ApCoCoA-1:NC.LC
NC.LC
Leading coefficient of a polynomial over a free associative K-algebra.
Syntax
NC.LC(F:LIST):K
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.
Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].
@return: an element of K which is leading term of F with respect to current ordering. If F=0, then return 0.
Example
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); NC.RingEnv(); Coefficient ring : Q (float type in C++) Alphabet : abc Ordering : ELIM ------------------------------- F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NC.LC(F); -- ELIM ordering 2 ------------------------------- NC.SetOrdering(<quotes>LLEX</quotes>); NC.LC(F); -- LLEX ordering 4 ------------------------------- NC.LC([]); 0 -------------------------------
See also
