ApCoCoA-1:NC.LC
NC.LC
Leading coefficient of polynomial over a free associative K-algebra.
Syntax
NC.LT(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
