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.Wed, 04 Jan 2017 12:11:07 +0100Linear Combination for Resultanthttps://ask.sagemath.org/question/36164/linear-combination-for-resultant/Let
R.<a, b, X> = ZZ[]
f = 1 - a*X^2
g = 1 - b*X^3
I need to compute polynomials `u` and `v` such that `u f + v g = r` where `r = f.resultant(g, X)`.
Pari has a function `polresultantext` for that purpose, so one solution for my problem is
(u, v, r) = (R(p) for p in f._pari_().polresultantext(g._pari_(), 'X'))
Nevertheless, I have a few questions:
* Is there a method in Sage which directly does this?
* Is the detour via Pari the recommended solution? Or is there an alternative, e.g., in singular?
* If there is currently no method in Sage for doing this directly, what name would you recommend? `resultant_ext` ?Wed, 04 Jan 2017 06:34:11 +0100https://ask.sagemath.org/question/36164/linear-combination-for-resultant/Answer by B r u n o for <p>Let</p>
<pre><code>R.<a, b, X> = ZZ[]
f = 1 - a*X^2
g = 1 - b*X^3
</code></pre>
<p>I need to compute polynomials <code>u</code> and <code>v</code> such that <code>u f + v g = r</code> where <code>r = f.resultant(g, X)</code>.</p>
<p>Pari has a function <code>polresultantext</code> for that purpose, so one solution for my problem is</p>
<pre><code>(u, v, r) = (R(p) for p in f._pari_().polresultantext(g._pari_(), 'X'))
</code></pre>
<p>Nevertheless, I have a few questions:</p>
<ul>
<li>Is there a method in Sage which directly does this?</li>
<li>Is the detour via Pari the recommended solution? Or is there an alternative, e.g., in singular?</li>
<li>If there is currently no method in Sage for doing this directly, what name would you recommend? <code>resultant_ext</code> ?</li>
</ul>
https://ask.sagemath.org/question/36164/linear-combination-for-resultant/?answer=36167#post-id-36167 - There is no such method yet, unfortunately.
- Singular does not seem to provide a method for this computation. See [this page](https://www.singular.uni-kl.de/Manual/4-0-3/sing_259.htm).
- There are discussions around this issue, for example [on sage-devel](https://groups.google.com/forum/#!topic/sage-devel/JV8fCPUqTzo) and ticket [#17674](https://trac.sagemath.org/ticket/17674). Personally, I would opt for something around `bezout_coefficients`.Wed, 04 Jan 2017 12:11:07 +0100https://ask.sagemath.org/question/36164/linear-combination-for-resultant/?answer=36167#post-id-36167