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

From ApCoCoAWiki
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</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetX(<quotes>abc</quotes>);
+
USE QQ[x[1..2]];
F:=[[1,<quotes>ab</quotes>],[1,<quotes>aa</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>]];
+
F:= [[x[1]^2], [2x[1],x[2]], [3x[2],x[1]],[4x[2]^2]]; -- x[1]^2+2x[1]x[2]+3x[2]x[1]+4x[2]^2
NC.LW(F); -- LLEX ordering (default ordering)
+
NC.SetOrdering(<quotes>LLEX</quotes>);
bab
+
NC.LW(F);
 +
 
 +
[x[1]^2]
 +
-------------------------------
 +
-- Done.
 +
-------------------------------
 +
NC.SetOrdering(<quotes>LRLEX</quotes>);
 +
NC.LW(F);
 +
 
 +
[x[2]^2]
 +
-------------------------------
 +
-- Done.
 
-------------------------------
 
-------------------------------
 
NC.SetOrdering(<quotes>ELIM</quotes>);
 
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.LW(F);  
+
NC.LW(F);
aa
+
 
 +
[x[1]^2]
 +
-------------------------------
 +
-- Done.
 +
-------------------------------
 +
NC.SetOrdering(<quotes>DEGRLEX</quotes>);
 +
NC.LW(F);
 +
 
 +
[x[1]^2]
 
-------------------------------
 
-------------------------------
NC.LW([]);
 
 
</example>
 
</example>
 
</description>
 
</description>

Revision as of 17:52, 3 May 2013

NC.LW

The leading word (or term) of a non-zero polynomial in a non-commutative polynomial ring.

Syntax

NC.LW(F:LIST):LIST
NC.LT(F: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 F: a non-zero non-commutative polynomial. 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 is the leading word of F with respect to the current word ordering.

Example

USE QQ[x[1..2]];
F:= [[x[1]^2], [2x[1],x[2]], [3x[2],x[1]],[4x[2]^2]]; -- x[1]^2+2x[1]x[2]+3x[2]x[1]+4x[2]^2
NC.SetOrdering(<quotes>LLEX</quotes>);
NC.LW(F);

[x[1]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering(<quotes>LRLEX</quotes>);
NC.LW(F);

[x[2]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.LW(F);

[x[1]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering(<quotes>DEGRLEX</quotes>);
NC.LW(F);

[x[1]^2]
-------------------------------

See also

Use

NC.SetOrdering

Introduction to CoCoAServer