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

From ApCoCoAWiki
Line 57: Line 57:
 
<see>NC.LT</see>
 
<see>NC.LT</see>
 
<see>NC.LTIdeal</see>
 
<see>NC.LTIdeal</see>
<see>NC.MinimalPolymonial</see>
+
<see>NC.MinimalPolynomial</see>
 
<see>NC.Multiply</see>
 
<see>NC.Multiply</see>
 
<see>NC.NR</see>
 
<see>NC.NR</see>

Revision as of 12:19, 19 July 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.

  • 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

NC.GB

NC.IsGB

NC.LC

NC.LT

NC.LTIdeal

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.SetFp

NC.SetOrdering

NC.SetRelations

NC.SetRules

NC.SetX

NC.Subtract

NC.UnsetFp

NC.UnsetOrdering

NC.UnsetRelations

NC.UnsetRules

NC.UnsetX

Gbmr.MRSubtract

Gbmr.MRMultiply

Gbmr.MRBP

Gbmr.MRIntersection

Gbmr.MRKernelOfHomomorphism

Gbmr.MRMinimalPolynomials

Introduction to CoCoAServer