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

From ApCoCoAWiki
Line 21: Line 21:
 
F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]];   
 
F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]];   
 
F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]];   
 
F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]];   
Polynomials := [F1, F2,F3,F4];  
+
G := [F1, F2,F3,F4];  
NC.IsGB(Polynomials); -- LLEX ordering (default ordering)
+
NC.IsGB(G); -- LLEX ordering (default ordering)
 
False
 
False
 
-------------------------------
 
-------------------------------
 
NC.SetOrdering(<quotes>ELIM</quotes>);
 
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.IsGB(Polynomials);
+
NC.IsGB(G);
 
False
 
False
 
-------------------------------
 
-------------------------------

Revision as of 12:50, 12 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>]];  
G := [F1, F2,F3,F4]; 
NC.IsGB(G); -- LLEX ordering (default ordering)
False
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.IsGB(G);
False
-------------------------------

See also

NC.Add

NC.Deg

NC.FindPolynomials

NC.GB

NC.HF

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.LTIdeal

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.ReducedGB

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