Are there any software to computer resultant for a system of equations (more than 2) with more than 2 variables?
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$\begingroup$ Fermat should do this home.bway.net/lewis And I think Magma can too, via either eliminating variables sequentially, or possibly with EliminationIdeal. They have an online calculator, if the problem is not too bulky. $\endgroup$– JunkieMar 8, 2012 at 4:04
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$\begingroup$ Junkie, IMHO the question is about multivariate resultant, rather than about how to eliminate variables in general. $\endgroup$– Dima PasechnikMar 8, 2012 at 4:20
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2$\begingroup$ If you mean multivariate polynomial resultant, then the best method is the Dixon Resultant (going back to Bezout). There is an expository article here: fordham.academia.edu/RobertLewis/Papers This is for exact symbolic computation. It probably won't work if there are more than, say, 10 equations. $\endgroup$– rhlewisMar 8, 2012 at 13:56
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2 Answers
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Maple will do it.
http://www.maplesoft.com/support/help/AddOns/view.aspx?path=Algebraic/Resultant
You can also do it in C, or Matlab with MARS:
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3$\begingroup$ Maple's docs say it's for resultant of two polynomials with coefficients being algebraic numbers. Looks a bit different from the original question to me. $\endgroup$ Mar 8, 2012 at 4:18
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$\begingroup$ Also the polynomials in Maple are univariate, not multivariate $\endgroup$– image357Aug 17, 2017 at 8:49
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Singular and Macaulay2 do it according to the documentation, though I haven't personally tried using either of them for this purpose. They are likely to be faster than Maple; I don't know about MARS.
answered Mar 8, 2012 at 3:57