Input: C hyperelliptic curve over an unramified extension K of ${\mathbb{Q}}_p$ with p a prime of good ordinary reduction, Points P, Q on C.

Output: ${\displaystyle {\int }_P^Q{\omega }_i}$ .

1) Construct an linear interpolation $x\left(t\right)\mathrm{,}y\left(t\right)$ from P to Q.

2) Formally integrate the power series in t: ${\displaystyle {\int }_P^Q{\omega }_i}={\displaystyle {\int }_P^Q{x}^i\frac{dx}{2y}}={\displaystyle {\int }_{P\left(t\right)}^{Q\left(t\right)}x{\left(t\right)}^i\frac{d\left(x\left(t\right)\right)}{2y\left(t\right)}}$ .

3) Return ${\displaystyle {\int }_P^Q{\omega }_i}$ .