Difference between revisions of "ApCoCoA-1:NC.Add"

From ApCoCoAWiki
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<see>NC.LC</see>
 
<see>NC.LC</see>
 
<see>NC.LT</see>
 
<see>NC.LT</see>
 +
<see>NC.LTIdeal</see>
 +
<see>NC.MinimalPolynomial</see>
 +
<see>NC.Multiply</see>
 
<see>NC.NR</see>
 
<see>NC.NR</see>
 
<see>NC.ReducedGB</see>
 
<see>NC.ReducedGB</see>

Revision as of 00:04, 12 December 2010

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.

Please set ring environment coefficient field K, alphabet (or indeterminates) X and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), 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 LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].

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

Example

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

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

Introduction to CoCoAServer