ApCoCoA-1:NC.Sub
NC.Subtract
Subtraction of two polynomials in a non-commutative polynomial ring.
Syntax
NC.Sub(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 NC.SetFp, NC.SetX and NC.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 subtraction 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
NC.SetX(<quotes>abc</quotes>); NC.SetOrdering(<quotes>ELIM</quotes>); F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]]; F2 := [[0,<quotes>b</quotes>],[1,<quotes>ba</quotes>]]; NC.Subtract(F1,F2); -- over Q (default field) [[-1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : ELIM ------------------------------- NC.SetFp(); -- set default Fp = F2 NC.RingEnv(); Coefficient ring : Fp = Z/(2) Alphabet : abc Ordering : ELIM ------------------------------- NC.Subtract(F1,F2); -- over F2 [[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes></quotes>]] ------------------------------- NC.Subtract(F1,F1); [ ] -------------------------------
See also
