I am a computer engineer and don't know much about advanced computer algebra concepts therefore I need your help in it. I would like someone to explain in general terms what grobner bases is. I have read about it but not understood it fully so need help of mathematics guys.
Suppose I have a set of equations in POS form
(x1 + 0) (x2 + 1) (y1 + 0) = 0
(x1 + 1) (x2 + 0) (y1 + 1) = 0
etc
How this is reduced to gobner of form y1 = function(x1,x2)? I heard of library risa/asir for computing these but I want to know how it works, I mean how POS form set of equations are solved to gobner form (in theory and also with the tool if someone knows)?
Roughly, computing a Groebner basis of a "set" of polynomials is a generalization of Gaussian reduction.
I don't think there a way of computing a GB directly from POS form... at least, I've never heard about it ;-)
Is what you want to do related with the "Logic Example" in
http://cocoa.dima.unige.it/WhatIsCoCoA/WhatIsCoCoA-English.html
?
Not quite, I guess, but you may find other examples there.
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