On Tue, 1 Jun 2021 at 05:16, Neil Girdhar mistersheik@gmail.com wrote:

Hi Oscar,

The problem that the original poster was trying to address with additional syntax is the automatic naming of symbols. He wants to omit this line:

x = symbols("x")

You're right that if you have many one-character symbol names, you can use a shortcut, but this benefit is lost if you want descriptive names like:

momentum = symbols('momentum')

He is proposing new syntax to eliminate the repeated name. The function approach specifies each name exactly once. This is one of the benefits of JAX over TensorFLow.

Second, the function approach allows the function to be a single object that can be used in calcuations. You might ask for:

grad(equation, 2)(2, 3, 4 5) # derivative with respect to parameter 2 of equation evaluated at (2, 3, 4, 5)

With the symbolic approach, you need to keep the equation object as well as the symbols that compose it to interact with it.

This makes more sense in a limited context for symbolic manipulation where symbols only represent function parameters so that all symbols are bound. How would you handle the situation where the same symbols are free in two different expressions that you want to manipulate in tandem though?

In this example we have two different equations containing the same symbols and we want to solve them as a system of equations:

p, m, h = symbols('p, m, h') E = p**2 / 2*m lamda = h / p

E1 = 5 lamda1 = 2 [(p1, m1)] = solve([Eq(E, E1), Eq(lamda, lamda1)], [p, m])

I don't see a good way of doing this without keeping track of the symbols as separate objects. I don't think this kind of thing comes up in Jax because it is only designed for the more limited symbolic task of evaluating and differentiating Python functions.

Also for simple expressions like this I think that a decorated function seems quite cumbersome:

@symbolic def E(p, m): return p**2 / (2*m)

@symbolic def lamda(h, p): return h / p

Finally, the function can just be called with concrete values:

equation(2, 3, 4, 5) # gives 25

which is convenient.

That is convenient but I think again this only really makes sense if all of your expressions are really just functions and all of your symbols are bound symbols representing function parameters. It is possible in sympy to convert an expression into a function but you need to specify the ordering of the symbols as function parameters:

expression = p**2 / (2*m) function = lambdify([p, m], expression) function(1, 2) # 0.25

The need to specify the ordering comes from the fact that the expression itself is not conceptually a function and does not have an ordered parameter list.

-- Oscar