On Wed, Mar 24, 2010 at 11:09 AM, Ondrej Certik <ond...@certik.cz> wrote:
> On Wed, Mar 24, 2010 at 11:01 AM, Freddie Witherden
> <fred...@witherden.org> wrote:
>> Hi all,
>>
>> After a discussion on IRC I am interested if there is any way to evaluate
>> sums of the form:
>>
>>>>> B = [ Symbols, expressions, ... ]
>>>>> Sum(n*B[n]*Sqrt(B[n]), (n, 0, len(b)-1))
>>
>> I ask because the project I am currently working on is based heavily around
>> sums of this form:
>> sum(sum(sum(sum(B[i]*A[i,j]*A[j,k]*A[k,l]*C[l],l,1,s),k,1,s),j,1,s),i,1,s) =
>> 1/120
>>
>> where s, A[i,j] (matrix) and C[i] (vector) are evaluate to Real numbers with
>> just B[i] being Symbols (so the result of the above expression is an
>> equation of the form x1*B[1] + x2*B[2] + ... + xn*B[n] with xn being Reals
>> (of course in Python the indices would be slightly different).
>>
>> Can anyone think of a clean way to evaluate these sorts of sums? (Extra
>> points if you know where such sums arise in practise ;)
>>
>> Currently my workflow is:
>> 1) Use Python to generate the sums;
>> 2) Evaluate using Maxima;
>> 3) Paste back into a Python script, parse with regex, solve.
>
> Can you paste your whole code so that we can try it? So your problem
> is that some (complicated?) sums can't be evaluated in sympy, but it
> works in maxima?
>
> Paste the exact expressions, let's see what can be done.
Ok, after chatting at IRC a bit, here are the examples of expressions
in maxima, that you need to work in sympy:
sum(sum(sum(sum(B[i1]*A[i1,i2]*A[i2,i3]*A[i3,i4]*C[i4]^1, i4, 1, i3),
i3, 1, i2), i2, 1, i1), i1, 1, s) - 1/120
sum(sum(sum(B[i1]*A[i1,i2]*A[i2,i3]*C[i3]^2, i3, 1, i2), i2, 1, i1),
i1, 1, s) - 1/60
sum(sum(sum(B[i1]*A[i1,i2]*C[i2]^1*A[i2,i3]*C[i3]^1, i3, 1, i2), i2,
1, i1), i1, 1, s) - 1/40
sum(sum(sum(B[i1]*C[i1]^1*A[i1,i2]*A[i2,i3]*C[i3]^1, i3, 1, i2), i2,
1, i1), i1, 1, s) - 1/30
sum(sum(B[i1]*A[i1,i2]*C[i2]^3, i2, 1, i1), i1, 1, s) - 1/20
sum(sum(B[i1]*C[i1]^1*A[i1,i2]*C[i2]^2, i2, 1, i1), i1, 1, s) - 1/15
sum(sum(sum(B[i1]*A[i1,i2]*C[i2]^1*A[i1,i3]*C[i3]^1, i3, 1, i1), i2,
1, i1), i1, 1, s) - 1/20
sum(sum(B[i1]*C[i1]^2*A[i1,i2]*C[i2]^1, i2, 1, i1), i1, 1, s) - 1/10
sum(B[i1]*C[i1]^4, i1, 1, s) - 1/5
e.g.:
(%i1) s : 17;
(%o1) 17
(%i2) sum(B[i1]*C[i1]^4, i1, 1, s) - 1/5;
4 4 4 4 4 4 4
(%o2) B C + B C + B C + B C + B C + B C + B C
17 17 16 16 15 15 14 14 13 13 12 12 11 11
4 4 4 4 4 4 4 4 4
+ B C + B C + B C + B C + B C + B C + B C + B C + B C
10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2
4 1
+ B C - -
1 1 5
Yes, this should be possible.
Ondrej
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