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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 GebauerMoeller, sugar strategy and tracelifting 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 tracelifting. 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.
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