ApCoCoA-1:NCo.PrefixNR

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NCo.PrefixNR

The prefix normal remainder of a polynomial with respect to a LIST of polynomials in a finitely presented monoid ring.

Syntax

NCo.PrefixNR(F:LIST, 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 ring environment coefficient field K, alphabet (or set of indeterminates) X, rewrite relations Relations and word ordering Ordering through the functions NCo.SetFp, NCo.SetX, NCo.SetRelations and NCo.SetOrdering, respectively, before using this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL, and the default ordering is the length-lexicographic ordering "LLEX". For more information, please check the relevant functions.

  • @param F: a LIST which represents a polynomial in the monoid ring. Each polynomial is represented as a LIST of LISTs, i.e. as [[C1,W1],...,[Cs,Ws]] where, for each i, Wi is a term represented as a STRING and Ci is the coefficient of Wi. For example, polynomial f=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].

  • @param G: a LIST of polynomials.

  • @return: a LIST which represents the prefix normal remainder of F with respect to G.

Example

NCo.SetX(<quotes>abc</quotes>);
NCo.SetOrdering(<quotes>LLEX</quotes>);
NCo.SetRelations([[<quotes>aa</quotes>,<quotes></quotes>], [<quotes>bb</quotes>,<quotes></quotes>], [<quotes>ab</quotes>,<quotes>c</quotes>], [<quotes>ac</quotes>, <quotes>b</quotes>], [<quotes>cb</quotes>, <quotes>a</quotes>]]);
F := [[1,<quotes>ba</quotes>]];
G:=[[[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]]];
NCo.PrefixNR(F, G);

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

NCo.PrefixGB

NCo.PrefixInterreduction

NCo.PrefixReducedGB

NCo.PrefixSaturation

NCo.SetFp

NCo.SetOrdering

NCo.SetRelations

NCo.SetX

Introduction to CoCoAServer