Difference between revisions of "ApCoCoA-1:NC.IsGB"
| Line 2: | Line 2: | ||
<title>NC.IsGB</title> | <title>NC.IsGB</title> | ||
<short_description> | <short_description> | ||
| − | Check whether a list of non-zero polynomials | + | Check whether a list of non-zero polynomials in a free monoid ring is a Groebner basis. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| Line 41: | Line 41: | ||
<see>NC.Interreduction</see> | <see>NC.Interreduction</see> | ||
<see>NC.Intersection</see> | <see>NC.Intersection</see> | ||
| + | <see>NC.IsFinite</see> | ||
<see>NC.IsGB</see> | <see>NC.IsGB</see> | ||
<see>NC.IsHomog</see> | <see>NC.IsHomog</see> | ||
| Line 58: | Line 59: | ||
<see>NC.SetX</see> | <see>NC.SetX</see> | ||
<see>NC.Subtract</see> | <see>NC.Subtract</see> | ||
| + | <see>NC.TruncatedGB</see> | ||
<see>NC.UnsetFp</see> | <see>NC.UnsetFp</see> | ||
<see>NC.UnsetOrdering</see> | <see>NC.UnsetOrdering</see> | ||
Revision as of 15:31, 8 June 2012
NC.IsGB
Check whether a list of non-zero polynomials in 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. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param G: a LIST of non-zero 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 w.r.t. the current ordering 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
