Recent changes to 40: nc_factorize wrong outputhttps://sourceforge.net/p/reduce-algebra/bugs/40/2016-02-29T21:02:06Z#40 nc_factorize wrong output2016-02-29T21:02:06Z2016-02-29T21:02:06ZRainer Schöpfhttps://sourceforge.net/u/schoepf/https://sourceforge.netd04ce6003e04c5a52a2603831769f3adb97e4095<div class="markdown_content"><p>The car/cdr of nil comes from an incorrect trace output - corrected</p></div>#40 nc_factorize wrong output2016-02-28T18:43:13Z2016-02-28T18:43:13ZThomas Sturmhttps://sourceforge.net/u/thomas-sturm/https://sourceforge.net73485876518137f24093d65845aa89a026311c66<div class="markdown_content"><p>I came across this one only today and spent some time on it:</p>
<p>Here is what I found out:</p>
<ul>
<li>Commutative factorization is combined with an approach where solve is applied. I guess that one tries to solve for the coefficients of generic candidates for factors.</li>
<li>There is a smaller example causing the problem (i.e. false negative): <code>h1 := (d^4+x+d*x)*(d+x+x*d);</code></li>
<li>An even smaller problem crashes with car access to an atom: <code>h1 := (d^4+x+d*x)*(d+x+x*d);</code></li>
<li>Trace output including the generated equations for solve can be obtained via <code>h1 := (d^4+x+d*x)*(d+x+x*d);</code></li>
</ul>
<p>I am attaching a file for playing.</p>
<p>Maybe there is someone more familiar with this code than I am?</p></div>nc_factorize wrong output2012-09-08T13:10:36Z2012-09-08T13:10:36ZAlbert Heinlehttps://sourceforge.net/u/ioah86/https://sourceforge.net067f91368c50d7bff6df194a068671fbab3eef3cHello 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