ApCoCoA-1:NC.Add

NC.Add

Addition of two polynomials over a free monoid ring.

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.

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. Default coefficient field is Q. 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 addition 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 an empty LIST [].

• @return: a LIST which represents the polynomial equal to F1+F2.

Example

NC.SetX(<quotes>abc</quotes>); 				
NC.SetOrdering(<quotes>ELIM</quotes>); 
NC.RingEnv();
Coefficient ring : Q
Alphabet : abc
Ordering : ELIE

-------------------------------	
F1 := [[1,<quotes>a</quotes>],[1,<quotes></quotes>]];
F2 := [[1,<quotes>b</quotes>],[1,<quotes>ba</quotes>]];
NC.Add(F1,F2); -- over Q
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]

-------------------------------
NC.SetFp(); -- set default Fp = F2
NC.RingEnv();
Coefficient ring : Fp = Z/(2)
Alphabet : abc
Ordering : ELIM

-------------------------------
NC.Add(F1,F2); -- over F2
[[1, <quotes>ba</quotes>], [1, <quotes>a</quotes>], [1, <quotes>b</quotes>], [1, <quotes></quotes>]]

-------------------------------
NC.Add(F1,F1); -- over F2
[ ]

-------------------------------

See also

NC.Add

NC.Deg

NC.FindPolynomials

NC.GB

NC.HF

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.LTIdeal

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.ReducedGB

NC.SetFp

NC.SetOrdering

NC.SetRelations

NC.SetRules

NC.SetX

NC.Subtract

NC.UnsetFp

NC.UnsetOrdering

NC.UnsetRelations

NC.UnsetRules

NC.UnsetX

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