Difference between revisions of "ApCoCoA-1:NC.IsGB"
| Line 42: | Line 42: | ||
<see>NC.LT</see> | <see>NC.LT</see> | ||
<see>NC.LTIdeal</see> | <see>NC.LTIdeal</see> | ||
| + | <see>NC.MRAdd</see> | ||
| + | <see>NC.MRBP</see> | ||
| + | <see>NC.MRIntersection</see> | ||
| + | <see>NC.MRKernelOfHomomorphism</see> | ||
| + | <see>NC.MRMinimalPolynomials</see> | ||
| + | <see>NC.MRMultiply</see> | ||
| + | <see>NC.MRReducedBP</see> | ||
| + | <see>NC.MRSubtract</see> | ||
<see>NC.MinimalPolynomial</see> | <see>NC.MinimalPolynomial</see> | ||
<see>NC.Multiply</see> | <see>NC.Multiply</see> | ||
<see>NC.NR</see> | <see>NC.NR</see> | ||
| + | <see>NC.ReducedBP</see> | ||
| + | <see>NC.ReducedGB</see> | ||
<see>NC.SetFp</see> | <see>NC.SetFp</see> | ||
<see>NC.SetOrdering</see> | <see>NC.SetOrdering</see> | ||
| Line 56: | Line 66: | ||
<see>NC.UnsetRules</see> | <see>NC.UnsetRules</see> | ||
<see>NC.UnsetX</see> | <see>NC.UnsetX</see> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
Revision as of 12:34, 12 October 2010
NC.IsGB
Check if a list of polynomials is a Groebner basis.
Syntax
NC.IsGB(Polynomials: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.
Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param Polynomials: a LIST of polynomials in K<X>. Each polynomial in K<X> is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in K and w is a word in X*. Unit in X* is empty word represented as an empty STRING "". 0 polynomial is represented as an empty LIST []. For example, polynomial F:=xy-y+1 in K<x,y> is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].
@return: a BOOL which is True if Polynomials is a GB 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
