On Sat, Nov 10, 2018 at 12:02 PM Waldek Hebisch
<[email protected]> wrote:
...
>
> I have now implemented the lift part of Davenport-Caruso method.
> You fetch code at:
>
> http://www.math.uni.wroc.pl/~hebisch/fricas/dcfact2.input
> http://www.math.uni.wroc.pl/~hebisch/fricas/nc_ini04c.input
>
> As before, dcfact2.input is an actual routine, nc_ini04c.input
> set up needed types.
>
> You can try things like:
>
> dc_fact(((x*z - z*x)^2 - 2)*((x*z - z*x)^2 - 3)*((x*z - z*x)^2 - 5))
>
> The idea is like in Caruso preprint, but code differs -- I coded
> what follows by working out solutions to lift equations.
>
> The code is unoptimized, for example for homogeneous polynomials
> it runs the whole lift, while we know that the factorization must
> be homogeneous... Also, code introduces extra parameters
> when there is overlap between leading monomials of top factors,
> while in many cases this parameter could be immediately eliminated.
> Still, it seem to work quite a bit faster than xdpolyf1.spad.
>
> --
This looks very promising however I did find this apparent failure:
(82) -> h3
(82) - z y x + z x y + y z x - y x z - x z y + x y z
Type:
XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer))
Time: 0.00 (OT) = 0.00 sec
(83) -> dc_fact((3+x*z*y)*h3)
(83)
[
- 3 z y x + 3 z x y + 3 y z x - 3 y x z - 3 x z y + 3 x y z - x z y z y x
+
2 2
x z y z x y + x z y z x - x z y x z - x z y x z y + x z y x y z
]
Type:
List(XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer)))
Time: 0.00 (OT) = 0.00 sec
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