Base extension for Dirichlet groups and characters via maps

[pjbruin]

This ticket implements the following improvement to change_ring for Dirichlet groups and characters:

sage: K.<i> = QuadraticField(-1)
sage: G = DirichletGroup(5, K)
sage: chi = G[1]
sage: chi(2)
i
sage: f = K.complex_embeddings()[0]
sage: G.change_ring(f)
Group of Dirichlet characters of modulus 5 over Complex Field with 53 bits of precision
sage: psi = chi.change_ring(f)
sage: psi(2)
-1.00000000000000*I

Component: modular forms

Keywords: Dirichlet group base extension

Author: Peter Bruin

Branch/Commit: dd63f09

Reviewer: Jean-Pierre Flori

Issue created by migration from https://trac.sagemath.org/ticket/18072

[pjbruin]

Branch: u/pbruin/18072-DirichletGroup_change_ring

[pjbruin]

Commit: dd63f09

[jpflori]

Reviewer: Jean-Pierre Flori

[jpflori]

comment:2

The diff Looks good to me.
Just one question: Couldn't we extend such a contruction to be more general in the sense it could work for the change_ring method of all (or most) objects?
We can still do that in another ticket.

Note I don't have access to anything to check it passes tests, but the patchbot should take care of it.

[pjbruin]

comment:3

Replying to @jpflori:

Just one question: Couldn't we extend such a contruction to be more general in the sense it could work for the change_ring method of all (or most) objects?
We can still do that in another ticket.

Yes, I hope this can be done more generally at some point. Ideally, if A is a parent with base ring R and f is a ring homomorphism from R to S, we should be able to do something like

g = A.base_extend(f, map=True)

which should return the canonical map from A to the base extension A_S of A to S via f. We could then do g(a) for elements a of A to get the image of a in A_S.

Furthermore, we could allow

g = A.base_extend(S, map=True)

which should do the same as above, taking for f a coercion map from R to S, if it exists.

With this approach, base_extend() only has to be implemented for parents; there could be a default method for Element looking like

class Element(...):
    ...
    def base_extend(self, S):
        # S can be a parent or a map
        g = self.parent().base_extend(S, map=True)
        return g(self)

(All of the above would be valid both for base_extend() and change_ring(); the only difference is whether conversion maps are allowed instead of coercion maps if S is given as a parent.)

Note I don't have access to anything to check it passes tests, but the patchbot should take care of it.

Thanks for the review!

[vbraun]

Changed branch from u/pbruin/18072-DirichletGroup_change_ring to dd63f09