\ should choose a space if none is inferrable

[dlfivefifty]

I wish I could type

D=Derivative()
B=dirichlet()
x=Fun(identity)
u=[B,D^2+x][1.,0.]

and it chooses the space from x. At the moment, the x is interpreted as Multiplication(x,AnySpace()) so that spaces can be inferred from other operators. (Since Chebyshev can multiply other spaces like Jacobi). Some system for choosing a default space should exist when it returns AnySpace.

[dlfivefifty]

I’m thinking of adding

choosedomainspace(operator,rangespace)

that will choose a domain space given the range space, but where the range space can be changed in the process. So we’d have

choosedomainspace(Derivative(),Ultrasperical{0}()) == Ultraspherical{0}()
choosedomainspace(Derivative(),Ultrasperical{1}()) == Ultraspherical{0}()
choosedomainspace(Derivative(),Ultrasperical{2}()) == Ultraspherical{1}()

choosedomainspace(RealOperator(),Laurent()) == ReImSpace(Laurent())

choosedomainspace(::,ds)=ds     # default, and equivalent to current situation

This would navigate down the tree and promote the spaces as neccesary on the way back up. One use case that's not clear is the original question: should

choosedomainsace(Multiplication(x,UnsetSpace()),AnySpace())

return domainspace(x)? there could be an issue with the "correct" space coming from another part of the tree... but maybe this is an edge situation where its fine to insist that spaces are specified by hand.

[dlfivefifty]

That was easier than expected :) It defaults to

choosedomainspace(A::Operator,::)=domainspace(A)

but operators that support UnsetSpace can override it. Right now only Multiplication does, but RealOperator is next