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

From ApCoCoAWiki
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</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetX(<quotes>abc</quotes>);
+
USE ZZ/(31)[x[1..2],y[1..2]];
NC.SetOrdering(<quotes>ELIM</quotes>);
+
F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]];
+
F2:= [[2y[1],y[2]], [19y[2]], [2]]; -- 2y[1]y[2]+19y[2]+2
F2 := [[0,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
+
NC.Sub(F1,F2);
NC.Subtract(F1,F2); -- over Q (default field)
+
 
[[-1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]]
+
[[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]]
 
-------------------------------
 
-------------------------------
NC.RingEnv();
+
NC.Sub([],F2); -- 0-F2
Coefficient ring : Q
+
 
Alphabet : abc
+
[[-2y[1], y[2]], [12y[2]], [-2]]
Ordering : ELIM
 
-------------------------------
 
NC.SetFp(); -- set default Fp = F2
 
NC.RingEnv();
 
Coefficient ring : Fp = Z/(2)
 
Alphabet : abc
 
Ordering : ELIM
 
-------------------------------
 
NC.Subtract(F1,F2); -- over F2
 
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]]
 
-------------------------------
 
NC.Subtract(F1,F1);
 
[ ]
 
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>

Revision as of 17:33, 3 May 2013

NC.Sub

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

Syntax

NC.Sub(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 subtraction 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.Sub(F1,F2);

[[2x[1], x[2]], [-2y[1], y[2]], [-6y[2]], [3]]
-------------------------------
NC.Sub([],F2); -- 0-F2

[[-2y[1], y[2]], [12y[2]], [-2]]
-------------------------------

See also

Use

NC.SetOrdering

Introduction to CoCoAServer