<< [[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), (reduceOnly), (gbCheck), (countDown) number (StopDegree) number, (forceReduction)>> Flags:<< [(ReduceLowerTerms) 1] system_variable >> << [(AutoReduce) 0] 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.