Difference between revisions of "ApCoCoA-1:NC.LW"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>NC.LW</title> | <title>NC.LW</title> | ||
<short_description> | <short_description> | ||
| − | + | The leading word (or term) of a non-zero polynomial in a non-commutative polynomial ring. | |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | NC.LW(F:LIST): | + | NC.LW(F:LIST):LIST |
| + | NC.LT(F:LIST):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set ring | + | Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) and word ordering (via the function <ref>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions. |
<itemize> | <itemize> | ||
| − | <item>@param <em>F</em>: a polynomial | + | <item>@param <em>F</em>: 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 <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> |
| − | <item>@return: a | + | <item>@return: a LIST, which is the leading word of F with respect to the current word ordering.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | USE QQ[x[1..2]]; | |
| − | F:=[[1, | + | 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); | + | NC.SetOrdering("LLEX"); |
| − | + | NC.LW(F); | |
| + | |||
| + | [x[1]^2] | ||
------------------------------- | ------------------------------- | ||
| − | NC.SetOrdering( | + | -- Done. |
| − | NC.LW(F); | + | ------------------------------- |
| − | + | NC.SetOrdering("LRLEX"); | |
| + | NC.LW(F); | ||
| + | |||
| + | [x[2]^2] | ||
| + | ------------------------------- | ||
| + | -- Done. | ||
| + | ------------------------------- | ||
| + | NC.SetOrdering("ELIM"); | ||
| + | NC.LW(F); | ||
| + | |||
| + | [x[1]^2] | ||
| + | ------------------------------- | ||
| + | -- Done. | ||
| + | ------------------------------- | ||
| + | NC.SetOrdering("DEGRLEX"); | ||
| + | NC.LT(F); | ||
| + | |||
| + | [x[1]^2] | ||
------------------------------- | ------------------------------- | ||
| − | |||
</example> | </example> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>NC.SetOrdering</see> | + | <see>ApCoCoA-1:Use|Use</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</see> |
| + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 40: | Line 61: | ||
<key>NC.LW</key> | <key>NC.LW</key> | ||
<key>LW</key> | <key>LW</key> | ||
| − | <wiki-category>Package_ncpoly</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:35, 29 October 2020
| This article is about a function from ApCoCoA-1. |
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("LLEX");
NC.LW(F);
[x[1]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("LRLEX");
NC.LW(F);
[x[2]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("ELIM");
NC.LW(F);
[x[1]^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("DEGRLEX");
NC.LT(F);
[x[1]^2]
-------------------------------
See also
