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

From ApCoCoAWiki
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<title>NC.Deg</title>
 
<title>NC.Deg</title>
 
<short_description>
 
<short_description>
(Standard) degree of a polynomial over a free associative K-algebra.
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(Standard) degree of a polynomial over a free associative <tt>K</tt>-algebra.
 
</short_description>
 
</short_description>
 
<syntax>
 
<syntax>
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
<par/>
 
<par/>
Before calling the function, please set ring environment alphabet <tt>X</tt> through the functions <ref>NC.SetX</ref>(X).
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Please set ring environment coefficient field <tt>K</tt>, alphabet (or indeterminates) <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering), respectively, before calling the function. Default coefficient field is <tt>Q</tt>. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.
 
<itemize>
 
<itemize>
<item>@param <em>F</em>: a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial in <tt>K&lt;X&gt;</tt> is represented as a LIST of LISTs, which are pairs of form <tt>[c, w]</tt> where c is in <tt>K</tt> and w is a word in <tt>X*</tt>.  Unit in <tt>X*</tt> is empty word represented as an empty string <quotes></quotes>. <tt>0</tt> polynomial is represented as an empty list. For example, polynomial <tt>F:=xy-y+1</tt> in <tt>K&lt;x,y&gt;</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]].</item>
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<item>@param <em>F</em>: a polynomial in <tt>K&lt;X&gt;</tt>. 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, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an empty LIST [].</item>
<item>@return: a positive integer which is (standard) degree <tt>F</tt>. If <tt>F=0</tt>, then return <tt>0</tt>. </item>
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<item>@return: a INT which represents a (standard) degree of F. If F=0, the function returns 0. </item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>

Revision as of 19:30, 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.BP

NC.FindPolynomials

NC.GB

NC.Intersection

NC.IsGB

NC.KernelOfHomomorphism

NC.LC

NC.LT

NC.LTIdeal

NC.MRAdd

NC.MRBP

NC.MRIntersection

NC.MRKernelOfHomomorphism

NC.MRMinimalPolynomials

NC.MRMultiply

NC.MRReducedBP

NC.MRSubtract

NC.MinimalPolynomial

NC.Multiply

NC.NR

NC.ReducedBP

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