PS: maxima.load('simplify_sum') didnt work
luigi
Il giorno giovedì 3 aprile 2014 17:36:14 UTC+2, Luigi Malagò ha scritto:
> Hello sage community,
> i'm new to sage, i would like to use it to double check some computations i
> have done, however i have some problems with simplifying expressions
> involving sums.
> Let
>
> >> alpha,t,i,j,k = var( 'alpha','t','i','j','k')
> >> def p1(alpha, t):
> >> return alpha * sum(exp(-alpha/2*i)*exp(-alpha*(t-1-i)),i,0,t-1)
>
> >> show(p1(alpha,t))
>
> this works. the geometric series is worked out correctly ;-)
> however, let
>
> >>def p2(alpha, t):
> >> return 1/2* alpha * sum(exp(-alpha/3*j)*p1(alpha,t-1-j),j,0,t-1)
>
> >>show(p2(alpha,t).factor())
>
> i obtain
>
> >>-1/2*alpha^2*sum(-(e^(3/2*alpha*j + 5/2*alpha) - e^(alpha*j +
> >>1/2*alpha*t + 2*alpha))*e^(-5/6*alpha*j - alpha*t), j, 0, t -
> >>1)/(e^(1/2*alpha) - e^alpha)
>
> where the sum is not computed explicitly. doing some simple algebra by hand,
> just factoring out terms form sum which do not depend on the summation index,
> i would obtain a simpler expression, where j disappears (which is what i want
> to obtain). i only need to factor out terms and apply the formula for
> geometric series.
> eventually i would expect something like (algebra should be fine):
>
> >>show(1/2*alpha^2*exp(- alpha*t+2*alpha)*(e^(alpha/2) *(e^(2/3*alpha*t) -1
> >>>>)/(e^(2/3*alpha) -1 ) - e^(alpha/2*t) * (e^(1/6*alpha*t) -1
> >>)/(e^(1/6*alpha) -1 )) >>/(e^(1/2*alpha) - e^alpha))
>
> is there a way to force sage to do such simplifications?
>
> thanks for your help,
>
> ciao,
> luigi
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