I almost forgot about my 5th one: a seg fault.
I'm running 'Sage Version 4.8, Release Date: 2012-01-20' on an intel
processor on Ubuntu 11.10
R.<x0>=PolynomialRing(ZZ,1)
F=x0^4-2*x0^2-x0
R.<x0,y0,z0,x1,y1,z1,a0,a1,a2,a3,a4,a5,a6,a7,a8>=PolynomialRing(QQ,order=TermOrder('degrevlex',
6) + TermOrder('degrevlex',10))
I = Ideal([a0-z1*z0,a1-(z1*y0 + y1*z0),a2-y1*y0,a3-(z1*x0 + x1*z0),a4-
(y1*x0 + x1*y0),a5-x1*x0,a6-(x0+x1),a7-(y0+y1),a8-(z0+z1)])
b=z0^2
b in I
causes:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_3.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding:
utf-8 -*-\\n" +
_support_.preparse_worksheet_cell(base64.b64decode("Ui48eDA
+PVBvbHlub21pYWxSaW5nKFpaLDEpCkY9eDBeNC0yKngwXjIteDAKUi48eDAseTAsejAseDEseTEsejEsYTAsYTEsYTIsYTMsYTQsYTUsYTYsYTcsYTg
+PVBvbHlub21pYWxSaW5nKFFRLG9yZGVyPVRlcm1PcmRlcignZGVncmV2bGV4Jyw2KSArIFRlcm1PcmRlcignZGVncmV2bGV4JywxMCkpCkkgPSBJZGVhbChbYTAtejEqejAsYTEtKHoxKnkwICsgeTEqejApLGEyLXkxKnkwLGEzLSh6MSp4MCArIHgxKnowKSxhNC0oeTEqeDAgKyB4MSp5MCksYTUteDEqeDAsYTYtKHgwK3gxKSxhNy0oeTAreTEpLGE4LSh6MCt6MSldKQpiPXowXjIKYiBpbiBJ"),globals())
+"\\n"); execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File "/tmp/tmpDHv_Hq/___code___.py", line 8, in <module>
exec compile(u'b in I
File "", line 1, in <module>
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/
rings/ideal.py", line 259, in __contains__
return self._contains_(self.__ring(x))
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.py", line 3387, in _contains_
g = f.reduce(self.groebner_basis())
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/misc/
cachefunc.py", line 555, in __call__
w = self._cachedmethod._instance_call(self._instance, *args,
**kwds)
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/misc/
cachefunc.py", line 778, in _instance_call
return self._cachedfunc.f(inst, *args, **kwds)
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.py", line 3158, in
groebner_basis
gb = self._groebner_basis_libsingular("groebner",
deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.py", line 502, in wrapper
return func(*args, **kwds)
File "/home/ben/sage-4.8/local/lib/python2.6/site-packages/sage/
rings/polynomial/multi_polynomial_ideal.py", line 1600, in
_groebner_basis_libsingular
S = groebner(self)
File "function.pyx", line 1036, in
sage.libs.singular.function.SingularFunction.__call__ (sage/libs/
singular/function.cpp:10130)
File "function.pyx", line 1204, in
sage.libs.singular.function.call_function (sage/libs/singular/
function.cpp:11392)
File "function.pyx", line 1206, in
sage.libs.singular.function.call_function (sage/libs/singular/
function.cpp:11306)
RuntimeError: Segmentation fault
If you change the 10 in the term order to the correct number of
variables: 9, then it works fine.
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