomial_rational_flint')]
sage: list(Polygen([QQ,QQ]))
[(((Rational Field,), {}), x), (((Rational Field,), {}), x)]
"""
n = self.ncpus
v = list(inputs)
import os, sys, signal
from sage.structure.sage_object import loads
from sage.misc.temporary_file import tmp_dir
dir = tmp_dir()
timeout = self.timeout
workers = {}
try:
while len(v) > 0 or len(workers) > 0:
# Spawn up to n subprocesses
while len(v) > 0 and len(workers) < n:
v0 = v.pop(0) # Input value for the next subprocess
with ContainChildren():
pid = os.fork()
# The way fork works is that pid returns the
# nonzero pid of the subprocess for the master
# process and returns 0 for the subprocess.
if not pid:
# This is the subprocess.
self._subprocess(f, dir, *v0)
workers[pid] = WorkerData(v0)
if len(workers) > 0:
# Now wait for one subprocess to finish and report the result.
# However, wait at most the time since the oldest process started.
T = walltime()
if timeout:
oldest = min(W.starttime for W in workers.values())
alarm(max(timeout - (T - oldest), 0.1))
try:
pid = os.wait()[0]
cancel_alarm()
W = workers.pop(pid)
except AlarmInterrupt:
# Kill workers that are too old
for pid, W in workers.items():
if T - W.starttime > timeout:
if self.verbose:
print(
"Killing subprocess %s with input %s which took too long"
% (pid, W.input) )
os.kill(pid, signal.SIGKILL)
W.failure = " (timed out)"
except KeyError:
# Some other process exited, not our problem...
pass
else:
# collect data from process that successfully terminated
sobj = os.path.join(dir, '%s.sobj'%pid)
try:
with open(sobj) as file:
data = file.read()
except IOError:
answer = "NO DATA" + W.failure
else:
os.unlink(sobj)
try:
answer = loads(data, compress=False)
except Exception as E:
answer = "INVALID DATA {}".format(E)
out = os.path.join(dir, '%s.out'%pid)
try:
with open(out) as file:
sys.stdout.write(file.read())
os.unlink(out)
except IOError:
pass
yield (W.input, answer)
finally:
# Send SIGKILL signal to workers that are left.
if workers:
if self.verbose:
print("Killing any remaining workers...")
sys.stdout.flush()
for pid in workers:
try:
os.kill(pid, signal.SIGKILL)
except OSError:
# If kill() failed, it is most likely because
# the process already exited.
pass
else:
try:
os.waitpid(pid, 0)
except OSError as msg:
if self.verbose:
print(msg)
# Clean up all temporary files.
rmtree(dir)
