Difference between revisions of "ApCoCoA-1:NC.LC"
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<command> | <command> | ||
<title>NC.LC</title> | <title>NC.LC</title> | ||
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<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 non-commutative polynomial ring (via the command <ref>Use</ref>) and word ordering (via the function <ref>NC.SetOrdering</ref>) before calling this function. The default word ordering is the length-lexicographic ordering ( | + | 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 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>@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> | ||
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<example> | <example> | ||
USE QQ[x[1..2]]; | 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.SetOrdering("LLEX"); | ||
| − | NC.LC( | + | NC.LC(F); |
[1] | [1] | ||
------------------------------- | ------------------------------- | ||
NC.SetOrdering("LRLEX"); | NC.SetOrdering("LRLEX"); | ||
| − | NC.LC( | + | NC.LC(F); |
[4] | [4] | ||
------------------------------- | ------------------------------- | ||
NC.SetOrdering("ELIM"); | NC.SetOrdering("ELIM"); | ||
| − | NC.LC( | + | NC.LC(F); |
[1] | [1] | ||
------------------------------- | ------------------------------- | ||
NC.SetOrdering("DEGRLEX"); | NC.SetOrdering("DEGRLEX"); | ||
| − | NC.LC( | + | NC.LC(F); |
[1] | [1] | ||
| Line 41: | Line 42: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Use</see> | + | <see>ApCoCoA-1:Use|Use</see> |
| − | <see>NC.SetOrdering</see> | + | <see>ApCoCoA-1:NC.SetOrdering|NC.SetOrdering</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 53: | Line 54: | ||
<key>NC.LC</key> | <key>NC.LC</key> | ||
<key>LC</key> | <key>LC</key> | ||
| − | <wiki-category>Package_ncpoly</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:34, 29 October 2020
| This article is about a function from ApCoCoA-1. |
NC.LC
Leading coefficient of a non-zero polynomial in a non-commutative polynomial ring.
Syntax
NC.LC(F:LIST):INT or RAT
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: an INT or a RAT, whhich is the leading coefficient 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.LC(F);
[1]
-------------------------------
NC.SetOrdering("LRLEX");
NC.LC(F);
[4]
-------------------------------
NC.SetOrdering("ELIM");
NC.LC(F);
[1]
-------------------------------
NC.SetOrdering("DEGRLEX");
NC.LC(F);
[1]
-------------------------------
See also
