multiplier ideal of a monomial ideal
- Usage:
- multiplierIdeal(I,t)
- Inputs:
- Outputs:
Computes the multiplier ideal of
I with coefficient
t using Howald's Theorem and the package
Normaliz.
R = QQ[x,y]; |
I = monomialIdeal(y^2,x^3); |
multiplierIdeal(I,5/6) |
J = monomialIdeal(x^8,y^6); -- Example 2 of [Howald 2000] |
multiplierIdeal(J,1) |
multiplier ideal of a hyperplane arrangement
- Usage:
- multiplierIdeal(A,m,s)
- Inputs:
- Outputs:
Computes the multiplier ideal of the ideal of
A with coefficient
s using the package
HyperplaneArrangements.
R = QQ[x,y,z]; |
f = toList factor((x^2 - y^2)*(x^2 - z^2)*(y^2 - z^2)*z) / first; |
A = arrangement f; |
multiplierIdeal(A,3/7) |
multiplier ideal of monomial space curve
- Usage:
- I = multiplierIdeal(R,n,t)
- Inputs:
- Outputs:
Computes the multiplier ideal of the space curve C parametrized by (ta,tb,tc) given by n=(a,b,c).
R = QQ[x,y,z]; |
n = {2,3,4}; |
t = 5/2; |
I = multiplierIdeal(R,n,t) |
multiplier ideal of a generic determinantal ideal
- Usage:
- multiplierIdeal(R,L,r,t)
- Inputs:
- R, a ring, a ring
- L, a list, dimensions {m,n} of a matrix
- r, an integer, the size of minors generating the determinantal ideal
- t, a rational number, a coefficient
- Outputs:
Computes the multiplier ideal of the ideal of
r ×r minors in a
m ×n matrix whose entries are independent variables in the ring
R (a generic matrix).
x = symbol x; |
R = QQ[x_1..x_20]; |
X = genericMatrix(R,4,5); |
multiplierIdeal(X,2,5/7) |