If anybody is interested:
In
A Standard Form in (some)
Free Fields: How to construct
Minimal Linear Representations
Konrad Schrempf
1803.10627.pdf
1) On page 7 "Scalar Multiplication" (first line) my original question
is defined/stated. I will follow up on checking how to access it in the
n
In principle what you want to do is not that difficult. You need the base
field to be something like Expression or maybe Fraction
MultivariatePolynomial, etc. , then the noncommutative polynomials are
defined over that. What is sometimes a bit tricky is to convince the
interpreter that certain symb
On 05/29/2018 09:24 AM, Bill Page wrote:
On Mon, May 28, 2018 at 9:55 AM, Franz Lehner wrote:
On Mon, 28 May 2018, Bill Page wrote:
That's a pity. Is the problem with the published algorithm or the source
code?
Factorization of noncommutative polynomials seems to be a difficult problem.
Se
>> https://arxiv.org/abs/1706.01806
Oho... That paper cites FriCAS directly (obviously for computing a
Gröbner basis).
Ralf
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On Mon, May 28, 2018 at 9:55 AM, Franz Lehner wrote:
> On Mon, 28 May 2018, Bill Page wrote:
>>
>> That's a pity. Is the problem with the published algorithm or the source
>> code?
>
> Factorization of noncommutative polynomials seems to be a difficult problem.
> See
> https://arxiv.org/abs/1706.
Hi Kurt
> The REDUCE ncpoly is quite slow
Perhaps, but it is useful for small expressions and is better than nothing.
> Singular's nfactor.lib is quite sophisticated
I just came across Singular. Looks pretty good.
> This might be a good opportunity for you to write a package ;)
I would love t
> That's a pity. Is the problem with the published algorithm or the source
code?
Fabrizio said there were some bugs in the code.
> The terms of XDPOLY consist of the "support" (an element of an
> FreeMonoid) and a coefficient. FreeMonoid exports "factors".
Thank you Bill!
On Mon, May 28, 201
Hi Marduk
You certainly know that this is not entirely trivial. The REDUCE ncpoly is quite
slow (at least it was some years go). IMO Singular's nfactor.lib is quite
sophisticated and could also be implemented in fricas (all structures are
already availabe, Ring, FreeModule(R,S) is nc ...
This migh
On Mon, 28 May 2018, Bill Page wrote:
That's a pity. Is the problem with the published algorithm or the source code?
Factorization of noncommutative polynomials seems to be a difficult
problem. See
https://arxiv.org/abs/1706.01806
for a recent new approach which reduces factorization to the so
On Mon, May 28, 2018 at 6:14 AM, Marduk BP wrote:
> It turns out that code was never released because it was buggy, so we
> can forget about it.
>
That's a pity. Is the problem with the published algorithm or the source code?
> But IMHO what I want to do does not require factoring a polynomial.
It turns out that code was never released because it was buggy, so we
can forget about it.
But IMHO what I want to do does not require factoring a polynomial. I just
want to extract the variables and their exponents from a monomial of
noncommutative variables.
There must be a (hopefully simple) w
Thank you Bill! I already contacted the author.
I also found out that REDUCE includes this functionality:
http://www.reduce-algebra.com/reduce38-docs/ncpoly.pdf
I think it should also be included in Axiom/FriCAS.
Marduk
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Perhaps this describes what you are looking for:
https://arxiv.org/abs/1002.3180
Factorization of Non-Commutative Polynomials
Fabrizio Caruso
(Submitted on 16 Feb 2010)
We describe an algorithm for the factorization of non-commutative
polynomials over a field. The first sketch of this algorithm
Dear all,
given a multivariate monomial defined with:
poly := MPOLY([x,y], Integer)
p : poly := 3*x*y
one can obtain the factors of the monomial with factors(p).
However, given a multivariate monomial with noncommutative variables
defined with:
ops := OVAR[A,B]
ncomm := XDPOLY(ops, Integer)
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