Random sum of functions

[Laurent Decreusefond]

Hi everyone,

say I have a function of both an integer n and a complex z

def f(n,z):

     return z**n

For any tuple of integer (a_1,a_2, ..., a_k), (actually, k and a_i are random), I want to form the function 

z -> sum_{i=1}^k |f(a_i, z)|^2

The result must still be a function. I guess it is something which can be done by redefining a new class but I'm a totally newbie at object programming.

Can you help me ?

[D. S. McNeil]

I don't think you need to make an explicit class here.  You can build a function from within another function, and return that:

sage: def f(n, z):

....:     return z**n

....: 

sage: def maker(tup):

....:     def g(z):

....:         return sum(abs(f(a_i,z))**2 for a_i in tup)

....:     return g

....: 

After which

sage: f(1, 3+2*I)

2*I + 3

sage: maker((1,5,3))

<function __main__.g>

sage: g = maker((1,5,3))

sage: g(5)

9781275

sage: abs(f(1,5))**2 + abs(f(5,5))**2 + abs(f(3,5))**2

9781275

I used Python functions here because that's what you started with.  A similar approach would have worked if you were making a Sage function instead, namely write a function which accepts a tuple and returns a new function.

Doug

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[Anton Sherwood]

On 2013-7-17 02:07, Laurent Decreusefond wrote:
> For any tuple of integer (a_1,a_2, ..., a_k), [...]

> I want to form the function
>
> z -> sum_{i=1}^k |f(a_i, z)|^2

Won't this work?

def ff(atuple,z):
return sum([ abs(f(n,z))**2 for n in atuple ])

--
*\\* Anton Sherwood *\\* www.bendwavy.org