Computes the threshold of inclusion of the monomial m=x^v in the multiplier ideal J(I^t), that is, the value t = sup{ c | m lies in J(I^c) } = min{ c | m does not lie in J(I^c)}. In other words, (1/t)*(v+(1,..,1)) lies on the boundary of the Newton polyhedron Newt(I). In addition, returns the linear inequalities for those facets of Newt(I) which contain (1/t)*(v+(1,..,1)). These are in the format of
Normaliz, i.e., a matrix (A | b) where the number of columns of A is the number of variables in the ring, b is a column vector, and the inequality on the column vector v is given by Av+b >= 0, entrywise. As a special case, the log canonical threshold is the threshold of the monomial 1_R = x^0.
i1 : R = QQ[x,y];
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i2 : I = monomialIdeal(x^13,x^6*y^4,y^9);
o2 : MonomialIdeal of R
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i3 : monomialThreshold(I,x^2*y)
1
o3 = (-, | 4 7 -52 |)
2 | 5 6 -54 |
o3 : Sequence
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