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## Fundamental functions

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.

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