ambient(SAGBIBasis) -- The ambient ring of a SAGBIBasis computation object

Synopsis

• Function: ambient

• Usage:

  result = ambient S

• Inputs:
  • S, an instance of the type SAGBIBasis,
• Outputs:
  • result, a ring,

Description

i1 : R = QQ[x,y,z];

i2 : S = sagbi {x^2, y^2, z^2}

o2 = SAGBIBasis Computation Object with 3 generators, Limit = 100.

o2 : SAGBIBasis

i3 : ambient S

o3 = R

o3 : PolynomialRing

i4 : Q = R / ideal(x^3 - y);

i5 : S' = sagbi {x^3, y^2}

o5 = SAGBIBasis Computation Object with 1 generators, Limit = 100.

o5 : SAGBIBasis

i6 : ambient S'

o6 = Q

o6 : QuotientRing

See also

• SAGBIBasis -- The type of all sagbi bases
• generators(SAGBIBasis) -- Returns a partial sagbi generating set
• ambient(SAGBIBasis) -- The ambient ring of a SAGBIBasis computation object
• ring(SAGBIBasis) -- The lifted ring of a SAGBIBasis computation object
• net(SAGBIBasis) -- Short summary of a sagbi basis computation object
• status(SAGBIBasis) -- status of the sagbi computation
• sagbiDegree -- The current degree of the sagbi computation
• sagbiLimit -- The current limit of the sagbi computation
• sagbi -- Compute a subalgebra basis (sagbi basis)