With the advent of the new coercion model, did we get the incredibly
cool possibility of adding canonical coercions locally, as promissed
at SD7? I'd love to be able to type something like:
K.<r2>=Numberfield(x^2-2)
E=EllipticCurve([0,0,r2,0,0]
for m in K.real_embeddings():
with CanonicalEmbedding(m):
R=Codomain(m)
E_over_R=E.base_extend(R)
print E.real_period()
in order to get the real periods of E wrt. the two real embeddings of
K into R.
In general, getting all the "derived" maps from a non-canonical base-
extension is very painful. If one could just locally make these things
"canonical", you'd get a free ride on the coercion infrastructure.
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