Let f be an element of a polynomial ring R and let d be the dimension of R. The function computes the first d-1 sectional Milnor numbers by computing the mixed multiplicities e0(m|J(f)),...,ed-1(m|J(f)), where m is the maximal homogeneous ideal of R and J(f) is the Jacobian ideal of f.
i1 : k = frac(QQ[t]) o1 = k o1 : FractionField |
i2 : R = k[x,y,z] o2 = R o2 : PolynomialRing |
i3 : secMilnorNumbers(z^5 + t*y^6*z + x*y^7 + x^15) o3 = HashTable{0 => 1 } 1 => 4 2 => 26 o3 : HashTable |
i4 : secMilnorNumbers(z^5 + x*y^7 + x^15) o4 = HashTable{0 => 1 } 1 => 4 2 => 28 o4 : HashTable |