ApCoCoA-1:NC.LC
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
NC.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NC.SetOrdering(<quotes>ELIM</quotes>); NC.LC(F); 2 ------------------------------- NC.SetOrdering(<quotes>LLEX</quotes>); NC.LC(F); 4 ------------------------------- NC.LC([]); -- 0 polynomial 0 -------------------------------
See also
