Difference between revisions of "ApCoCoA-1:NC.LC"
Line 16: | Line 16: | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
− | + | USE QQ[x[1..2]]; | |
− | + | F1:= [[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( | + | NC.LC(F1); |
− | + | ||
+ | [1] | ||
------------------------------- | ------------------------------- | ||
− | NC.SetOrdering( | + | NC.SetOrdering("LRLEX"); |
− | NC.LC( | + | NC.LC(F1); |
− | 4 | + | |
+ | [4] | ||
------------------------------- | ------------------------------- | ||
− | NC.LC([]); | + | NC.SetOrdering("ELIM"); |
− | + | NC.LC(F1); | |
+ | |||
+ | [1] | ||
+ | ------------------------------- | ||
+ | NC.SetOrdering("DEGRLEX"); | ||
+ | NC.LC(F1); | ||
+ | |||
+ | [1] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> |
Revision as of 17:48, 3 May 2013
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]]; F1:= [[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(F1); [1] ------------------------------- NC.SetOrdering("LRLEX"); NC.LC(F1); [4] ------------------------------- NC.SetOrdering("ELIM"); NC.LC(F1); [1] ------------------------------- NC.SetOrdering("DEGRLEX"); NC.LC(F1); [1] -------------------------------
See also