Define `==` for `JetSpace`

[schillic]

TaylorSeries.jl/src/total_order.jl

Lines 23 to 29 in 7a8ccbd

	function ==(a::TaylorN{T}, b::TaylorN{T}) where {T<:Number}
	space(a) === space(b) || return false
	if order(a) != order(b)
	a, b = fixorder(a, b)
	end
	return a.coeffs == b.coeffs
	end

The code above compares the spaces. But there is no definition of ==, so it uses the fallback ===. This should change, as you can create a new space that is identical and then the comparison should return true (in my opinion).

[lbenet]

I think this is by design, though @PerezHz may comment on that. During the review of #410, there was a somewhat related comment; see here.

[schillic]

I understand this from the perspective of a simple script where you would not redefine your space if you know that you work in the same dimension. But it does not work for library code that needs to be generic and hence does not assume the dimension but rather automatically creates the space for the user via variables!.

This is very inconvenient for tests now. We compared two Taylor models that were created by different function calls. Both calls use variables! in the beginning because they allow for arbitrary dimensions. Is there any convenient way to compare two Taylor models other than with ==? I do not want to write my own function because it would depend on internal implementation details, which may suddenly change.

[schillic]

Maybe related to that: how can I avoid creating a new space? Do I have to manually check that it does not exist already? Is there an API function that does this for me?

┌ Warning: Updating TaylorSeries.default_space[]; existing TaylorN and HomogeneousPolynomial objects keep their original JetSpace, while future default-space constructors use the new default JetSpace.
│   old_order = 3
│   old_numvars = 3
│   new_order = 3
│   new_numvars = 3
└ @ TaylorSeries ~/.julia/packages/TaylorSeries/erD0i/src/hash_tables.jl:260

[lbenet]

I guess that the way to proceed is to define a JetSpace (with an order large enough), or if you want to use the default space, perhaps use TS.set_default_space!, and the use variables(::JetSpace, order=order). If you work with the default_space, then you should use variables(order::Int) to change it.

[lbenet]

Can you provide some MWE?