Difference between revisions of "ApCoCoA-1:NC.LC"
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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>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 ( | + | 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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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 | 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( | + | NC.SetOrdering("LLEX"); |
NC.LC(F); | NC.LC(F); | ||
[1] | [1] | ||
------------------------------- | ------------------------------- | ||
| − | NC.SetOrdering( | + | NC.SetOrdering("LRLEX"); |
NC.LC(F); | NC.LC(F); | ||
[4] | [4] | ||
------------------------------- | ------------------------------- | ||
| − | NC.SetOrdering( | + | NC.SetOrdering("ELIM"); |
NC.LC(F); | NC.LC(F); | ||
[1] | [1] | ||
------------------------------- | ------------------------------- | ||
| − | NC.SetOrdering( | + | NC.SetOrdering("DEGRLEX"); |
NC.LC(F); | NC.LC(F); | ||
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
