isFRational -- whether a ring is F-rational

Synopsis

• Usage:

  isFRational(R)

• Inputs:
  • R, a ring,
• Optional inputs:
  • AtOrigin => a Boolean value, default value false, specifies that $F$-rationality be checked only at the origin, and that the Cohen-Macaulayness test be done with the isCM command, from the Depth package
  • AssumeCM => a Boolean value, default value false, assumes the ring is Cohen-Macaulay
  • AssumeDomain => a Boolean value, default value false, assumes the ring is an integral domain
  • FrobeniusRootStrategy => a symbol, default value Substitution, selects the strategy for internal frobeniusRoot calls
• Outputs:
  • a Boolean value,

Description

i1 : T = ZZ/5[x,y];

i2 : S = ZZ/5[a,b,c,d];

i3 : g = map(T, S, {x^3, x^2*y, x*y^2, y^3});

o3 : RingMap T <-- S

i4 : R = S/(ker g);

i5 : isFRational(R)

o5 = true

i6 : R = ZZ/7[x,y,z]/(x^3 + y^3 + z^3);

i7 : isFRational(R)

o7 = false

i8 : S = ZZ/3[a,b,c,d,t];

i9 : M = matrix{{a^2 + t^4, b, d}, {c, a^2, b^3 - d}};

             2      3
o9 : Matrix S  <-- S

i10 : I = minors(2, M);

o10 : Ideal of S

i11 : R = S/I;

i12 : isFRational(R)

o12 = true

Caveat