The genus of an algebraic curve
genus(f, x, y, opt)
squarefree polynomial specifying an algebraic curve
(optional) a sequence of options
The genus of an irreducible algebraic curve is a non-negative integer. It equals the dimension of the holomorphic differentials. It also equals (d-1)(d-2)/2 minus the sum of the delta invariants, which can be computed with algcurves[singularities]. Here d is the degree of the curve.
The polynomial f must be squarefree and have degree at least 1, otherwise an error message follows. A complete irreducibility check is not performed, only a few partial tests.
This f is a polynomial of degree 10 having a maximal number of cusps according to the Plucker formulas. It was found by Rob Koelman. It has 26 cusps and no other singularities, hence the genus is (10-1)*(10-2)/2 - 26 = 10.
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