Here are the main steps of the algorithm:

- Compute a -basis of .
- For increasing compute successively the lattices in terms of , and in terms of up to order until and is the saturation of .
- Compute a -basis of .
- Compute in terms of up to order .
- Compute in terms of up to order .
- Compute in terms of .
- Compute the -filtration on in terms of .
- Compute the induced -filtration on in terms of .