How to apply a function (like the sum) among all elements of a list?

edit

The easiest are sum and product (corresponding to + and *): if a is a list (or a tuple, or any iterable) of numbers or symbolic expressions, sum(a) gets you the sum of its elements, prod(a) their product.

Here is an example with numbers.

sage: sum([1, 2, 3, 4, 5])
15
sage: prod([1, 2, 3, 4, 5])
120

Here is an example with symbolic expressions.

sage: x, y, z = SR.var("x y z")
sage: sum([x, y, z])
x + y + z
sage: prod([x, y, z])
x*y*z

Of course you could mix the two.

sage: sum([x, y, z, 1, 2, 3])
x + y + z + 6
sage: prod([x, y, z, 5, 6])
30*x*y*z

Next are all and any (for the and and or operators).

sage: all(is_prime(k) for k in (3, 5, .. 11))
False
sage: any(is_prime(k) for k in (3, 5, .. 11))
True

For a more general operator, use reduce.

sage: a = [720, 3, 4, 5]
sage: reduce(lambda x, y: x // y, a)
12

Optionally, include a start value outside the list.

sage: a = [3, 4, 5]
sage: reduce(lambda x, y: x // y, a, 720)
12