I recently started using Sage in earnest, and was trying to define a function on functions. But:
inner_product(f,g) = integral(f(x) * g(x), (x,0,1))
inner_product
returns:
(f, g) |--> 1/3
Not surprisingly, trying to use it, it behaves as described:
e1(x) = 1
inner_product(e1,e1)
returns:
1/3
And curiously:
inner_product(f,g) = integral(f(x) * 1, (x,0,1))
inner_product
returns:
(f, g) |--> 1/2
What's going on here?
