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

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{{Version|1}}
 
<command>
 
<command>
 
<title>NC.Deg</title>
 
<title>NC.Deg</title>
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<description>
 
<description>
 
<par/>
 
<par/>
Please set non-commutative polynomial ring (via the command <ref>Use</ref>) before calling this function. For more information, please check the relevant commands and functions.
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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 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>
 
<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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</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetX(<quotes>abc</quotes>);
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USE QQ[x[1..2],y[1..2]];
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
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F1:= [[2x[1],x[2]], [13y[2]], [5]]; -- 2x[1]x[2]+13y[2]+5
NC.Deg(F);
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NC.Deg(F1);
3
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2
 
-------------------------------
 
-------------------------------
NC.Deg([]); -- 0 polynomial
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NC.Deg([]);
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0
 
0
 
-------------------------------
 
-------------------------------
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</description>
 
</description>
 
<seealso>
 
<seealso>
<see>Use</see>
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<see>ApCoCoA-1:Use|Use</see>
 
</seealso>
 
</seealso>
 
<types>
 
<types>
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<key>NC.Deg</key>
 
<key>NC.Deg</key>
 
<key>Deg</key>
 
<key>Deg</key>
<wiki-category>Package_ncpoly</wiki-category>
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<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