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

Synopsis

• Function: ambient

• Usage:

  result = ambient S

• Inputs:
  • S, a 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 = 20.

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 = 20.

o5 : SAGBIBasis

i6 : ambient S'

o6 = Q

o6 : QuotientRing

See also

• Subring -- The type of all subrings
• subring -- Constructs a subring of a polynomial ring.
• SAGBIBasis -- The type of all subalgebra bases
• sagbiBasis -- Constructs a computation object from a subring.
• generators(SAGBIBasis) -- Returns generators of a SAGBIBasis computation object
• ambient(Subring) -- The ambient ring of a subring