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

From ApCoCoAWiki
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<see>NC.LT</see>
 
<see>NC.LT</see>
 
<see>NC.LTIdeal</see>
 
<see>NC.LTIdeal</see>
 +
<see>NC.MinimalPolymonial</see>
 
<see>NC.Multiply</see>
 
<see>NC.Multiply</see>
 
<see>NC.NR</see>
 
<see>NC.NR</see>

Revision as of 12:17, 19 July 2010

NC.LC

Leading coefficient of a polynomial over a free associative K-algebra.

Syntax

NC.LC(F:LIST):K

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 F: 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,""]].

  • @return: an element of K which is leading term of F with respect to current ordering. If F=0, then return 0.

Example

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

-------------------------------
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; 
NC.LC(F); -- ELIM ordering
2
-------------------------------
NC.SetOrdering(<quotes>LLEX</quotes>); 
NC.LC(F); -- LLEX ordering
4
-------------------------------
NC.LC([]);
0
-------------------------------

See also

NC.Add

NC.GB

NC.IsGB

NC.LT

NC.LTIdeal

NC.MinimalPolymonial

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