I have cc'd this to the FriCAS list in hopes of getting more feedback.
On Wed, Jul 18, 2018 at 3:19 PM, Raymond Rogers
<[email protected]> wrote:
> Finally got back to this. Success and (3*x*y+5*y*x)^3 takes
> almost exactly the same amount of time with your process and
> mine.
> Some organization questions.
> 1) I downloaded the ncpoly package from github and there seems to be a wide
> discrepancy between nc_ini04.input between the two; so I used your attached
> one. The attached works fine.
> 2) The xdpoly_fact.input had a XDP assignment p_1 before function
>definition but I just commented it out.
No problem. This is just temporary initialization for test/development
anyway. We really need a proper testsuite-style input file to include
in the distribution.
> 3) I can't
> )trace factor
> I presume that this buried some way.
?? buried ?? I almost never use )trace so maybe this isn't quite what
you meant. First note that in this case 'factor' is not exported by a
domain but rather it is a function/operator exported by the package
called XDPOLYF1.
This seems to work:
(45) -> )trace XDPOLYF1 )ops factor
Packages traced:
XDistributedPolynomialFunctions1([x,y,z,w,x1,x2,x3,x4,x5],
Integer)
Parameterized constructors traced:
XDPOLYF1
(45) -> factor f10
1<enter XDistributedPolynomialFunctions1.factor,142 : (((#1=(1 . 1)
...
1>exit XDistributedPolynomialFunctions1.factor,142 : ((((#1=(1 . 1)
#2=(2 . 1))
. -1)
(NIL . 1))
((((2 . 1) #1#) . 1)
(NIL . 2))
(((#2# (3 . 1)) . -1)
(NIL . 3))
((((3 . 1) #2#) . -1)
(NIL . 2))
(((#1# (3 . 1)) . -1)
(NIL . 1)))
(45) [1 - x y, 2 + y x, 3 - y z, 2 - z y, 1 - x z]
Type:
List(XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Integer))
Time: 0.70 (EV) = 0.70 sec
(46) ->
> Should I write a factor wrapper
> factor_1 (probably three lines) to use trace timing although that
> won't allow me to peek inside but I don't particularly want to if it
> works.
I am not sure. You might be able to get better advice from other
people who are more familiar with using the )trace facilities.
> 4) Your f10 seems to have a problem; have you resolved it or do
> you think it's intrinsic?
The main limitation has to do with the total number of equations (>> 1000).
> I keep hoping to think of some trick to get my extended
> polynomial and things like f10 under control.
> "no joy in Mudville"
>
The code that I committed yesterday to ncpoly on github yesterday
contains a heuristic that allows the f10 example to be computed in a
few seconds. It seems that using this technique it is possible to
factor dense non-commutative polynomials up to at least degree 10.
Some sparse polynomials of higher degree also work but it seems easy
generate examples that fail or take too long (> 5 minutes).
> Finally, my mind pulled up some references from the distant past:
> Integral Matrices by Morris Newman and my Generating Function work.
> It amazing how similar the equations and procedures are to Konrad's
> references.
> Unfortunately Morris's relevant development seems concentrated on
> commutative Principal Ideal Rings whereas the nc_poly theory is based
> on noncommunative Principal Ideal Rings (which I really hope is proved
> somewhere in the references).
> In any case I will get back to the test harness construction shortly.
> Probably not for a couple of days, I am going to try out using a SSD
> and usually manage to expand an hours worth of work to days. I'll
> see.
>
As I see it, the xdpoly stuff is mostly separate from Konrad's ncpoly
domain but it may be useful for testing and as a benchmark.
> Are you going to push your recent coding to github?
>
See:
https://github.com/billpage/ncpoly/blob/master/xdpolyf1.spad
Please pull the new version. I have also included a lot more comments
in the code. I would be happy to receive comments and questions.
Bill Page.
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