ambient(Subring) -- The ambient ring of a subring

Synopsis

• Function: ambient

• Usage:

  result = ambient S

• Inputs:
  • S, a subring,
• Outputs:
  • result, a ring,

Description

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

i2 : S = subring({x^2, y^2, z^2});

i3 : ambient S

o3 = R

o3 : PolynomialRing

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

i5 : S' = subring({x^3, y^2});

i6 : ambient S'

o6 = Q

o6 : QuotientRing

See also

• Subring -- The type of all subrings
• subring -- Constructs a subring of a polynomial ring.
• generators(Subring) -- A generating set of a subring
• ambient(SAGBIBasis) -- The ambient ring of a SAGBIBasis computation object