Souvignier-Plesken algorithm with additional fixed quadratic forms

[vadym-kl]

I'd like to check if two lattices L_1, L_2 over a number filed are isomorphic with the restriction that the isomorphism is an automorphism group of the third lattice L_3. This can be achieved by using Magma's IsIsomorphic by providing additional quadratic forms that the isomorphism must preserve. Is there a similar functionality available within Hecke's internals?

It seems to me that an almost identical functionality is required for computing isomorphisms of lattices over number fields.

Another similar use case I have is computing intersection of the automorphism groups of two lattices over a number field.

I did try looking through the sources myself but found it hard to figure out my question.
Thank you for your help.

[thofma]

Internally we also have the version, where one can provide additional forms. If you can share the Magma code, we can probably translate it. Same applies to the second question.