ApCoCoA-1:NCo.Multiply
NCo.Multiply
Multiplication of two polynomials in a free monoid ring.
Syntax
NCo.Multiply(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.
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 calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F1, F2: two polynomials in K<X>, which are left and right operands of multiplication respectively. Each polynomial is represented as a LIST of monomials, which are pairs 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 LIST which represents the polynomial equal to F1*F2.
Example
NCo.SetFp(3); NCo.SetX(<quotes>abc</quotes>); NCo.RingEnv(); Coefficient ring : Fp = Z/(3) Alphabet : abc Ordering : LLEX ------------------------------- F1 := [[2,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[2,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NCo.Multiply(F1,F2); -- over F3 [[2, <quotes>aba</quotes>], [1, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NCo.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [2, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NCo.Multiply(F1,[]); [ ] ------------------------------- NCo.Multiply([],F1); [ ] ------------------------------- NCo.Multiply([],[]); [ ] ------------------------------- NCo.UnsetFp(); NCo.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : LLEX ------------------------------- NCo.Multiply(F1,F2); -- over Q [[2, <quotes>aba</quotes>], [4, <quotes>ab</quotes>], [1, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] ------------------------------- NCo.Multiply(F2,F1); [[2, <quotes>baa</quotes>], [5, <quotes>ba</quotes>], [2, <quotes>b</quotes>]] -------------------------------
See also
