Symbolic functions without named variables
Is there a way to define a symbolic function that can (e.g.) be differentiated, but doesn't remember the name of its input variable(s)? For instance, consider:
sage: f(x) = x^2 sage: g(x) = x^2 sage: h(t) = t^2
Mathematically, f, g, and h, should all be the same function. However, Sage doesn't think so:
sage: f+g x |--> 2*x^2 sage: f+h (t, x) |--> t^2 + x^2
I guess that this is happening because a "function" defined with
f(x)=x^2 is actually just a symbolic expression equipped with an ordering on its variables, rather than what a mathematician would call a "function". Is there a way to define an actual mathematical function?