up previous next
NCo.MRIsGB

Check whether a finite LIST of non-zero polynomials in a finitely presented monoid ring is a Groebner basis.
Syntax
          
NCo.MRIsGB(X:STRING, Ordering:STRING, Relations:LIST, G:LIST):BOOL

          

Description
Note that, given a word ordering Ordering, a set G of non-zero polynomials is called a Groebner basis with respect to Ordering if, for every non-zero polynomial f in the ideal , there exists a polynomial g in G such that MRLW(f) is a multiple of MRLW(g). The function check whether a given finite set G of non-zero polynomials is a Groebner basis by using the Buchberger Criterion, i.e. G is a Groebner basis if the S-polynomials of all obstructions of G have the zero normal remainder with respect to G.

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 coefficient field via the function NCo.SetFp (or NCo.UnsetFp) before calling this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL. For more information, please check the relevant functions.

Example
X := "xyzt"; 
Ordering := "LLEX"; 
Relations:=[]; 
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]; 
NCo.MRIsGB(X, Ordering, Relations, G);
False
-------------------------------


See Also