A new version with some improvements:
http://www.math.uni.wroc.pl/~hebisch/fricas/xpfact2.spad
In particular
factor((x^4 + 5)*(x^4 + x + 7))
is now much faster (previously needed 2397.40 sec on my machine).
--
Waldek Hebisch
--
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I have now put Spad version of factorization code at:
http://www.math.uni.wroc.pl/~hebisch/fricas/xpfact.spad
--
Waldek Hebisch
--
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Bill Page wrote:
>
>
> Since the number of factorizations of a non-commutative polynomial
> over a unique factorization domain is finite but not unique there may
> be some applications where it maybe interesting to know more than one
> or even all possible factorizations. Your current
Waldek,
On Sat, Nov 10, 2018 at 12:02 PM you wrote:
>
> One update to what I wrote before. In
>
> J. P. Bell, A. Heinle, and V. Levandovskyy,
> On Noncommutative Finite Factorization Domains,
> Trans. Amer. Math. Soc. 369 (2017), 2675-2695
>
> there is proof of finite number of factorizations.
>
>
> That looks great!
>
> As a performance test I tried this:
>
> (79) -> h2323:=((h2*h3*h2*h3)^2);
>
> Type:
> XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer))
>Time: 0.00 (IN) + 2.71 (EV) + 0.00 (OT) = 2.71 sec
> (80) ->
Bill Page wrote:
>
> As a performance test I tried this:
>
> (79) -> h2323:=((h2*h3*h2*h3)^2);
>
> Type:
> XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer))
>Time: 0.00 (IN) + 2.71 (EV) + 0.00 (OT) = 2.71 sec
> (80) -> dc_fact
That looks great!
As a performance test I tried this:
(79) -> h2323:=((h2*h3*h2*h3)^2);
Type:
XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Fraction(Integer))
Time: 0.00 (IN) + 2.71 (EV) + 0.00 (OT) = 2.71 sec
(80) -> dc_fact h2323
(80)
Bill Page wrote:
>
> On Sat, Nov 10, 2018 at 12:02 PM Waldek Hebisch
> 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
> >
> > On Sat, Nov 10, 2018 at 12:02 PM Waldek Hebisch
> > 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
> > >
On Sat, Nov 10, 2018 at 9:08 PM Bill Page wrote:
>
> On Sat, Nov 10, 2018 at 12:02 PM Waldek Hebisch
> 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
> >
On Sat, Nov 10, 2018 at 12:02 PM Waldek Hebisch
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,
One update to what I wrote before. In
J. P. Bell, A. Heinle, and V. Levandovskyy,
On Noncommutative Finite Factorization Domains,
Trans. Amer. Math. Soc. 369 (2017), 2675-2695
there is proof of finite number of factorizations.
I have now implemented the lift part of Davenport-Caruso method.
Bill Page wrote:
>
> On Tue, Nov 6, 2018 at 5:32 PM Bill Page wrote:
> >
> > On Tue, Nov 6, 2018 at 8:35 AM Waldek Hebisch
> > wrote:
> >
> > > Since nobody seems to be interested in coding Davenport method
> > > I did that.
> > ...
> > (111) -> homo_fact((x^2-1)^2)
> >
> > 2
Surprisingly a non-homogeneous polynomial of the same degree works OK
(69) -> factor((h3+1)*(h3+1))
(69)
[1 - z y x + z x y + y z x - y x z - x z y + x y z,
1 - z y x + z x y + y z x - y x z - x z y + x y z]
Type:
On Wed, Nov 7, 2018 at 8:37 AM Ray wrote:
> ...
> So homo_fact((x^2-y^2)^2)
> would succeed?
>
Yes.
(66) -> homo_fact((x^2-y^2)^2)
22 22
(66) [- y + x , - y + x ]
Type:
List(XDistributedPolynomial(OrderedVariableList([x,y,z,w,x1,x2,x3,x4,x5]),Integer))
On 11/7/18 8:34 AM, Bill Page wrote:
> On Tue, Nov 6, 2018 at 5:32 PM Bill Page wrote:
>>
>> On Tue, Nov 6, 2018 at 8:35 AM Waldek Hebisch
>> wrote:
>>
>>> Since nobody seems to be interested in coding Davenport method
>>> I did that.
>> ...
>> (111) -> homo_fact((x^2-1)^2)
>>
>>
On Tue, Nov 6, 2018 at 5:32 PM Bill Page wrote:
>
> On Tue, Nov 6, 2018 at 8:35 AM Waldek Hebisch
> wrote:
>
> > Since nobody seems to be interested in coding Davenport method
> > I did that.
> ...
> (111) -> homo_fact((x^2-1)^2)
>
> 24
>(111) [1 - 2 x + x ]
> Type:
On Tue, Nov 6, 2018 at 8:35 AM Waldek Hebisch wrote:
>
> > earlier patch. Here is a revised patch that corrects this problem.
> > (Only one additional change at the beginning.)
>
> I have tried:
>
> h3 := x*y*z - x*z*y + z*x*y - z*y*x + y*z*x - y*x*z
> factor(h3*h3)
>
> and after about hour I
> earlier patch. Here is a revised patch that corrects this problem.
> (Only one additional change at the beginning.)
I have tried:
h3 := x*y*z - x*z*y + z*x*y - z*y*x + y*z*x - y*x*z
factor(h3*h3)
and after about hour I did not get answer.
Since nobody seems to be interested in coding
On Sun, Nov 4, 2018 at 8:03 AM Waldek Hebisch wrote:
...
>
> > enough. The following patch corrects this problem:
>
> Before the patch
>
> f101 := (x*z - z*x)^2 - 2
>
> was immediately recognized as irreducible. With the patch I did not
> get answer for several minutes (may be I am not patient
Bill Page wrote:
>
> > On 10/22/18 9:55 AM, Waldek Hebisch wrote:
> > > I looked at noncommutative factorization code and AFAICS
> > > 'xdpolyf1.spad' has serious problem. One example is:
> > >
> > > (58) -> factor((x^2 - 2)*(y - 1)*(x - 1))
> > >
> > > 2
I should amend my previous mail on this. Fist, why I wrote
about finite number of factorizations? The reason is that
when we have finite number of soultion to the equation system
coming from factorization, then one can find if solution is
in base field. In fact, simple method of filtering out
I looked more at the problem. It seems that Cohn claims
that there are finitely many factorizations, but he jumps
over few subtle points so I need to check his arguments
more carefuly.
AFAICS Caruso (after Davenport) gives correct proof that
factorization of homogeneous polynomials is unique and
Bill Page wrote:
>
> On Wed, Oct 24, 2018 at 5:05 PM Waldek Hebisch
> wrote:
> >
> > If you could find solution _in the fraction field_ then
> > the method would be fine. However, in general finding
> > rational solutions to polynomial system of equations is
> > uncomputable.
>
> Can you
On 10/24/18 9:27 PM, Bill Page wrote:
> On Wed, Oct 24, 2018 at 5:05 PM Waldek Hebisch
> wrote:
>>
>> If you could find solution _in the fraction field_ then
>> the method would be fine. However, in general finding
>> rational solutions to polynomial system of equations is
>> uncomputable.
>
On Wed, Oct 24, 2018 at 5:05 PM Waldek Hebisch wrote:
>
> If you could find solution _in the fraction field_ then
> the method would be fine. However, in general finding
> rational solutions to polynomial system of equations is
> uncomputable.
Can you suggest a reference? I could not find this
On 10/24/18 4:09 PM, Bill Page wrote:
>> I tried this on my saved version (part of a test -harness) and it works
>> correctly.
>> Here is the result
>> (52) -> aa:=(x^2 - 2)*(y - 1)*(x - 1)
>>
>> 22 32
>>(52) - 2 + 2 y + 2 x - 2 y x + x - x
Raymond Rogers wrote:
> Attached is a test file.
> Let me know if you are interested in a full test suite and harness?
> I also have Konrad Schrempf's next to last entry solving factoring.
> I have personal copies (more than I need) of both with a plethora of
> testing :)
> I defined "aa" to make
Bill Page wrote:
>
> > On 10/22/18 9:55 AM, Waldek Hebisch wrote:
>
> > > More generally, factorization via equation solving directly
> > > gives absolute factorization, that is factorization over algebraic
> > > closure of base field. To get factorization over base field
> > > one needs to
> On 10/22/18 9:55 AM, Waldek Hebisch wrote:
> > I looked at noncommutative factorization code and AFAICS
> > 'xdpolyf1.spad' has serious problem. One example is:
> >
> > (58) -> factor((x^2 - 2)*(y - 1)*(x - 1))
> >
> > 22 32
> >(58) [- 2 + 2
On 10/22/18 9:55 AM, Waldek Hebisch wrote:
> I looked ate noncommutative factorization code and AFAICS
> 'xdpolyf1.spad' has serious problem. One example is:
>
> (58) -> factor((x^2 - 2)*(y - 1)*(x - 1))
>
> 22 32
>(58) [- 2 + 2 y + 2 x -
I looked ate noncommutative factorization code and AFAICS
'xdpolyf1.spad' has serious problem. One example is:
(58) -> factor((x^2 - 2)*(y - 1)*(x - 1))
22 32
(58) [- 2 + 2 y + 2 x - 2 y x + x - x y - x + x y x]
Type:
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