ApCoCoA-1:NC.Mul

This article is about a function from ApCoCoA-1.

NC.Mul

Multiplication of two polynomials in a non-commutative polynomial ring.

Syntax

NC.Mul(F1:LIST, F2: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 F1, F2: two non-commutative polynomials, which are left and right operands of multiplication respectively. 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 represents the polynomial equal to F1*F2.

Example

USE ZZ/(31)[x[1..2],y[1..2]];
F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2
NC.Mul(F1,F2);

[[4x[1], x[2], y[1], y[2]], [7x[1], x[2], y[2]], [4x[1], x[2]], [-5y[2], y[1], y[2]], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]]
-------------------------------
NC.Mul(F2,F1);

[[4y[1], y[2], x[1], x[2]], [7y[2], x[1], x[2]], [4x[1], x[2]], [-5y[1], y[2]^2], [10y[1], y[2]], [-y[2]^2], [-3y[2]], [10]]
-------------------------------
NC.Mul([],F1);

[ ]
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See also

Use

NC.SetOrdering

Introduction to CoCoAServer