Cartesian equation of Luroth's quartics
I'm in search of the Cartesian equation of Luroth's quartics, i.e. of those curves passing through the 10 vertices of a pentalateral complete.
I have found in Internet a formula of the type
1 / L0*l0 + 1 / L1*l1 + 1 / L2*l2 + 1 / L3*l3 + 1 / L4*l4
but I can't obtain from this formula the Cartesian equation of the quartic equations of Luroth in the form
a * x^4 + b * y^4 + c * x^3 * y + ... + D = 0
Ii think that L0, L1, L2, L3, L4 are of the coefficients of the quartic equations and that l0, l1, l2, l3, l4 are linked to the cartesian equations of the pentalateral, but more than this i don't know ...
Who can help me?
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Re: Cartesian equation of Luroth's quartics
I surmise you would find the answer in the article Mathematische Annalen, Volume 1, Number 1 - SpringerLink
Look up the source in your library, the above site charges money for access. Hopefully you can read German!