This is Magma code for computing the mod p Dieudonne module of the Jacobian of a hyperelliptic curve over F_p. Elementary modifications to the code will allow one to compute the canonical and final types for the Jacobian of any hyperelliptic curve the user may desire.
In its current state (v1), the code is not optimal --- improvements are certainly possible. For a fixed curve, the code runs quickly, but it grows exponentially in the genus when counting the different final types (for a fixed prime p).
The reader is referred to Devalapurkar-Halliday, "The Dieudonn'e modules and Ekedahl-Oort types of Jacobians of hyperelliptic curves in odd characteristic", for a derivation of the formulae implemented here.