#40 nc_factorize wrong output

open
nobody
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5
2012-11-20
2012-09-08
Albert Heinle
No

Hello Reduce-Team,

I am working with noncommutative Polynomials in the first Weyl algebra, and Reduce provides a tool to factorize elements in that algebra.
While doing that, I discovered a reducible polynomial that was not factorized by reduce. I will provide you the input:

1: load_package "ncpoly";

2: nc_setup({x,d},{d*x-x*d=1});

3: h := (d^4+x^2+d*x+x)*(d^2+x^4+x*d+d);

6 5 5 4 4 4 3 3 3 2 2 2 5
h := x + x *d + x + x *d + 5*x + 16*x *d + x *d + 74*x *d + 2*x *d + x*d

3 2 6 5 4 2
+ x*d + 2*x*d + 99*x*d + d + d + 4*d + d + d + 24

4: nc_factorize(h);

6 5 5 4 4 4 3 3 3 2 2 2 5
{x + x *d + x + x *d + 5*x + 16*x *d + x *d + 74*x *d + 2*x *d + x*d

3 2 6 5 4 2
+ x*d + 2*x*d + 99*x*d + d + d + 4*d + d + d + 24}

As you see, h was clearly given reducible, but the output was just the trivial factorization, i.e. the polynomial itself.

Best regards,

Albert Heinle

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