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

From ApCoCoAWiki
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<seealso>
 
<seealso>
 
<see>NC.Add</see>
 
<see>NC.Add</see>
 +
<see>NC.Deg</see>
 
<see>NC.FindPolynomials</see>
 
<see>NC.FindPolynomials</see>
 
<see>NC.GB</see>
 
<see>NC.GB</see>

Revision as of 23:16, 11 December 2010

NC.Deg

(Standard) degree of a polynomial over a free associative K-algebra.

Syntax

NC.Deg(F:LIST):INT

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 F: a polynomial in K<X>. 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 INT which represents a (standard) degree of F. If F=0, the function returns 0.

Example

NC.SetX(<quotes>abc</quotes>);
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
NC.Deg(F);
3
-------------------------------
NC.Deg([]); -- 0 polynomial
0
-------------------------------

See also

NC.Add

NC.Deg

NC.FindPolynomials

NC.GB

NC.HF

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.NR

NC.ReducedGB

NC.MRBP

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