Difference between revisions of "ApCoCoA-1:NC.IsGB"

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<seealso>
 
<seealso>
 
<see>NC.Add</see>
 
<see>NC.Add</see>
<see>NC.BP</see>
 
 
<see>NC.Deg</see>
 
<see>NC.Deg</see>
 
<see>NC.FindPolynomials</see>
 
<see>NC.FindPolynomials</see>
 
<see>NC.GB</see>
 
<see>NC.GB</see>
 +
<see>NC.HF</see>
 
<see>NC.Intersection</see>
 
<see>NC.Intersection</see>
 +
<see>NC.IsGB</see>
 
<see>NC.KernelOfHomomorphism</see>
 
<see>NC.KernelOfHomomorphism</see>
 
<see>NC.LC</see>
 
<see>NC.LC</see>
 
<see>NC.LT</see>
 
<see>NC.LT</see>
<see>NC.LTIdeal</see>
 
<see>NC.MRAdd</see>
 
<see>NC.MRBP</see>
 
<see>NC.MRIntersection</see>
 
<see>NC.MRKernelOfHomomorphism</see>
 
<see>NC.MRMinimalPolynomials</see>
 
<see>NC.MRMultiply</see>
 
<see>NC.MRReducedBP</see>
 
<see>NC.MRSubtract</see>
 
<see>NC.MinimalPolynomial</see>
 
<see>NC.Multiply</see>
 
 
<see>NC.NR</see>
 
<see>NC.NR</see>
<see>NC.ReducedBP</see>
 
 
<see>NC.ReducedGB</see>
 
<see>NC.ReducedGB</see>
 +
<see>NC.MRBP</see>
 
<see>NC.SetFp</see>
 
<see>NC.SetFp</see>
 
<see>NC.SetOrdering</see>
 
<see>NC.SetOrdering</see>

Revision as of 23:18, 11 December 2010

NC.IsGB

Checks whether a list of polynomials over a free associative K-algebra is a Groebner basis of the ideal generated by polynomials.

Syntax

NC.IsGB(G: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.

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

  • @param G: a LIST of polynomials in K<X>. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].

  • @return: a BOOL value which is True if G is a Groebner basis and False otherwise.

Example

NC.SetX(<quotes>xyt</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); -- LLEX ordering (default ordering)
False
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.IsGB(Polynomials);
False
-------------------------------

See also

NC.Add

NC.Deg

NC.FindPolynomials

NC.GB

NC.HF

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.NR

NC.ReducedGB

NC.MRBP

NC.SetFp

NC.SetOrdering

NC.SetRelations

NC.SetRules

NC.SetX

NC.Subtract

NC.UnsetFp

NC.UnsetOrdering

NC.UnsetRelations

NC.UnsetRules

NC.UnsetX

Introduction to CoCoAServer