RE: Multiple Summation Question

["McLaughlin, James" <jmclaughlin@wcupa.edu>]

Thanks!! I was doubtful whether that was possible, but your neat program did what I wanted
(
except 
f(i,J)=1+prod(j=1,i,J[j])+2^(i*J[i]-(i-1)*J[i-1]) not
                            ^
f(i,J)=1+prod(j=1,i,J[i])+2^(i*J[i]-(i-1)*J[i-1])
                            ^
).

Now that you have explained the method, I will be able to adapt for what I really want to do.

Thanks again,

Jimmy Mc Laughlin


________________________________________
From: Bill Allombert [Bill.Allombert@math.u-bordeaux1.fr]
Sent: Saturday, June 04, 2011 5:51 AM
To: pari-users@list.cr.yp.to
Subject: Re: Multiple Summation Question

On Sat, Jun 04, 2011 at 03:09:39AM +0000, McLaughlin, James wrote:
> >Well, you can start by defining a function f that takes i, [j_1,...,j_k] and the other parameters
                                                              ^^^^^^^^^^^^^
> >and returns f_i (j_1,j_2, ..., j_i, other parameters).
>
> >At this point you should be able to finish with forvec.
>
> Displaying my ignorance again, but I don't see how to define such a function f in k variables j_1,j_2, ..., j_k when k is a parameter that changes.

You missed the brackets above: the idea was to pass the variables as a single vector

> Just to keep it simple, set j_0=0, and
>  F(k)=
> Sum_{j_1=1}^1 Sum_{j_2=1}^2 ... Sum_{j_k=1}^k
> Product_{i=1}^k f_i (j_1,j_2, ..., j_i)
> where
> f_i (j_1,j_2, ..., j_i) = 1+ j_1*j_2*...*j_i + 2^(i*j_i - (i-1)*j_{i-1}).
>
> I can write a program to evaluate this kind of expression for any particular k, but I still can't really see how to do it for every k.

Define f as follow:

f(i,J)=1+prod(j=1,i,J[i])+2^(i*J[i]-(i-1)*J[i-1])
F(k)=my(s=0);forvec(J=vector(k,i,[1,i]),s+=prod(i=1,k,f(i,J)));s

(you will have to fix f for i=1)

Cheers,
Bill.