ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 22 Feb 2013 19:15:39 +0100Polynomial as a sum of simply factored expressions?https://ask.sagemath.org/question/9761/polynomial-as-a-sum-of-simply-factored-expressions/The polynomial
p^9 + p^8 + 7*p^6 + 6*p^4 + 3*p^3 + 4*p^2 + 2
can't be factored (over the rationals). However, it can be expressed in simpler form as
(p^3+1)^3 + (p^2+1)^4
Is there any way (other than trial and error) of finding such a sum, for a given (multivariate) polynomial?Tue, 19 Feb 2013 04:56:58 +0100https://ask.sagemath.org/question/9761/polynomial-as-a-sum-of-simply-factored-expressions/Answer by lftabera for <p>The polynomial</p>
<pre><code>p^9 + p^8 + 7*p^6 + 6*p^4 + 3*p^3 + 4*p^2 + 2
</code></pre>
<p>can't be factored (over the rationals). However, it can be expressed in simpler form as</p>
<pre><code>(p^3+1)^3 + (p^2+1)^4
</code></pre>
<p>Is there any way (other than trial and error) of finding such a sum, for a given (multivariate) polynomial?</p>
https://ask.sagemath.org/question/9761/polynomial-as-a-sum-of-simply-factored-expressions/?answer=14581#post-id-14581Not that I am aware of, I think that you are looking for a sort of arithmetic circuit evaluating your polynomial
http://en.wikipedia.org/wiki/Arithmetic_circuit_complexityFri, 22 Feb 2013 19:15:39 +0100https://ask.sagemath.org/question/9761/polynomial-as-a-sum-of-simply-factored-expressions/?answer=14581#post-id-14581