Symbolic Computation Group

The Jacobian of a hyperelliptic curve is the subject of many conjectures and open problems in algebraic geometry and number theory. Efficient Jacobian arithmetic plays a crucial role in the experimental investigation of these problems. For curves of low genus, explicit formulas effectively realize this arithmetic, but manually developing such formulas is not feasible in higher genera.

We introduce the first software package for automating the process of generating and verifying explicit formulas for curves of arbitrary genus. Our formulas outperform generic algorithms for Jacobian arithmetic and exhibit comparable operation counts against manually fine-tuned formulas for small genera.