ApCoCoA-1:NCo.LC
NCo.LC
The leading coefficient of a non-zero polynomial in a free monoid ring.
Syntax
NCo.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 ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before using this function. The default coefficient field is Q, and the default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a non-zero polynomial in K<X>. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If F=0, the function returns 0.
Example
NCo.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NCo.SetOrdering(<quotes>ELIM</quotes>); NCo.LC(F); 2 ------------------------------- NCo.SetOrdering(<quotes>LLEX</quotes>); NCo.LC(F); 4 ------------------------------- NCo.LC([]); -- 0 polynomial 0 -------------------------------
See also
