gb -- compute a Groebner basis

Synopsis

• Usage:

  gb I

• Inputs:

  • I, an ideal, module, or matrix
• Outputs:

  • a Groebner basis, a Groebner basis computation object
• Optional inputs:

  • Algorithm => ..., -- set the Groebner basis algorithm
  • BasisElementLimit => ...,
  • ChangeMatrix => ...,
  • CodimensionLimit => ...,
  • DegreeLimit => ...,
  • GBDegrees => ...,
  • HardDegreeLimit => ...,
  • Hilbert => ...,
  • PairLimit => ...,
  • StopBeforeComputation => ..., -- do not actually compute a Groebner basis
  • StopWithMinimalGenerators => ...,
  • Strategy => ..., -- set the Groebner basis strategy
  • SubringLimit => ...,
  • Syzygies => ...,
  • SyzygyLimit => ..., -- stop when this number of syzygies is obtained
  • SyzygyRows => ...,

Description

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(a^3-b^2*c, b*c^2-c*d^2, c^3),

              3    2      2      2   3
o2 = (ideal (a  - b c, b*c  - c*d , c ), )

o2 : Sequence

i3 : G = gens gb I

o3 = | c3 bc2-cd2 a3-b2c c2d2 cd4 |

             1       5
o3 : Matrix R  <--- R

See also

• Groebner bases
• generators(GroebnerBasis) -- the generator matrix of a Groebner basis