ApCoCoA-1:NC.IsGB

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NC.IsGB

Check if a list of polynomials if Groebner basis.

Syntax

NC.IsGB(Polynomials:LIST):BOOL

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

  • Before calling the function, please set ring environment coefficient field (K), alphabet (X) and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param Polynomials: a LIST of polynomials in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].

  • @return: a BOOL value. True if Polynomials is a GB; False, otherwise.

Example

NC.SetX(<quotes>xyt</quotes>); 
NC.SetOrdering(<quotes>LLEX</quotes>); 
F1 := [[1,<quotes>xx</quotes>], [-1,<quotes>yx</quotes>]];   
F2 := [[1,<quotes>xy</quotes>], [-1,<quotes>ty</quotes>]];  
F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]];  
F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]];  
Polynomials := [F1, F2,F3,F4]; 
NC.IsGB(Polynomials);
False
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.IsGB(Polynomials);
False
-------------------------------

See also

NC.Add

NC.LT

NC.Multiply

NC.NR

NC.Subtract

Gbmr.MRSubtract

Gbmr.MRMultiply

Gbmr.MRBP

Gbmr.MRIntersection

Gbmr.MRKernelOfHomomorphism

Gbmr.MRMinimalPolynomials

Introduction to CoCoAServer