Difference between revisions of "ApCoCoA-1:NC.IsGB"
From ApCoCoAWiki
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<title>NC.IsGB</title> | <title>NC.IsGB</title> | ||
<short_description> | <short_description> | ||
| − | + | Check whether a list of non-zero polynomials over a free monoid ring is a Groebner basis. | |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
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<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 | + | 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. 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>G</em>: a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of | + | <item>@param <em>G</em>: 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>]].</item> |
| − | <item>@return: a BOOL value which is True if G is a Groebner basis and False otherwise.</item> | + | <item>@return: a BOOL value which is True if <tt>G</tt> is a Groebner basis and False otherwise.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| Line 24: | Line 24: | ||
NC.IsGB(G); -- LLEX ordering (default ordering) | NC.IsGB(G); -- LLEX ordering (default ordering) | ||
False | False | ||
| + | |||
------------------------------- | ------------------------------- | ||
NC.SetOrdering(<quotes>ELIM</quotes>); | NC.SetOrdering(<quotes>ELIM</quotes>); | ||
NC.IsGB(G); | NC.IsGB(G); | ||
False | False | ||
| + | |||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| Line 37: | Line 39: | ||
<see>NC.GB</see> | <see>NC.GB</see> | ||
<see>NC.HF</see> | <see>NC.HF</see> | ||
| + | <see>NC.Interreduction</see> | ||
<see>NC.Intersection</see> | <see>NC.Intersection</see> | ||
<see>NC.IsGB</see> | <see>NC.IsGB</see> | ||
Revision as of 14:36, 7 June 2012
NC.IsGB
Check whether a list of non-zero polynomials over a free monoid ring is a Groebner basis.
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 set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, 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 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,""]].
@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>]]; G := [F1, F2,F3,F4]; NC.IsGB(G); -- LLEX ordering (default ordering) False ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.IsGB(G); False -------------------------------
See also
