testModule(QQ,Ideal) -- computes the test ideal of a pair

• Function: testModule

• Usage:

  J = testModule(t, I)

• Inputs:
  • t, a rational number, a rational number
  • I, an ideal, an ideal
• Optional inputs:
  • AssumeDomain => ..., default value false,
  • CanonicalIdeal => ..., default value null,
  • CurrentRing => ..., default value null,
  • FrobeniusRootStrategy => ..., default value Substitution,
  • GeneratorList => ..., default value null,
• Outputs:
  • L, a list, a list with the test module and the canonical module

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

i2 : I = ideal(x^2, y^3);

o2 : Ideal of R

i3 : testModule(5/6, I)

o3 = (ideal (y, x), ideal 1)

o3 : Sequence

i4 : testModule(5/6-1/25, I)

o4 = (ideal 1, ideal 1)

o4 : Sequence

i5 : T = ZZ/2[a,b,c,d];

i6 : S = ZZ/2[x,y];

i7 : f = map(S, T, {x^3, x^2*y, x*y^2, y^3});

o7 : RingMap S <-- T

i8 : R = T/(ker f);

i9 : m = ideal(a,b,c,d);

o9 : Ideal of R

i10 : testModule(1, m)

                                   2
o10 = (ideal (b*d, a*d, a*c, a*b, a ), ideal (b, a))

o10 : Sequence

i11 : testModule(1-1/16, m)

o11 = (ideal (b, a), ideal (b, a))

o11 : Sequence