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

From ApCoCoAWiki
m (insert version info)
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
 +
{{Version|1}}
 
<command>
 
<command>
 
<title>NC.IsHomog</title>
 
<title>NC.IsHomog</title>
Line 8: Line 9:
 
</syntax>
 
</syntax>
 
<description>
 
<description>
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 or a LIST of non-commutative polynomials. 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 or a LIST of non-commutative polynomials. 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>
Line 14: Line 15:
 
</itemize>
 
</itemize>
 
<example>
 
<example>
NC.SetX(<quotes>xy</quotes>);  
+
USE QQ[x[1..2],y[1..2]];
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]];
+
F1:= [[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3]]; -- 2x[1]y[1]x[2]^2-9y[2]x[1]^2x[2]^3
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]];  
+
F2:= [[2x[1],y[1],x[2]^2], [y[2],x[2]^3]]; -- 2x[1]y[1]x[2]^2+y[2]x[2]^3
F := [F1,F2];  
+
F3:= [[2x[1],y[1],x[2]]]; -- 2x[1]y[1]x[2]
NC.IsHomog(F);
+
NC.IsHomog(F1);
 +
NC.IsHomog(F2);
 +
NC.IsHomog(F3);
 +
NC.IsHomog([F1,F2,F3]);
 +
NC.IsHomog([F2,F3]);
 +
 
 
False
 
False
 
-------------------------------
 
-------------------------------
NC.IsHomog(F1);
 
 
True
 
True
 
-------------------------------
 
-------------------------------
NC.IsHomog(F2);
+
True
 +
-------------------------------
 
False
 
False
 +
-------------------------------
 +
True
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
 
</description>
 
</description>
 
<seealso>
 
<seealso>
<see>Use</see>
+
<see>ApCoCoA-1:Use|Use</see>
 
</seealso>
 
</seealso>
 
<types>
 
<types>
Line 40: Line 48:
 
<key>NC.IsHomog</key>
 
<key>NC.IsHomog</key>
 
<key>IsHomog</key>
 
<key>IsHomog</key>
<wiki-category>Package_ncpoly</wiki-category>
+
<wiki-category>ApCoCoA-1:Package_ncpoly</wiki-category>
 
</command>
 
</command>

Latest revision as of 10:14, 7 October 2020

This article is about a function from ApCoCoA-1.

NC.IsHomog

Check whether a polynomial or a LIST of polynomials is homogeneous in a non-commutative polynomial ring.

Syntax

NC.IsHomog(F:LIST):BOOL

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 or a LIST of non-commutative polynomials. 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: a BOOL, which is True if F is homogeneous and False otherwise.

Example

USE QQ[x[1..2],y[1..2]];
F1:= [[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3]]; -- 2x[1]y[1]x[2]^2-9y[2]x[1]^2x[2]^3
F2:= [[2x[1],y[1],x[2]^2], [y[2],x[2]^3]]; -- 2x[1]y[1]x[2]^2+y[2]x[2]^3
F3:= [[2x[1],y[1],x[2]]]; -- 2x[1]y[1]x[2]
NC.IsHomog(F1);
NC.IsHomog(F2);
NC.IsHomog(F3);
NC.IsHomog([F1,F2,F3]);
NC.IsHomog([F2,F3]);

False
-------------------------------
True
-------------------------------
True
-------------------------------
False
-------------------------------
True
-------------------------------

See also

Use