On Tuesday, March 31, 2015 at 9:51:36 AM UTC-7, [email protected] wrote:
>
> I tried the following code (in
>
> 'Sage Version 6.5, Release Date: 2015-02-17')
>
>
> reset()
> x,y,z = QQ['x,y,z'].gens()
> C= Curve(x^3 - x^2*y - 2*x*y*z + y^2*z - z^3);
> C.genus();
>
> and got
>
>
> 4294967295
>
>
Well, if we interpret that value as "-1" then it is equal to (3-1)*(3-2)/2
- degree(singular locus), so it might be telling you a bit more than that
the curve is reducible (for one thing, it's compatible with defining the
genus in terms of the Euler characteristic as chi=2-2*g, which is additive
over components) Indeed, for
sage: C=Curve((x-y)*(y-z)*(z-x))
sage: C.genus()
4294967294
It may be noteworthy that on sage 5.10 I am getting -1 and -2, so we
somewhere had a regression where a 32bit integer from singular lands in a
64bit integer and thus we lose the sign.
It drills down to:
sage: import sage.libs.singular.function_factory
sage: sing_genus = sage.libs.singular.function_factory.ff.normal__lib.genus
sage: I=C.defining_ideal()
sage: sing_genus(I)
4294967294
sage: type(sing_genus)
<type 'sage.libs.singular.function.SingularLibraryFunction'>
In singular itself we do get a negative number:
> LIB "normal.lib";
> ring r=0,(x,y,z),dp;
> ideal i=(x-y)*(y-z)*(z-x);
> genus(i);
-2
so it's really in our conversion:
The line sage.lib.singular.function.pyx:951 seems to be to blame:
elif rtyp == INT_CMD:
return <long>to_convert.data
so somehow, singular has a 32-bit signed int there, and sage thinks `long`
means 64 bit. It's surprising to me that singular uses 32-bit integers
there, because looking through the singular code a bit, it seems that
functions that are listed as returning an "INT_CMD" do tend to cast their
result to `(long)`, which in C++ should usually mean 64-bit on a 64-bit
machine as well, I'd expect. This is now:
http://trac.sagemath.org/ticket/18096
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