groebner

<< [[f1 ... fn] [options]] groebner 
   [[g1 ... gm] backward-transformation syzygy]>>
poly f1, ..., fn; poly g1, ..., gm;
optional return value: matrix of poly backward-transformation, syzygy;
Computation of the Groebner basis of f1,...,fn. The basis is {g1,...,gm}.
Options:  << (needBack), (needSyz), (countDown) number (StopDegree) number, (forceReduction)>>
Flags:<< [(ReduceLowerTerms) 1] system_variable >>
      << [(UseCriterion1) 0]    system_variable >>
      << [(UseCriterion2B) 0]   system_variable >>
      << [(Sugar) 0]            system_variable >>
      << [(Homogenize) 1]       system_variable >>
      << [(CheckHomogenization) 1] system_variable >>
      << [(Statistics) 1]       system_variable >>
      << [(KanGBmessage) 1]     system_variable >>
      << [(Verbose) 0]          system_variable >>
Example: [(x0,x1) ring_of_polynomials 0] define_ring
         [(x0^2+x1^2-h^2). (x0 x1 -4 h^2).] /ff set ;
         [ff] groebner /gg set ;
         gg ::
cf. homogenize, groebner_sugar, define_ring, 
    ring_of_polynomials, ring_of_differential_operators.