I am using SageMath's implementation of SR and encountered the above error
when trying to display the solutions to a polynomial system using the
variety function for ideals, as specified
here:
https://doc.sagemath.org/html/en/reference/cryptography/sage/crypto/mq/sr.html.
I am running SageMath 9.2 on Windows 10 with an Intel Core i5-6600K CPU @
3.50GHz, 3501 Mhz, 4 Core(s), 4 Logical Processor(s).
I use the following commands:
sage: sr = mq.SR(2,1,1,4, gf2=True, polybori=True,
allow_zero_inversions=True)
sage: K = sr.base_ring()
sage: a = K.gen()
sage: K = [a]
sage: P = [1]
sage: F,s = sr.polynomial_system(P=P, K=K)
sage: I = F.ideal()
sage: for V in I.variety():
....: for k,v in sorted(V.items()):
....: print("{} {}".format(k, v))
....: print("\n")
This works only for SR(1,1,1,4) i.e. SR using only one round. If I even
increase the round number to 2 I encounter the following error:
RuntimeError: error in Singular function call 'groebner':
int overflow in hilb 1
error occurred in or before standard.lib::stdhilb line 350: ` i = std(i,
hi);`
leaving standard.lib::stdhilb
leaving standard.lib::groebner
Any help with this would be much appreciated, thank you.
The entire error message is much larger:
AttributeError Traceback (most recent call last)
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in dimension(self, singular)
1141 try:
-> 1142 return self.__dimension
1143 except AttributeError:
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/element.pyx
in sage.structure.element.Element.__getattr__
(build/cythonized/sage/structure/element.c:4703)()
492 """
--> 493 return self.getattr_from_category(name)
494
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/element.pyx
in sage.structure.element.Element.getattr_from_category
(build/cythonized/sage/structure/element.c:4815)()
505 cls = P._abstract_element_class
--> 506 return getattr_from_other_class(self, cls, name)
507
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/cpython/getattr.pyx
in sage.cpython.getattr.getattr_from_other_class
(build/cythonized/sage/cpython/getattr.c:2619)()
371 dummy_error_message.name = name
--> 372 raise AttributeError(dummy_error_message)
373 attribute = <object>attr
AttributeError: 'MPolynomialIdeal' object has no attribute '_cache__gens'
During handling of the above exception, another exception occurred:
KeyError Traceback (most recent call last)
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller.__call__
(build/cythonized/sage/misc/cachefunc.c:10304)()
1942 try:
-> 1943 return cache[k]
1944 except TypeError: # k is not hashable
KeyError: (('', None, None, False), ())
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last)
RuntimeError: Error raised calling singular function
Exception ignored in:
'sage.libs.singular.function.LibraryCallHandler.handle_call'
RuntimeError: Error raised calling singular function
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in dimension(self, singular)
1141 try:
-> 1142 return self.__dimension
1143 except AttributeError:
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/element.pyx
in sage.structure.element.Element.__getattr__
(build/cythonized/sage/structure/element.c:4703)()
492 """
--> 493 return self.getattr_from_category(name)
494
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/structure/element.pyx
in sage.structure.element.Element.getattr_from_category
(build/cythonized/sage/structure/element.c:4815)()
505 cls = P._abstract_element_class
--> 506 return getattr_from_other_class(self, cls, name)
507
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/cpython/getattr.pyx
in sage.cpython.getattr.getattr_from_other_class
(build/cythonized/sage/cpython/getattr.c:2619)()
371 dummy_error_message.name = name
--> 372 raise AttributeError(dummy_error_message)
373 attribute = <object>attr
AttributeError: 'Singular' object has no attribute '_strip_prompt'
During handling of the above exception, another exception occurred:
KeyError Traceback (most recent call last)
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller.__call__
(build/cythonized/sage/misc/cachefunc.c:10304)()
1942 try:
-> 1943 return cache[k]
1944 except TypeError: # k is not hashable
KeyError: (('', None, None, False), ())
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last)
<ipython-input-11-f2c1e1116d2f> in <module>
----> 1 for V in I.variety():
2 for k,v in sorted(V.items()):
3 print("{} {}".format(k, v))
4 print("\n")
5
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/pbori/pbori.pyx
in sage.rings.polynomial.pbori.pbori.BooleanPolynomialIdeal.variety
(build/cythonized/sage/rings/polynomial/pbori/pbori.cpp:43416)()
5198 I = R.ideal([R(f) for f in self.groebner_basis()])
5199 J = FieldIdeal(R)
-> 5200 solutions = (I + J).variety(**kwds)
5201 return [KeyConvertingDict(R_bool, s) for s in solutions]
5202
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in __call__(self, *args, **kwds)
295 if not R.base_ring().is_field():
296 raise ValueError("Coefficient ring must be a field for
function '%s'."%(self.f.__name__))
--> 297 return self.f(self._instance, *args, **kwds)
298
299 require_field = RequireField
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in variety(self, ring)
2566 if ring is not None: P = P.change_ring(ring)
2567 try:
-> 2568 TI = self.triangular_decomposition('singular:triangLfak')
2569 T = [list(each.gens()) for each in TI]
2570 except TypeError: # conversion to Singular not supported
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in __call__(self, *args, **kwds)
295 if not R.base_ring().is_field():
296 raise ValueError("Coefficient ring must be a field for
function '%s'."%(self.f.__name__))
--> 297 return self.f(self._instance, *args, **kwds)
298
299 require_field = RequireField
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/qqbar_decorators.py
in wrapper(*args, **kwds)
94 or is_PolynomialSequence(a)
95 and
is_AlgebraicField_common(a.ring().base_ring()) for a in args):
---> 96 return func(*args, **kwds)
97
98 polynomials = []
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/interfaces/singular.py
in wrapper(*args, **kwds)
2782 def wrapper(*args, **kwds):
2783 with SingularGBDefaultContext():
-> 2784 return func(*args, **kwds)
2785 return wrapper
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/libs/singular/standard_options.py
in wrapper(*args, **kwds)
139 """
140 with LibSingularGBDefaultContext():
--> 141 return func(*args, **kwds)
142 return wrapper
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in triangular_decomposition(self, algorithm, singular)
1059 I = MPolynomialIdeal(Q, I.groebner_basis()[::-1])
1060
-> 1061 if I.dimension() != 0:
1062 raise TypeError("dimension must be zero")
1063
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in __call__(self, *args, **kwds)
295 if not R.base_ring().is_field():
296 raise ValueError("Coefficient ring must be a field for
function '%s'."%(self.f.__name__))
--> 297 return self.f(self._instance, *args, **kwds)
298
299 require_field = RequireField
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/qqbar_decorators.py
in wrapper(*args, **kwds)
94 or is_PolynomialSequence(a)
95 and
is_AlgebraicField_common(a.ring().base_ring()) for a in args):
---> 96 return func(*args, **kwds)
97
98 polynomials = []
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in dimension(self, singular)
1145 import sage.libs.singular.function_factory
1146 dim = sage.libs.singular.function_factory.ff.dim
-> 1147 v =
MPolynomialIdeal(self.ring(),self.groebner_basis())
1148 self.__dimension = Integer(dim(v,
attributes={v:{'isSB':1}}))
1149 except TypeError:
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller.__call__
(build/cythonized/sage/misc/cachefunc.c:10438)()
1946 return cache[k]
1947 except KeyError:
-> 1948 w = self._instance_call(*args, **kwds)
1949 cache[k] = w
1950 return w
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller._instance_call
(build/cythonized/sage/misc/cachefunc.c:9917)()
1822 True
1823 """
-> 1824 return self.f(self._instance, *args, **kwds)
1825
1826 cdef fix_args_kwds(self, tuple args, dict kwds):
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/qqbar_decorators.py
in wrapper(*args, **kwds)
94 or is_PolynomialSequence(a)
95 and
is_AlgebraicField_common(a.ring().base_ring()) for a in args):
---> 96 return func(*args, **kwds)
97
98 polynomials = []
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in groebner_basis(self, algorithm, deg_bound, mult_bound, prot, *args,
**kwds)
4294 if not algorithm:
4295 try:
-> 4296 gb = self._groebner_basis_libsingular("groebner",
deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)
4297 except (TypeError, NameError): # conversion to Singular
not supported
4298 try:
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/libs/singular/standard_options.py
in wrapper(*args, **kwds)
139 """
140 with LibSingularGBDefaultContext():
--> 141 return func(*args, **kwds)
142 return wrapper
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/rings/polynomial/multi_polynomial_ideal.py
in _groebner_basis_libsingular(self, algorithm, *args, **kwds)
537 S = slimgb_libsingular(self)
538 elif algorithm == "groebner":
--> 539 S = groebner(self)
540 else:
541 try:
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/libs/singular/function.pyx
in sage.libs.singular.function.SingularFunction.__call__
(build/cythonized/sage/libs/singular/function.cpp:15176)()
1332 if not (isinstance(ring, MPolynomialRing_libsingular) or
isinstance(ring, NCPolynomialRing_plural)):
1333 raise TypeError("Cannot call Singular function '%s'
with ring parameter of type '%s'"%(self._name,type(ring)))
-> 1334 return call_function(self, args, ring, interruptible,
attributes)
1335
1336 def _instancedoc_(self):
/opt/sagemath-9.2/local/lib/python3.7/site-packages/sage/libs/singular/function.pyx
in sage.libs.singular.function.call_function
(build/cythonized/sage/libs/singular/function.cpp:17178)()
1530 if errorreported:
1531 errorreported = 0
-> 1532 raise RuntimeError("error in Singular function call
%r:\n%s" %
1533 (self._name, "\n".join(error_messages)))
1534
RuntimeError: error in Singular function call 'groebner':
int overflow in hilb 1
error occurred in or before standard.lib::stdhilb line 350: ` i = std(i,
hi);`
leaving standard.lib::stdhilb
leaving standard.lib::groebner
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