- Introduction
- Representation and Monomial Orders
- Polynomial Rings and Ideals
- Creation of Polynomial Rings and Accessing their Monomial Orders
- PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
- PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
- PolynomialRing(R, n, T) : Rng, RngIntElt, Tup -> RngMPol
- MonomialOrder(P) : RngMPol -> Tup
- MonomialOrderWeightVectors(P) : RngMPol -> [ [ FldRatElt ] ]
- SetSparseMonomialMinRank(R) : RngIntElt ->
- GetSparseMonomialMinRank() : -> RngIntElt
- Example GB_Order (H112E1)
- Creation of Graded Polynomial Rings
- Element Operations Using the Grading
- Creation of Ideals and Accessing their Bases
- Gröbner Bases
- Gröbner Bases over Fields
- Gröbner Bases over Euclidean Rings
- Construction of Gröbner Bases
- The Dense Variant of the F4 algorithm
- Related Functions
- HasGroebnerBasis(I) : RngMPol -> BoolElt
- EasyIdeal(I) : RngMPol -> RngMPol, [ RngIntElt ]
- EasyBasis(I) : RngMPol -> [ RngMPolElt ]
- SmallBasis(I) : RngMPol -> [ RngMPolElt ]
- MarkGroebner(I) : RngMPol ->
- IsGroebner(S) : { RngMPolElt } -> BoolElt
- Coordinates(I, f) : RngMPol, RngMPolElt -> [ RngMPolElt ]
- CoordinateMatrix(I) : RngMPol -> Matrix
- NormalForm(f, I) : RngMPolElt, RngMPol -> RngMPolElt
- NormalForm(f, S) : RngMPolElt, [ RngMPolElt ] -> RngMPolElt, [ RngMPolElt ]
- SPolynomial(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
- Reduce(S) : [ RngMPolElt ] -> [ RngMPolElt ]
- ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]
- Gröbner Bases of Boolean Polynomial Rings
- Construction of Input Systems
- MinRankSystem(K, n, k, r) : FldFin, RngIntElt, RngIntElt, RngIntElt -> [ RngMPolBool ]
- HFESystem(q, n, D) : RngIntElt, RngIntElt, RngIntElt -> [ RngMPolBool ]
- Verbosity
- SetVerbose("Groebner", v) : MonStgElt, RngIntElt ->
- SetVerbose("Buchberger", v) : MonStgElt, RngIntElt ->
- SetVerbose("Faugere", v) : MonStgElt, RngIntElt ->
- SetVerbose("FGLM", v) : MonStgElt, RngIntElt ->
- SetVerbose("GroebnerWalk", v) : MonStgElt, RngIntElt ->
- Example GB_Cyclic6 (H112E3)
- Example GB_RungeKutta2 (H112E4)
- Example GB_SolveOverGF2 (H112E5)
- Example GB_GBoverZ (H112E6)
- Example GB_FindingPrimes (H112E7)
- Example GB_QuadraticOrderGB (H112E8)
- Example GB_Coordinates (H112E9)
- Example GB_ValuationRing (H112E10)
- Degree-d Gröbner Bases
- Changing Coefficient Ring
- Changing Monomial Order
- Hilbert-driven Gröbner Basis Construction
- SAT solver
- Bibliography
V2.28, 13 July 2023