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 $e_0(m|J(f)),...,e_{d-1}(m|J(f))$, 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 |
The object secMilnorNumbers is a method function with options.