[ < ] | [ > ] | [ << ] | [ Up ] | [ >> ] | [Top] | [Contents] | [Index] | [ ? ] |
There are many functions and options defined in the package `gr'.
Usually not so many of them are used. Top level functions for Groebner
basis computation are the following three functions.
In the following description, plist, vlist, order
and p stand for a list of polynomials, a list of variables
(indeterminates), a type of term ordering and a prime less than
2^27
respectively.
gr(plist,vlist,order)
Function that computes Groebner bases over the rationals. The algorithm is Buchberger algorithm with useless pair elimination criteria by Gebauer-Moeller, sugar strategy and trace-lifting by Traverso. For ordinary computation, this function is used.
hgr(plist,vlist,order)
After homogenizing the input polynomials a candidate of the \gr basis is computed by trace-lifting. Then the candidate is dehomogenized and checked whether it is indeed a Groebner basis of the input. Sugar strategy often causes intermediate coefficient swells. It is empirically known that the combination of homogenization and supresses the swells for such cases.
gr_mod(plist,vlist,order,p)
Function that computes Groebner bases over GF(p). The same
algorithm as gr()
is used.