On Monday 29 July 2024 at 22:13:27 UTC-7 Andrew wrote:
[Not sure if this belongs here or in sage-dev...]
I am trying to implement coercions between algebras that are related by
base change. For example,consider
A=CombinatorialFreeModule(ZZ['x'], ['1','2'])
B=CombinatorialFreeModule(ZZ, ['1','2'])
A.module_morphism(
lambda a: B._from_dict({b: c.subtitute(x=1) for (b,c) in a}),
codomain=B, category=A.category()
).register_as_coercion()
Are you sure you want to register that as a *coercion*? Those are to be
used in other coercion discoveries as well and can be used implicitly to
resolve things like a+b, where a in A and b in B (and extensions of these!)
This is entirely reasonable because I have not specified how Z is a
Z[x]-module, but when I try to define this it seems I need slightly
different syntax:
Rx = ZZ['x]
R = ZZ
Rx.module_morphism(function=lambda f: f.substitute(x=1), codomain=R)
These are bases, so I think you should define a ring homomorphism between
them (I think a CombinatorialFreeModule has a ring as its base). And then
you see how you'd get a problem if you insert a coercion from ZZ['x'] to
ZZ: there's already one in the oppositie direction and sage really prefers
its coercion graph to not have directed cycles.
So I expect that your original map A -> B should really be one from a
ZZ['x']-module to a ZZ-module, where ZZ is really ZZ['x']/(x-1).
In fact, with
P.<x>=ZZ[]
R=P.quo(x-1)
A=CombinatorialFreeModule(P, ['1','2'])
B=CombinatorialFreeModule(R, ['1','2'])
I get:
sage: x*A('1')+B('2')
B['1'] + B['2']
so it seems to discover the coercion correctly. (I do get that A('1')
prints as B['1'] so there is something fishy there. Are combinatorial
modules always printing as `B`? or is that the default name for its
"basis"?)
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