def __getattr__(self, name):
"""
EXAMPLE::
sage: groebner = sage.libs.singular.ff.groebner
sage: groebner
groebner (singular function)
sage: primdecSY = sage.libs.singular.ff.primdec__lib.primdecSY
sage: primdecSY
primdecSY (singular function)
"""
if name.startswith("_"):
raise AttributeError(
"Singular Function Factory has no attribute '%s'" % name)
try:
return singular_function(name)
except NameError:
if name.endswith("__lib"):
name = name[:-5]
lib(name + ".lib")
return SingularFunctionFactory()
else:
raise NameError("function or package '%s' unknown." % (name))
def __getattr__(self, name):
"""
EXAMPLE::
sage: import sage.libs.singular.function_factory
sage: groebner = sage.libs.singular.function_factory.ff.groebner
sage: groebner
groebner (singular function)
sage: import sage.libs.singular.function_factory
sage: primdecSY = sage.libs.singular.function_factory.ff.primdec__lib.primdecSY
sage: primdecSY
primdecSY (singular function)
"""
if name.startswith("_"):
raise AttributeError("Singular Function Factory has no attribute '%s'" % name)
try:
return singular_function(name)
except NameError:
if name.endswith("__lib"):
name = name[:-5]
lib(name + ".lib")
return SingularFunctionFactory()
else:
raise NameError("function or package '%s' unknown." % (name))
def radical_singular(I):
r""" Return the radical of this ideal.
INPUT:
- ``I`` -- an ideal of a polynomial ring over `\mathbb{Z}`
OUTPUT: the radical of `I`
"""
singular_lib('primdecint.lib')
return singular_function('radicalZ')(I)
def minimal_ass_primes_singular(I):
r""" Return the list of minimal associated primes of an ideal.
INPUT:
- ``I`` -- an ideal of a polynomial ring over `\mathbb{Z}`
OUTPUT: the list of all minimal associated prime ideals of `I`
"""
singular_lib('primdecint.lib')
R = I.ring()
return [R.ideal(G) for G in singular_function('minAssZ')(I)]
def horizontal_minimal_ass_primes(I):
r""" Return the list of horizontal minimal associated primes of I.
INPUT:
- ``I`` -- an ideal of a polynomial ring over `\mathbb{Z}`
OUTPUT: the list of all horizontal minimal associated prime ideals of `I`.
Here a prime ideal `P` of a polynomial ring `R = \mathbb{Z}[x_1,\ldots,x_n]`
is called *horizontal* if `P\cap\mathbb{Z}=(0)`.
"""
singular_lib('primdecint.lib')
R = I.ring()
P_list = [R.ideal(G) for G in singular_function('minAssZ')(I)]
return [P for P in P_list if P.elimination_ideal(R.gens()).is_zero()]
gcd(
self.brackets_dict[(f, g)],
self.brackets_dict[(f, h)],
)).degree() == 0)
for a in l:
return a
return None
def weight_of_basis(self):
f, g, _ = self.relatively_prime_3forms_maybe()
c = self.brackets_dict[(f, g)]
c_deg = degree(c)
return (f[1] - c_deg, g[1] - c_deg)
smodule = singular_function("module")
sideal = singular_function("ideal")
squotient = singular_function("quotient")
smres = singular_function("mres")
slist = singular_function("list")
sintersect = singular_function("intersect")
ssyz = singular_function("syz")
@cached_function
def load_min_resol_prim(i, parity):
fname = join(DATA_DIR, "str%s_%s_cand.sobj" % (i, parity))
return load(fname)
@cached_function
M.add_multiple_of_row(u, i, -b)
#print "\nafter: \n", M
Mt = M[:, -MI.nrows():]
Mres = M[:, :M0.ncols()]
assert (Mt * (apply_swap(M0, swapped)) == Mres)
return Mres, Mt, tuple(swapped)
from sage.libs.singular.function import singular_function
from sage.libs.singular.function import lib as singular_lib
singular_lib('primdecint.lib')
primdecZ = singular_function('primdecZ')
radicalZ = singular_function('radicalZ')
def primdec_ZZ(I):
R = I.ring()
P = primdecZ(I)
V = [R.ideal(X[0]) for X in P]
return V
def radical_ZZ(I):
R = I.ring()
r = radicalZ(I)
return R.ideal(r)
M.set_row_to_multiple_of_row(u, u, a)
M.add_multiple_of_row(u,i,-b)
#print "\nafter: \n", M
Mt = M[:,- MI.nrows():]
Mres = M[:,:M0.ncols()]
assert(Mt*(apply_swap(M0,swapped)) == Mres)
return Mres,Mt,tuple(swapped)
from sage.libs.singular.function import singular_function
from sage.libs.singular.function import lib as singular_lib
singular_lib('primdecint.lib')
primdecZ = singular_function('primdecZ')
radicalZ = singular_function('radicalZ')
def primdec_ZZ(I):
R = I.ring()
P = primdecZ(I)
V = [ R.ideal(X[0]) for X in P]
return V
def radical_ZZ(I):
R = I.ring()
r = radicalZ(I)
return R.ideal(r)
class FoundAttack(Exception):
def __init__(self, value):
