def __call__(self, x):
"""
EXAMPLES::
sage: a = sage0(4)
sage: a.parent()
Sage
sage: a is sage0(a)
True
TESTS::
sage: sage0(axiom(x^2+1)) #optional - axiom
x^2 + 1
"""
if isinstance(x, ExpectElement):
if x.parent() is self:
return x
else:
return self(x.sage())
if isinstance(x, str):
return SageElement(self, x)
if self.is_local():
open(self._local_tmpfile(),'w').write(cPickle.dumps(x,2))
return SageElement(self, 'cPickle.load(open("%s"))'%self._local_tmpfile())
else:
open(self._local_tmpfile(),'w').write(dumps(x)) # my dumps is compressed by default
self._send_tmpfile_to_server()
return SageElement(self, 'loads(open("%s").read())'%self._remote_tmpfile())
def __call__(self, x):
"""
EXAMPLES::
sage: a = sage0(4)
sage: a.parent()
Sage
sage: a is sage0(a)
True
TESTS::
sage: sage0(axiom(x^2+1)) #optional - axiom
x^2 + 1
"""
if isinstance(x, ExpectElement):
if x.parent() is self:
return x
else:
return self(x.sage())
if isinstance(x, str):
return SageElement(self, x)
if self.is_local():
open(self._local_tmpfile(), 'w').write(cPickle.dumps(x, 2))
return SageElement(
self, 'cPickle.load(open("%s"))' % self._local_tmpfile())
else:
open(self._local_tmpfile(),
'w').write(dumps(x)) # my dumps is compressed by default
self._send_tmpfile_to_server()
return SageElement(
self, 'loads(open("%s").read())' % self._remote_tmpfile())
def __call__(self, x):
"""
EXAMPLES::
sage: a = sage0(4)
sage: a.parent()
Sage
sage: a is sage0(a)
True
"""
if isinstance(x, SageElement) and x.parent() is self:
return x
if isinstance(x, str):
return SageElement(self, x)
if self.is_local():
open(self._local_tmpfile(),'w').write(cPickle.dumps(x,2))
return SageElement(self, 'cPickle.load(open("%s"))'%self._local_tmpfile())
else:
open(self._local_tmpfile(),'w').write(dumps(x)) # my dumps is compressed by default
self._send_tmpfile_to_server()
return SageElement(self, 'loads(open("%s").read())'%self._remote_tmpfile())
def __call__(self, x):
"""
EXAMPLES::
sage: a = sage0(4)
sage: a.parent()
Sage
sage: a is sage0(a)
True
"""
if isinstance(x, SageElement) and x.parent() is self:
return x
if isinstance(x, str):
return SageElement(self, x)
if self.is_local():
open(self._local_tmpfile(),'w').write(cPickle.dumps(x,2))
return SageElement(self, 'cPickle.load(open("%s"))'%self._local_tmpfile())
else:
open(self._local_tmpfile(),'w').write(dumps(x)) # my dumps is compressed by default
self._send_tmpfile_to_server()
return SageElement(self, 'loads(open("%s").read())'%self._remote_tmpfile())
def __call__(self, x):
"""
EXAMPLES::
sage: a = sage0(4)
sage: a.parent()
Sage
sage: a is sage0(a)
True
TESTS::
sage: sage0(axiom(x^2+1)) #optional - axiom
x^2 + 1
"""
if isinstance(x, ExpectElement):
if x.parent() is self:
return x
else:
return self(x.sage())
if isinstance(x, string_types):
return SageElement(self, x)
if self.is_local():
with open(self._local_tmpfile(), 'wb') as fobj:
fobj.write(cPickle.dumps(x, 2))
code = '_sage0_load_local({!r})'.format(self._local_tmpfile())
return SageElement(self, code)
else:
with open(self._local_tmpfile(), 'wb') as fobj:
fobj.write(dumps(x)) # my dumps is compressed by default
self._send_tmpfile_to_server()
code = '_sage0_load_remote({!r})'.format(self._remote_tmpfile())
return SageElement(self, code)
def hash_sage_object(x):
return hashlib.sha512(dumps(x)).digest()
def hash_sage_object(x):
return hashlib.sha512(dumps(x)).digest()
def test_correctness_and_precision_of_solve_diff_eqn(number=20, verbosity=1):
"""
``number`` is how many different random distributions to check.
Currently, avoids the prime 2.
"""
from sage.misc.prandom import randint
from sage.rings.arith import random_prime
from sage.rings.padics.factory import ZpCA
from sage.modular.pollack_stevens.coeffmod_OMS_space import OverconvergentDistributions
from sage.structure.sage_object import dumps
errors = []
munus = []
for i in range(number):
Mspace = randint(1, 20) #Moments of space
M = randint(max(0, Mspace - 5), Mspace)
p = random_prime(13, lbound=3)
k = randint(0, 6)
Rprec = Mspace + randint(0, 5)
R = ZpCA(p, Rprec)
D = OverconvergentDistributions(k, base=R, prec_cap=Mspace)
S0 = D.action().actor()
Delta_mat = S0([1,1,0,1])
mu = D.random_element(M)
mu_save = dumps(mu)#[deepcopy(mu.ordp), deepcopy(mu._moments)]
if verbosity > 0:
print "\nTest #{0} data (Mspace, M, p, k, Rprec) =".format(i+1), (Mspace, M, p, k, Rprec)
print "mu =", mu
nu = mu * Delta_mat - mu
nu_save = [deepcopy(nu.ordp), deepcopy(nu._moments)]
mu2 = nu.solve_diff_eqn()
nu_abs_prec = nu.precision_absolute()
expected = nu_abs_prec - nu_abs_prec.exact_log(p) - 1
if M != 1:
try:
agree = (mu - mu2).is_zero(expected)
except PrecisionError:
print (Mspace, M, p, k, Rprec), mu_save._repr_(), nu_save
assert False
else:
agree = mu2.is_zero(expected)
if verbosity > 1:
print " Just so you know:"
print " mured =", mu.reduce_precision_absolute(expected)
print " mu2 =", mu2
print " nu = ", nu
if not agree:
errors.append((i+1, 1))
munus.append((mu_save, nu_save, mu2, (Mspace, M, p, k, Rprec)))
if verbosity > 0:
print " Test finding mu from mu|Delta accurate: %s"%(agree)
print " nu_abs_prec soln_abs_prec_expected actual agree"
mu2_abs_prec = mu2.precision_absolute()
agree = (expected == mu2_abs_prec)
if verbosity > 0:
print " %s %s %s %s"%(nu_abs_prec, expected, mu2_abs_prec, agree)
if not agree:
errors.append((i+1, 2))
munus.append((mu_save, nu_save, mu2, (Mspace, M, p, k, Rprec)))
if mu.precision_relative() > 0:
mu._moments[0] = R(0, mu.precision_relative())
mu_save = [deepcopy(mu.ordp), deepcopy(mu._moments)]
if verbosity > 0:
print " mu modified =", mu
nu = mu.solve_diff_eqn()
mu_abs_prec = mu.precision_absolute()
expected = mu_abs_prec - mu_abs_prec.exact_log(p) - 1
nud = nu * Delta_mat - nu
nu_save = [deepcopy(nu.ordp), deepcopy(nu._moments)]
agree = (nud - mu).is_zero(expected)
if verbosity > 1:
print " Just so you know:"
print " mu =", mu
print " mured =", mu.reduce_precision_absolute(expected)
print " nud =", nud
if not agree:
errors.append((i+1, 3))
munus.append((mu_save, nu_save, (Mspace, M, p, k, Rprec)))
if verbosity > 0:
print " Test finding nu with nu|Delta == mu: %s"%(agree)
print " mu_abs_prec soln_abs_prec_expected actual agree"
nu_abs_prec = nu.precision_absolute()
agree = (expected == nu_abs_prec)
if verbosity > 0:
print " %s %s %s %s"%(mu_abs_prec, expected, nu_abs_prec, agree)
if not agree:
errors.append((i+1, 4))
munus.append((mu_save, nu_save, (Mspace, M, p, k, Rprec)))
if len(errors) == 0:
if verbosity > 0:
print "\nTest passed with no errors."
return
if verbosity > 0:
print "\nTest failed with errors: %s\n"%(errors)
return errors, munus