Difference between revisions of "ApCoCoA-1:NC.IsHomog"
| Line 1: | Line 1: | ||
<command> | <command> | ||
| − | <title> | + | <title>NC.IsHomog</title> |
<short_description> | <short_description> | ||
Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial ring. | Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial ring. | ||
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | + | NC.IsHomog(F:LIST):BOOL | |
</syntax> | </syntax> | ||
<description> | <description> | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref> | + | Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NC.SetFp</ref>, <ref>NC.SetX</ref> and <ref>NC.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. |
<itemize> | <itemize> | ||
<item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | <item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | ||
| Line 16: | Line 16: | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | NC.SetX(<quotes>xy</quotes>); | |
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | ||
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | ||
F := [F1,F2]; | F := [F1,F2]; | ||
| − | + | NC.IsHomog(F); | |
False | False | ||
------------------------------- | ------------------------------- | ||
| − | + | NC.IsHomog(F1); | |
True | True | ||
------------------------------- | ------------------------------- | ||
| − | + | NC.IsHomog(F2); | |
False | False | ||
------------------------------- | ------------------------------- | ||
| Line 41: | Line 41: | ||
</types> | </types> | ||
<key>ncpoly.IsHomog</key> | <key>ncpoly.IsHomog</key> | ||
| − | <key> | + | <key>NC.IsHomog</key> |
<key>IsHomog</key> | <key>IsHomog</key> | ||
<wiki-category>Package_ncpoly</wiki-category> | <wiki-category>Package_ncpoly</wiki-category> | ||
</command> | </command> | ||
Revision as of 17:26, 25 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 note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial or a LIST of polynomials in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.
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
