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NC.RedGB

Enumerate reduced (partial) Groebner bases of finitely generated two-sided ideals in a non-commutative polynomial ring.
Syntax
          
NC.RedGB(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). A Groebner basis Gb of I is reduced if Gb is interreduced (see NC.Interreduction) and all polynomials in Gb are monic. Note that each ideal has a unique (not necessarily finite) reduced Groebner basis.

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)[x,y,t];
NC.SetOrdering("LLEX"); 
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
F5:=[[y,t,x],[1]]; 
G := [F1, F2,F3,F4,F5];
NC.RedGB(G);

[[[x], [t]], [[t^3], [1]], [[y], [t]]]
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See Also