Can arbitrary n-number container be introduced?

[mcpl-sympy]

I reckon that this may be helpful for introducing function with arbitrary number of arguments. Maybe what we need is SymPy-version generator.
Perhaps we can allow n-numbered Cartesian product of set as well? S.Reals**Symbol('n', integer=True, positive=True) currently raises error.

[oscarbenjamin]

I think that Reals**n for a symbol n makes sense. I'm not sure what we could do with it though. I don't know how you would implement it though given that there is no set power object. Currently Reals ** 3 is just ProductSet(Reals, Reals, Reals).

Generally a product set represents a set of Tuples so I guess when you say "n-number container" you mean a symbolic object that somehow represents a Tuple of length n where n is given as a symbol/expression. That would probably need to be a purely symbolic stand in though like MatrixSymbol.

[sylee957]

I think that a cartesian power class should be introduced also to remove the need to copy S.Reals n times.
But I can't think of the name that can align with ProductSet

[oscarbenjamin]

Another possibility is that the CartesianProduct class could gain an exponent for each base set. That would make it possible to define something like the set of n+1 tuples of n reals and one integer as ProductSet((Reals, n), (Integers, 1)). That's not the same as ProductSet(Reals**n, Integers) which would be a set of 2-tuples where the first element is a tuple of n reals.

[asmeurer]

You'd need a way to represent the elements of such a set first.

There's also A**B which is the set of functions from B to A. A**n is isomorphic to A**{1, 2, ..., n}, though I think it's worth keeping those distinct for the purposes of the type system.

[Smit-create]

Similar issue #17267

[sylee957]

Is the cartesian product A**B able to represent variadic functions?
I think that the only thing needed is a way to represent variadic functions, which is used often in python like *args as how people define functions, but which lacks mathematical machinery.