isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test

Synopsis

• Function: isInMultiplierIdeal

• Usage:

  b = isInMultiplierIdeal(g,I,c)

• Inputs:
  • g, a ring element, a polynomial
  • I, an ideal, an ideal in a polynomial ring
  • c, a rational number, coefficient (or a list of coefficients)
• Optional inputs:
  • Strategy => ..., default value generalizedBFunction
• Outputs:
  • b, a Boolean value, answers: is in the multiplier ideal J_I(c)?

Description

Test if the given polynomial is in the multiplier ideal for given ideal and coefficient. In general, the test is cheaper than computing the whole multiplier ideal.

• generalizedBFunction -- via computation of the generalized Bernstein-Sato polynomial
• mGeneralizedBFunction -- via computation of the m-generalized Bernstein-Sato polynomial

i1 : R = QQ[x_1..x_4];

i2 : isInMultiplierIdeal(x_1, ideal {x_1^3 - x_2^2, x_2^3 - x_3^2}, 31/18)

o2 = false

i3 : isInMultiplierIdeal(x_1*x_2, ideal {x_1^3 - x_2^2, x_2^3 - x_3^2}, 31/18)

o3 = true

See also

• multiplierIdeal -- multiplier ideal
• jumpingCoefficients -- jumping coefficients and corresponding multiplier ideals
• generalB -- global generalized Bernstein-Sato polynomial