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MixedMultiplicity :: secMilnorNumbers

secMilnorNumbers -- Compute the sectional Milnor numbers of a hypersurface with an isolated singularity

Synopsis

Description

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

Ways to use secMilnorNumbers :