Difference between revisions of "ApCoCoA-1:NC.IsHomog"
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<command> | <command> | ||
<title>NC.IsHomog</title> | <title>NC.IsHomog</title> | ||
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</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> | ||
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</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | USE QQ[x[1..2],y[1..2]]; | |
| − | F1 := [[1, | + | 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 | + | 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( | + | NC.IsHomog(F1); |
| + | NC.IsHomog(F2); | ||
| + | NC.IsHomog(F3); | ||
| + | NC.IsHomog([F1,F2,F3]); | ||
| + | NC.IsHomog([F2,F3]); | ||
| + | |||
False | False | ||
------------------------------- | ------------------------------- | ||
| − | |||
True | True | ||
------------------------------- | ------------------------------- | ||
| − | + | 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
