User pbelmans - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T05:30:53Z http://mathoverflow.net/feeds/user/6263 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106826/algorithms-in-invariant-theory/106840#106840 Answer by pbelmans for Algorithms in Invariant Theory pbelmans 2012-09-10T19:54:00Z 2012-09-10T19:54:00Z <p><a href="http://magma.maths.usyd.edu.au/magma/" rel="nofollow">Magma</a> (not free, unfortunately) is capable of this. The method <a href="http://magma.maths.usyd.edu.au/magma/handbook/text/1197#12744" rel="nofollow"><code>FundamentalInvariants(R) : RngInvar -&gt; RngMPol</code></a> should do what you need.</p> http://mathoverflow.net/questions/75272/computer-platforms-for-combinatorial-search-problems-mathematical-music-theory/75279#75279 Answer by pbelmans for Computer platforms for combinatorial search problems/mathematical music theory? pbelmans 2011-09-13T06:43:28Z 2011-09-13T06:43:28Z <p>A possible solution could be <a href="http://strasheela.sourceforge.net/strasheela/doc/index.html" rel="nofollow">Strasheela</a>, a library of music-related stuff built upon the <a href="http://www.mozart-oz.org/" rel="nofollow">Mozart programming system</a> which is an interactive environment for the <a href="http://www.mozart-oz.org/" rel="nofollow">Oz programming language</a>, a multi-paradigm programming language that supports constraint programming. The website states many uses, from Fuxian counterpoint to harmonic analysis but also realtime generation of rhythmic patterns. And due to the integration of many output formats (Lilypond for typeset music, MIDI for ugly beeps, Csound for less ugly beeps, Fomus for other compositional tools, ...) it will be easy to actually use your results.</p> <p>The problem you describe sounds like it's doable in Strasheela (based on my own tiny bit of experience in it). It will also be able to find <em>all</em> solutions if you ask it to do so, but it might take some time (or be untractable) depending on the problem and the size of the solution space.</p> <p>The idea of the language is different from your combinatorial approach, but it has great support of music theory and finding stuff, so you can use the terms for music theory without translating everything to a more mathematically oriented lingo. You'll have to phrase your actual problem in another way though: less combinatorial and more artificial intelligence-ish.</p>