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

• Function: testIdeal

• Usage:

  J = testIdeal(t, I)

• Inputs:
  • t, a rational number, a rational number
  • I, an ideal, an ideal
• Optional inputs:
  • AssumeDomain => ..., default value false,
  • FrobeniusRootStrategy => ..., default value Substitution,
  • MaxCartierIndex => ..., default value 10,
  • QGorensteinIndex => ..., default value 0,
• Outputs:
  • J, an ideal, an ideal, the test ideal

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

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

o2 : Ideal of R

i3 : testIdeal(5/6, I)

o3 = ideal (y, x)

o3 : Ideal of R

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

o4 = ideal 1

o4 : Ideal of R

i5 : testIdeal(2, I)

             2    3   4     3
o5 = ideal (x y, x , y , x*y )

o5 : Ideal of R

i6 : R = ZZ/3[x,y,z]/ideal(x^2-y*z);

i7 : I = ideal(x,y);

o7 : Ideal of R

i8 : testIdeal(1, I)

o8 = ideal (y, x)

o8 : Ideal of R

i9 : I2 = ideal(x,y,z);

o9 : Ideal of R

i10 : testIdeal(3/2,I2)

o10 = ideal (z, y, x)

o10 : Ideal of R