Hello,

Ursula Whitcher <urs...@yarntheory.net> wrote:

> Asking Sage to compute the cardinality of point sets of projective
> varieties over finite fields produces an infinite recursion error.
> This is weird, since the count_points() function works just fine
> (albeit slowly) in this situation.

This is very likely the bug reported at
<https://trac.sagemath.org/ticket/18400>.

Peter


> Here's an example.
> Entering:
> F = FiniteField(37)
> P3.<x,y,z,w> = ProjectiveSpace(3,F)
> P3.point_set().cardinality()
> yields an error that begins:
> Error in lines 3-3 Traceback (most recent call last): File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/smc_sagews/sage_server.py",
> line 976, in execute exec compile(block+'\n', '', 'single') in namespace,
> locals File "", line 1, in <module> File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in cardinality return sum(ZZ.one() for point in self) File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in <genexpr> return sum(ZZ.one() for point in self) File
> "sage/structure/parent.pyx", line 1596, in
> sage.structure.parent.Parent.__getitem__
> (/projects/sage/sage-7.3/src/build/cythonized/sage/structure/parent.c:12913)
> return self.list()[n] File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 602, in list return tuple(self) File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in cardinality return sum(ZZ.one() for point in self) File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in <genexpr> return sum(ZZ.one() for point in self) File
> "sage/structure/parent.pyx", line 1596, in
> sage.structure.parent.Parent.__getitem__
> (/projects/sage/sage-7.3/src/build/cythonized/sage/structure/parent.c:12913)
> return self.list()[n]
> continues looping for a while, and ends:
> File "sage/structure/parent.pyx", line 1596, in
> sage.structure.parent.Parent.__getitem__
> (/projects/sage/sage-7.3/src/build/cythonized/sage/structure/parent.c:12913)
> return self.list()[n] File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 602, in list return tuple(self) File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in cardinality return sum(ZZ.one() for point in self) File
> "/projects/sage/sage-7.3/local/lib/python2.7/site-packages/sage/schemes/generic/homset.py",
> line 584, in <genexpr> return sum(ZZ.one() for point in self) File
> "sage/structure/parent.pyx", line 1590, in
> sage.structure.parent.Parent.__getitem__
> (/projects/sage/sage-7.3/src/build/cythonized/sage/structure/parent.c:12742)
> meth = getattr_from_other_class(self, self._category.parent_class,
> '__getitem__') File "sage/structure/misc.pyx", line 250, in
> sage.structure.misc.getattr_from_other_class
> (/projects/sage/sage-7.3/src/build/cythonized/sage/structure/misc.c:1731)
> if isinstance(self, cls): RuntimeError: maximum recursion depth exceeded
> while calling a Python object
> On the other hand,
> P3.count_points(1)
> returns [52060].
> --Ursula.
>
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