On Feb 15, 10:59 am, Simon King <simon.k...@uni-jena.de> wrote:
> On 15 Feb., 16:37, Simon King <simon.k...@uni-jena.de> wrote:
>
> > Yep:
> > sage: a = SR(-1)
> > sage: b = SR(-1/5)
> > sage: sage.rings.arith.gcd(a,b)
> > 1 # or 1/5 with my patch.
>
> No, I was mistaken. Everything can be traced back to g_gcd, which is
> called in sage.symbolic.expression.Expression.gcd. At that point, I
> lost track: I can not find the code of g_gcd (even "grep g_gcd" does
> not give me a hint). In particular, I did not change g_gcd, but it
> seems that my patch had a side effect on it.
>
This is undoubtedly the Ginac gcd. In libs/ginac/decl.pxi:
# Algorithms
GEx g_gcd "gcd"(GEx a, GEx b) except +
So it is using the Ginac gcd, and calling it 'g_gcd'. And all of that
is in a call
cdef extern from "ginac_wrap.h":
which lives in devel/sage/c_lib/include. I understand nearly
nothing about headers, but I think that
py_funcs_struct py_funcs "GiNaC::py_funcs"
means that py_gcd is going to be under this. Notice that Pynac
headers live in $SAGE_ROOT/local/include/pynac.
Anyway, in Ginac the gcd is defined in numeric.cpp, and if we look at
http://pynac.sagemath.org/hg/file/b233d9dadcfa/ginac/numeric.cpp#l1
we get
/** Greatest Common Divisor.
2527 *
2528 * @return The GCD of two numbers if both are integer, a
numerical 1
2529 * if they are not. */
2530 const numeric gcd(const numeric &a, const numeric &b)
2531 {
2532 verbose("gcd(a,b)");
2533 PyObject *aa = Number_T_to_pyobject(a.value), *bb =
Number_T_to_pyobject(b.value);
2534 PyObject *ans = py_funcs.py_gcd(aa, bb);
2535 if (!ans) py_error("gcd");
2536 Py_DECREF(aa); Py_DECREF(bb);
2537 return ans;
2538 }
Which means that in fact it does use the Sage GCD as in my earlier
post. And I think it's probable that it uses this in some way to
decide whether to take out a -1? I'm sorry I can't help further - the
internals and C++ are beyond me. I don't know if we want to modify
Ginac to change this, though.
- kcrisman
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