ApCoCoA-1:NC.NR

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NC.NR

Normal remainder of polynomial with respect to a LIST of polynomials in a non-commutative polynomial ring.

Syntax

NC.NR(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 and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

  • @param F: a polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the 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 non-zero polynomials in K<X>.

  • @return: a LIST which represents the normal remainder of F w.r.t. G.

Example

NC.SetX(<quotes>abc</quotes>);
NC.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : LLEX
-------------------------------
F:=[[1,<quotes>ab</quotes>],[1,<quotes>aca</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>],[1,<quotes></quotes>]];
F1 := [[1,<quotes>a</quotes>],[1,<quotes>c</quotes>]]; 
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
G:=[F1,F2];
NC.NR(F,G);
[[1, <quotes>bcb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes></quotes>]]
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.NR(F,G);
[[1, <quotes>bcb</quotes>], [-1, <quotes>bb</quotes>], [1, <quotes>cb</quotes>], [-1, <quotes>ccc</quotes>], [-1, <quotes></quotes>]]
-------------------------------

See also

NC.SetOrdering

Introduction to CoCoAServer