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

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{{Version|1}}
 
<command>
 
<command>
 
<title>NC.Deg</title>
 
<title>NC.Deg</title>
 
<short_description>
 
<short_description>
−
(Standard) degree of a polynomial over a free monoid ring.
+
The standard degree of a polynomial in a non-commutative polynomial ring.
 
</short_description>
 
</short_description>
 
<syntax>
 
<syntax>
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</syntax>
 
</syntax>
 
<description>
 
<description>
−
<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/>
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Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NC.SetFp</ref>, <ref>NC.SetX</ref> and <ref>NC.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions.
+
Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) before calling this function. For more information, please check the relevant commands and functions.
 
<itemize>
 
<itemize>
−
<item>@param <em>F</em>: a polynomial in <tt>K&lt;X&gt;</tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as an empty LIST [].</item>
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<item>@param <em>F</em>: a non-commutative polynomial. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial <tt>f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5</tt> is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item>
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<item>@return: an INT which represents the (standard) degree of F. If <tt>F=0</tt>, the function returns <tt>0</tt>. </item>
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<item>@return: an INT which represents the standard degree of F. Note that the standard degree of <tt>0</tt> is 0. </item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
−
NC.SetX(<quotes>abc</quotes>);
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USE QQ[x[1..2],y[1..2]];
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F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
+
F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
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NC.Deg(F);
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NC.Deg(F1);
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3
 
  
 +
2
 
-------------------------------
 
-------------------------------
−
NC.Deg([]); -- 0 polynomial
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NC.Deg([]);
 +
 
 
0
 
0
−
 
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
</description>
 
</description>
 
<seealso>
 
<seealso>
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<see>NC.Add</see>
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<see>ApCoCoA-1:Use|Use</see>
−
<see>NC.Deg</see>
 
−
<see>NC.FindPolynomials</see>
 
−
<see>NC.GB</see>
 
−
<see>NC.HF</see>
 
−
<see>NC.Interreduction</see>
 
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<see>NC.Intersection</see>
 
−
<see>NC.IsGB</see>
 
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<see>NC.IsHomog</see>
 
−
<see>NC.KernelOfHomomorphism</see>
 
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<see>NC.LC</see>
 
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<see>NC.LT</see>
 
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<see>NC.LTIdeal</see>
 
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<see>NC.MinimalPolynomial</see>
 
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<see>NC.Multiply</see>
 
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<see>NC.NR</see>
 
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<see>NC.ReducedGB</see>
 
−
<see>NC.SetFp</see>
 
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<see>NC.SetOrdering</see>
 
−
<see>NC.SetRelations</see>
 
−
<see>NC.SetRules</see>
 
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<see>NC.SetX</see>
 
−
<see>NC.Subtract</see>
 
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<see>NC.UnsetFp</see>
 
−
<see>NC.UnsetOrdering</see>
 
−
<see>NC.UnsetRelations</see>
 
−
<see>NC.UnsetRules</see>
 
−
<see>NC.UnsetX</see>
 
−
<see>Introduction to CoCoAServer</see>
 
 
</seealso>
 
</seealso>
 
<types>
 
<types>
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<type>non_commutative</type>
 
<type>non_commutative</type>
 
</types>
 
</types>
−
<key>gbmr.Deg</key>
+
<key>ncpoly.Deg</key>
 
<key>NC.Deg</key>
 
<key>NC.Deg</key>
 
<key>Deg</key>
 
<key>Deg</key>
−
<wiki-category>Package_gbmr</wiki-category>
+
<wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:13, 7 October 2020

This article is about a function from ApCoCoA-1.

NC.Deg

The standard degree of a polynomial in a non-commutative polynomial ring.

Syntax

NC.Deg(F:LIST):INT

Description


Please set non-commutative polynomial ring (via the command Use) before calling this function. For more information, please check the relevant commands and functions.

  • @param F: a non-commutative polynomial. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial 0 is represented as the empty LIST [].

  • @return: an INT which represents the standard degree of F. Note that the standard degree of 0 is 0.

Example

USE QQ[x[1..2],y[1..2]];
F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
NC.Deg(F1);

2
-------------------------------
NC.Deg([]);

0
-------------------------------

See also

Use




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