On Sat, Nov 10, 2018 at 9:08 PM Bill Page <[email protected]> wrote:
>
> 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.
...
>
> 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
For comparison here is the output of Konrad Schrempf's program:
(1) -> )r nc_ini14.input
...
(52) -> h3 := x*y*z - x*z*y + z*x*y - z*y*x + y*z*x - y*x*z
(52)
AGGSET
+1 - x - z 0 - y 0 0 0 + + 0 +
| | | |
| 1 0 z 0 0 y 0 | | 0 |
| | | |
| 1 - x 0 y 0 0 | | 0 |
| | | |
| 1 0 0 0 y | | 0 |
| |s = | |
| 1 - z - x 0 | | 0 |
| | | |
| 1 0 x | | 0 |
| | | |
| 1 - z| | 0 |
| | | |
+ 1 + +- 1+
,
MR
,
- z y x + z x y + y z x - y x z - x z y + x y z
Type:
FreeDivisionAlgebra(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer))
Time: 0.00 (IN) + 0.03 (EV) + 0.01 (OT) = 0.04 sec
(53) -> map(x+->x::XDP,factor((3+x*z*y)*h3))
(53) [3 + x z y, - z y x + z x y + y z x - y x z - x z y + x y z]
Type:
List(XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer)))
Time: 0.00 (IN) + 0.16 (EV) + 0.01 (OT) = 0.17 sec
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