Difference between revisions of "ApCoCoA-1:NC.IsGB"
| Line 2: | Line 2: | ||
<title>NC.IsGB</title> | <title>NC.IsGB</title> | ||
<short_description> | <short_description> | ||
| − | Checks whether a list of polynomials | + | Checks whether a list of polynomials over a free associative <tt>K</tt>-algebra is a Groebner basis of the ideal generated by polynomials. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | NC.IsGB( | + | NC.IsGB(G: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 coefficient field <tt>K</tt>, alphabet (or indeterminates) <tt>X</tt> and ordering through the functions <ref>NC.SetFp</ref>(Prime), <ref>NC.SetX</ref>(X) and <ref>NC.SetOrdering</ref>(Ordering), respectively, before calling the function. Default coefficient field is <tt>Q</tt>. Default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. | |
<itemize> | <itemize> | ||
| − | <item>@param <em> | + | <item>@param <em>G</em>: a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, unit is represented as an empty string <quotes></quotes>. Then, polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. <tt>0</tt> polynomial is represented as an empty LIST [].</item> |
| − | <item>@return: a | + | <item>@return: a BOOL value which is True if G is a Groebner basis and False otherwise.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 19:38, 11 December 2010
NC.IsGB
Checks whether a list of polynomials over a free associative K-algebra is a Groebner basis of the ideal generated by polynomials.
Syntax
NC.IsGB(G: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 indeterminates) X and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param G: a LIST of polynomials in K<X>. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. 0 polynomial is represented as an empty LIST [].
@return: a BOOL value which is True if G is a Groebner basis and False otherwise.
Example
NC.SetX(<quotes>xyt</quotes>); F1 := [[1,<quotes>xx</quotes>], [-1,<quotes>yx</quotes>]]; F2 := [[1,<quotes>xy</quotes>], [-1,<quotes>ty</quotes>]]; F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]]; F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]]; Polynomials := [F1, F2,F3,F4]; NC.IsGB(Polynomials); -- LLEX ordering (default ordering) False ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.IsGB(Polynomials); False -------------------------------
See also
