ApCoCoA-1:NC.Interreduction

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NC.Interreduction

Interreduction of a LIST of polynomials in a non-commutative polynomial ring.

Note that, given a word ordering, a set of non-zero polynomial G is called interreduced if, for all g in G, no element of Supp(g) is a multiple of any element in LT{G\{g}}.

Syntax

NC.Interreduction(G:LIST):LIST

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 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.

  • @param G: a LIST of non-commutative polynomials. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial 0 is represented as the empty LIST [].

  • @return: a LIST, which is an interreduced set of G.

Example

NC.SetX(<quotes>abc</quotes>);
NC.SetOrdering(<quotes>ELIM</quotes>);
G:=[[[1,<quotes>ba</quotes>]], [[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]]];
NC.Interreduction(G);

[[[1, <quotes>a</quotes>]], [[1, <quotes>b</quotes>], [1, <quotes></quotes>]], [[1, <quotes>c</quotes>]]]
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See also

Use

NC.SetOrdering

Introduction to CoCoAServer