Define JetSpace equality

[PerezHz]

This PR is an attempt to fix #417:

• Adds structural JetSpace == and matching hash. By structural I mean comparing order, number of variables, variable names, and symbols, not caches/locks.
• Updates TaylorN and HomogeneousPolynomial equality to use space(a) == space(b).
• Leaves arithmetic checks identity-based via _check_same_space, so mixed-space operations still throw.
• Updates set_default_space! to keep and return the existing default object when the incoming space is structurally equal.
• Updates variables! to reuse the existing default space instead of constructing/replacing an equivalent one.
• Adds tests for equality, hashing, no-warning reuse, and continued arithmetic rejection across distinct space identities.

cc: @lbenet @schillic

[coveralls]

Coverage is 89.357% — PerezHz:jp/jetspace-equality into JuliaDiff:master. No base build found for JuliaDiff:master.

[schillic]

Thanks, in my later comments of #417 I did not mean to change the definition of == anymore. But if you think it makes sense, I will also not complain 🙂

[schillic]

Suggested change

old_space === space && return space

This line is now redundant.

[schillic]

Not sure this qualifies as a patch version. It changes the behavior.

[schillic]

Sorry, while this is helpful, it is not solving all of my issues.
Is there a reason why HomogeneousPolynomials need to have the same space? In particular, it could be sufficient that the relevant variables are the same. Consider the extreme case below where both polynomials are constants but created for different spaces.

julia> cp
 33.0

julia> cq
 33.0

julia> cp.space
JetSpace
    Expansion order:        3
    Number of variables:    3
    Variable names:         ["x₁", "x₂", "x₃"]
    Variable symbols:       [:x₁, :x₂, :x₃]

julia> cq.space
JetSpace
    Expansion order:        3
    Number of variables:    5
    Variable names:         ["x₁", "x₂", "x₃", "x₄", "x₅"]
    Variable symbols:       [:x₁, :x₂, :x₃, :x₄, :x₅]

julia> cp == cq
false

I understand that this is much more intricate to implement. So would it be possible to provide a function (again, it does not have to be ==) to check equality of polynomials while ignoring the space?

[lbenet]

Is there a reason why HomogeneousPolynomials need to have the same space?

My naive guess to answer this question is that HomogeneousPolynomials are the basic consitituents of TaylorN, and in that sense they need to be related to a JetSpace.