ApCoCoA-1:NC.Add
NC.Add
Addition of two polynomials over a free associative K-algebra.
Syntax
NC.Add(F1:LIST, F2:LIST):LIST
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 F1: left operand of addition operator. It is 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,""]].
@param F2: right operand of addition operator. It is a polynomial in K<X>.
@return: a LIST which represents polynomial F1+F2.
Example
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Add(F1,F2); -- computation over Q [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.RingEnv(); Coefficient ring : Q (float type in C++) Alphabet : abc Ordering : ELIM ------------------------------- NC.SetFp(); -- default Fp = F2 NC.RingEnv(); Coefficient ring : Fp = Z/(2) Alphabet : abc Ordering : ELIM ------------------------------- NC.Add(F1,F2); -- computation over F2 [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.Add(F1,F1); -- computation over F2 [ ] ------------------------------- NC.UnsetFp(); -- set the coefficient field back to Q NC.RingEnv(); Coefficient ring : Q (float type in C++) Alphabet : abc Ordering : ELIM -------------------------------
See also
