Difference between revisions of "ApCoCoA-1:NC.IsHomog"
From ApCoCoAWiki
| Line 2: | Line 2: | ||
<title>NC.IsHomog</title> | <title>NC.IsHomog</title> | ||
<short_description> | <short_description> | ||
| − | Check whether a polynomial or a | + | Check whether a polynomial or a LIST of polynomials is homogeneous in a non-commutative polynomial ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 8: | Line 8: | ||
</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 ring | ||
<itemize> | <itemize> | ||
| − | <item>@param <em>F</em>: a polynomial or a LIST of polynomials | + | <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>@return: a BOOL | + | <item>@return: a BOOL, which is True if F is homogeneous and False otherwise.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| Line 32: | Line 30: | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see> | + | <see>Use</see> |
</seealso> | </seealso> | ||
<types> | <types> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
| − | <type> | + | <type>polynomial</type> |
| − | |||
<type>non_commutative</type> | <type>non_commutative</type> | ||
</types> | </types> | ||
Revision as of 12:23, 29 April 2013
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
NC.SetX(<quotes>xy</quotes>); F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; F := [F1,F2]; NC.IsHomog(F); False ------------------------------- NC.IsHomog(F1); True ------------------------------- NC.IsHomog(F2); False -------------------------------
See also
