Difference between revisions of "ApCoCoA-1:NC.Deg"
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<command> | <command> | ||
<title>NC.Deg</title> | <title>NC.Deg</title> | ||
<short_description> | <short_description> | ||
| − | The | + | The standard degree of a polynomial in a non-commutative polynomial ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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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. | + | 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> | ||
| − | + | 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( | + | NC.Deg(F1); |
| − | + | ||
| + | 2 | ||
------------------------------- | ------------------------------- | ||
| − | NC.Deg([]); | + | NC.Deg([]); |
| + | |||
0 | 0 | ||
------------------------------- | ------------------------------- | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>Use</see> | + | <see>ApCoCoA-1:Use|Use</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
| Line 36: | Line 39: | ||
<key>NC.Deg</key> | <key>NC.Deg</key> | ||
<key>Deg</key> | <key>Deg</key> | ||
| − | <wiki-category>Package_ncpoly</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
