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.

Warning, negative genus so the curve is reducible