groebnerMembershipTest -- Extrinsic method for subring membership

Synopsis

• Usage:

  result = groebnerMembershipTest(f, S)

• Inputs:
  • f, a ring element,
  • S, a subring,
• Outputs:
  • result, a Boolean value, which indicates if $f$ belongs to $S$.

Description

i1 : R = QQ[x,y];

i2 : S = subring {x^2 - x*y, x^4};

i3 : f1 = x^2*y^2 - 2*x^3*y;

i4 : groebnerMembershipTest(f1, S)

o4 = true

i5 : f2 = x^10;

i6 : groebnerMembershipTest(f2, S)

o6 = false

See also

• Subring -- The type of all subrings
• RingElement % Subring -- Remainder modulo a subring
• groebnerSubductionQuotient -- Extrinsic method for subduction quotients
• RingElement // Subring -- Subduction quotient with respect to a subring
• sagbi -- Compute a subalgebra basis (sagbi basis)