I believe there is a Heisenbug in src/sage/rings/function_field/ideal.py.
Here is a specific test that can sometimes fail:
sage: K.<x> = FunctionField(GF(3^2)); R.<t> = K[]
sage: F.<y> = K.extension(t^3 + t^2 - x^4)
sage: Oinf = F.maximal_order_infinite()
sage: I = Oinf.ideal(1/y)
sage: I.factor() # This will sometimes fail
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-2-b9ca13965ba4> in <module>()
----> 1 I.factor()
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/
function_field/ideal.pyc in factor(self)
2671 defined by y^2 + y + (x^2 + 1)/x)^2
2672 """
-> 2673 return Factorization(self._factor(), cr=True)
2674
2675 def _factor(self):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/function_field/ideal.pyc
in _factor(self)
2693
2694 factors = []
-> 2695 for iprime, exp in O._to_iF(self).factor():
2696 prime = FunctionFieldIdealInfinite_global(O, iprime)
2697 factors.append((prime, exp))
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/function_field/ideal.pyc
in factor(self)
1572 True
1573 """
-> 1574 return Factorization(self._factor(), cr=True)
1575
1576 def _factor(self):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/
function_field/ideal.pyc in _factor(self)
1598 primes = set([o.ideal(p) for p,_ in d.factor()] + [p for p,_
in i.ideal_below().factor()])
1599 for prime in primes:
-> 1600 qs = [q[0] for q in O.decomposition(prime)]
1601 for q in qs:
1602 exp = q.valuation(self)
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller.__call__ (build/cythonized/sage/
misc/cachefunc.c:10824)()
1951 return cache[k]
1952 except KeyError:
-> 1953 w = self._instance_call(*args, **kwds)
1954 cache[k] = w
1955 return w
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/misc/cachefunc.pyx
in sage.misc.cachefunc.CachedMethodCaller._instance_call (build/cythonized/
sage/misc/cachefunc.c:10280)()
1827 True
1828 """
-> 1829 return self.f(self._instance, *args, **kwds)
1830
1831 cdef fix_args_kwds(self, tuple args, dict kwds):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/function_field/order.pyc
in decomposition(self, ideal)
1838
1839 # J_1, J_2, ...
-> 1840 Jb =[Kb[0]] + [div(Kb[j],Kb[j-1]) for j in
range(1,len(Kb))]
1841
1842 # H_1, H_2, ...
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/function_field/order.pyc
in div(Ib, Jb)
1805 sJb = Jb.row_space()
1806 sIb = Ib.row_space()
-> 1807 sJbsIb,proj_sJbsIb,lift_sJbsIb =
sJb.quotient_abstract(sIb)
1808 supplement_basis = [lift_sJbsIb(v) for v in
sJbsIb.basis()]
1809
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/modules/free_module.pyc
in quotient_abstract(self, sub, check)
4546 # Calling is_subspace may be way too slow and repeat work
done below.
4547 # It will be very desirable to somehow do this step better.
-> 4548 if check and (not is_FreeModule(sub) or not
sub.is_subspace(self)):
4549 try:
4550 sub = self.subspace(sub)
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/modules/free_module.pyc
in is_subspace(self, other)
3790 True
3791 """
-> 3792 return self.is_submodule(other)
3793
3794 def span(self, gens, base_ring=None, check=True,
already_echelonized=False):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/modules/
free_module.pyc in is_submodule(self, other)
1458 from sage.misc.flatten import flatten
1459 return all(x in S for x in flatten(M))
-> 1460 return all(x in S for x in M.list())
1461
1462 def __iter__(self):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/matrix/matrix0.pyx
in sage.matrix.matrix0.Matrix.list (build/cythonized/sage/matrix/matrix0.c:
4165)()
154 [ y x 2*x + y]
155 """
--> 156 return list(self._list())
157
158 def _list(self):
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/matrix/matrix_gfpn_dense.pyx
in sage.matrix.matrix_gfpn_dense.Matrix_gfpn_dense._list
(build/cythonized/sage/matrix/matrix_gfpn_dense.c:9038)()
908 FfStepPtr(&(p))
909 sig_check()
--> 910
x.extend([self._converter.int_to_field(FfToInt(FfExtract(p,j))) for j in
range(self.Data.Noc)])
911 self.cache('list', x)
912 return x
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/matrix/matrix_gfpn_dense.pyx
in sage.matrix.matrix_gfpn_dense.FieldConverter_class.int_to_field
(build/cythonized/sage/matrix/matrix_gfpn_dense.c:3717)()
135
136 """
--> 137 return self.field(x)
138 cpdef int field_to_int(self, x):
139 """
/home/uqtscrim/sage/local/lib/python2.7/site-packages/sage/rings/finite_rings/element_givaro.pyx
in sage.rings.finite_rings.element_givaro.Cache_givaro.fetch_int
(build/cythonized/sage/rings/finite_rings/element_givaro.cpp:8618)()
591
592 if n<0 or n>k.cardinality():
--> 593 raise TypeError("n must be between 0 and self.order()")
594
595 for i from 0 <= i < k.exponent():
TypeError: n must be between 0 and self.order()
sage: I.factor()
(Ideal (1/x,1/x^3*y^2) of Maximal infinite order of Function field in y
defined by y^3 + y^2 + 2*x^4)^4
In the file, I can get anywhere between 0 and 6 tests failing. Note that
once this works, it never seems to fail. Also, inserting output into the
error, n = 255 and self.order() = 9. I suspect the problem is in
Matrix_gfpn_dense as this is not a problem when I go to GF(19^2). I should
note that I do have meataxe installed, and I suspect people without meataxe
will not have this failure.
Best,
Travis
On Monday, October 1, 2018 at 8:55:05 AM UTC+10, Volker Braun wrote:
>
> As always, you can get the latest beta version from the "develop" git
> branch. Alternatively, the self-contained source tarball is at
> http://www.sagemath.org/download-latest.html
>
>
> a1bfef8cf3 (tag: 8.4.beta7, trac/develop) Updated SageMath version to
> 8.4.beta7
> cbd85e1df0 Trac #26353: MR1: Remove special case for Cygwin for BLAS
> detection when installing fflas_ffpack
> a090fd23c8 Trac #25913: Allow input as packed words for Hopf algebra WQSym
> 4048cdea8c Trac #26352: Lie algebra quotients are incorrect for some basis
> orders
> 958b066cf6 Trac #26232: enhance pari conversion of elliptic curves over
> number field
> dfa5859869 Trac #25435: Global function fields: orders and ideals
> cf373c1968 Trac #12567: Implement p-adic n-th roots
> 83f13e288a Trac #26350: Add citations to polymake papers
> e643ef4bf4 Trac #26346: py3: a bit of work in src/doc
> fdfbfef6ab Trac #26347: clean deprecation warning in doctests for paths.py
> + animate.py
> 15dbacc580 Trac #26342: Improve triconnectivity algorithm: avoid recursive
> calls
> 24442c1091 Trac #25057: Building ecl-16.1.2 fails on some Cygwin versions
> 19cff46d56 Trac #24589: Pickling matrices over GF(2) does not preserve
> their immutability
> 039b874739 Trac #26080: The Baker-Campbell-Hausdorff formula for nilpotent
> Lie algebras
> d72db87107 Trac #26016: py3: miscellaneous fixes and cleanup to
> sage.sandpiles
> 02e5631e78 Trac #26011: Copying package files is really slow
> 6e84381666 Trac #26341: py3: misc open(...) -> with open(...) fixes
> bbc97631c5 Trac #26325: Upgrade nose to 1.3.7
> d8efd6a554 Trac #26323: small update of faq_usage
> cabf20b1dd Trac #26299: py3: use repr for floats in plot3d file format
> outputs
> 9ad5cf0c99 Trac #26335: PicoSAT solver
> df44cb2c3c Trac #26334: Package pycosat
> a74f7590ad Trac #26329: Allow xor clause in DIMACS files (format extended
> by cryptominisat)
> 957af679a7 Trac #25395: Support for binary quintics in invariant_theory
> e2e3f3f9bd Trac #26338: Fix documentation formatting in modular symbol
> space
> 7c8d581c7c Trac #26336: Fix latex typos in sfa.py
> 614c0368ec Trac #26227: Make search_doc independent of sage_setup
> b84538eeea (tag: 8.4.beta6) Updated SageMath version to 8.4.beta6
>
>
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