Difference between revisions of "ApCoCoA-1:NC.Mul"

From ApCoCoAWiki
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</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetFp(3);
+
USE ZZ/(31)[x[1..2],y[1..2]];
NC.SetX(<quotes>abc</quotes>);
+
F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
NC.RingEnv();
+
F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2
Coefficient ring : Fp = Z/(3)
+
NC.Mul(F1,F2);
Alphabet : abc
+
 
Ordering : LLEX
+
[[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]]
 
-------------------------------
 
-------------------------------
F1 := [[2,<quotes>a</quotes>],[1,<quotes></quotes>]];
+
NC.Mul(F2,F1);
F2 := [[2,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
+
 
NC.Multiply(F1,F2); -- over F3
+
[[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]]
[[2, <quotes>aba</quotes>], [1, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
 
 
-------------------------------
 
-------------------------------
NC.Multiply(F2,F1);
+
NC.Mul([],F1);
[[2, <quotes>baa</quotes>], [2, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
+
 
-------------------------------
 
NC.Multiply(F1,[]);
 
[ ]
 
-------------------------------
 
NC.Multiply([],F1);
 
[ ]
 
-------------------------------
 
NC.Multiply([],[]);
 
 
[ ]
 
[ ]
-------------------------------
 
NC.UnsetFp();
 
NC.RingEnv();
 
Coefficient ring : Q
 
Alphabet : abc
 
Ordering : LLEX
 
-------------------------------
 
NC.Multiply(F1,F2); -- over Q
 
[[2, <quotes>aba</quotes>], [4, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
 
-------------------------------
 
NC.Multiply(F2,F1);
 
[[2, <quotes>baa</quotes>], [5, <quotes>ba</quotes>], [2, <quotes>b</quotes>]]
 
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>

Revision as of 17:39, 3 May 2013

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);

[ ]
-------------------------------

See also

Use

NC.SetOrdering

Introduction to CoCoAServer