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NC.GB

Enumerate (partial) Groebner bases of finitely generated two-sided ideals in a non-commutative polynomial ring via the Buchberger procedure.
Syntax
          
NC.GB(G:LIST[, Optimize:INT, OFlag:INT, DB:INT, LB:INT]):LIST

          

Description
Given a word ordering and a two-sided ideal I, a set of non-zero polynomials Gb is called a Groebner basis of I if the leading word set LW{Gb} generates the leading word ideal LW(I). Note that it may not exist finite Groebner basis of the ideal I.

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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions. About 4 optional parameters:

Example
Use ZZ/(2)[t,x,y];
NC.SetOrdering("ELIM"); 
F1 := [[x^2], [y,x]]; -- x^2+yx
F2 := [[x,y], [t,y]]; -- xy+ty
F3 := [[x,t], [t,x]]; -- xt+tx
F4 := [[y,t], [t,y]]; -- yt+ty
G := [F1, F2,F3,F4]; 
NC.GB(G);
Len(It);

[[[x^2], [y, x]], [[t, y], [x, y]], [[y, t], [x, y]], [[t, x], [x, t]], 
[[x, y, x], [y^2, x]], [[x, y^2], [y, x, y]], [[y, x, t], [y^2, x]]]
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See Also