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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.

Example
NC.SetX("xyt");  
F1 := [[1,"xx"], [-1,"yx"]];   
F2 := [[1,"xy"], [-1,"ty"]];  
F3 := [[1,"xt"], [-1, "tx"]];  
F4 := [[1,"yt"], [-1, "ty"]];  
G := [F1, F2,F3,F4]; 
NC.IsGB(G); -- LLEX ordering (default ordering)
False
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NC.SetOrdering("ELIM");
NC.IsGB(G);
False
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See Also