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by defrost
1222 days ago
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Maxima sees serious 'more free' versions of computational algorithms that migrate out from less free acedemic systems. On the computational real actual algebra side (ie. a bit past computing a quadractic at 'x') a number of things that appear in Magma follow into Maxima (but not all the things, although with time they will come). https://en.wikipedia.org/wiki/Hidden_Field_Equations https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis The first HFE cryptosystem challenge of J. Patarin is solved by Magma in 82.5 seconds, using 1.3GB memory; with 4 threads the time taken is just 29.0 seconds. This involves solving a system of 80 quadratic equations in 80 variables over GF(2) (each input polynomial has about 1600 terms). The challenge was first solved by J.-C. Faugère in 52 hours on an 1GHz Alpha in 2002 using his unpublished F5/2 algorithm. At the time of writing, there is apparently still no publically-available software besides Magma which can solve the challenge.
http://magma.maths.usyd.edu.au/magma/overview/2/27/13/#subsu...https://maxima.sourceforge.io/docs/manual/maxima_257.html Notes on the grobner package: The code is a little bit out of date now. Modern implementation use the fast F4 algorithm described in "A new efficient algorithm for computing Gröbner bases (F4)" Jean-Charles Faugère
( *NB a somewhat old example, I'm not keeping up on the comp.algebra lists and I'm assuming here the online manuals are up to date ) |
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