move genus method to libsingular in function field

[fchapoton]

switch the genus method to use libsingular

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[kwankyu]

On my system:

sage: K.<x> = FunctionField(QQ); R.<y> = K[]
sage: L.<y> = K.extension(y^3 - (x^3 + 2*x*y + 1/x))
sage: self = L
sage: from sage.libs.singular.function import singular_function, lib as singular_lib
....: # making the auxiliary ring which only has polynomials
....: # with integral coefficients.
....: tmpAuxRing = PolynomialRing(self._base_field.constant_field(),
....:     str(self._base_field.gen()) + ',' + str(self._ring.gen()))
....: intMinPoly, d = self._make_monic_integral(self._polynomial)
....: curveIdeal = tmpAuxRing.ideal(intMinPoly)
....: 
sage: singular_lib('normal.lib')  # loading genus method in Singular
sage: genus = singular_function("genus")
sage: from sage.interfaces.singular import singular
sage: singular.lib('normal.lib')  # loading genus method in Singular 
sage: timeit('genus(curveIdeal)')
5 loops, best of 3: 62.5 ms per loop
sage: timeit('int(curveIdeal._singular_().genus())')
25 loops, best of 3: 20.3 ms per loop
sage: timeit('genus(curveIdeal)')
5 loops, best of 3: 62.4 ms per loop
sage: timeit('int(curveIdeal._singular_().genus())')
25 loops, best of 3: 20.4 ms per loop

[fchapoton]

damn.. This is a bit schoking..

[kwankyu]

Yeah.. That is against my expectation too :-(

[kwankyu]

We may be just unlucky -- The example may be too small. I didn't try other examples.

[fchapoton]

on my system (ubuntu Linux 22.04), with your exemple :

sage: timeit('genus(curveIdeal)')
5 loops, best of 3: 15.7 ms per loop
sage: timeit('int(curveIdeal._singular_().genus())')
25 loops, best of 3: 16.1 ms per loop
sage: timeit('genus(curveIdeal)')
25 loops, best of 3: 15.6 ms per loop
sage: timeit('int(curveIdeal._singular_().genus())')
25 loops, best of 3: 16.2 ms per loop

so libsingular wins for me by a small amount..

[kwankyu]

My system is mac. Unfortunately, the loss on mac is much more significant than the gain on linux...

@tscrim @mkoeppe: how about on your system?

[fchapoton]

This may hint at a serious underlying speed issue for libsingular on mac ?