There have been fairly reliable, but much less ambitious programs
to solve (say) linear recurrences. (in Macsyma..)
http://portal.acm.org/citation.cfm?doid=355769.355772
corrections at
http://portal.acm.org/citation.cfm?doid=2701.356114
note that the first of these was published in 1978, years before
Mathematica existed.
If other programs doing the same thing are broken, I suggest
just typing in Ivie's program.
RJF
Barton Willis wrote:
>There is some Maxima code for finding explicit formulae for recursively
>defined sequences.
>Unfortunately, the code is so bug-ridden, I hesitate to encourage anyone
>to try it. See
>the bug report at
>
>http://sourceforge.net/tracker/index.php?func=detail&aid=844521&group_id=4933&atid=104933
>
>For your problem, Maxima is gets a correct value
>
>(%i4) load("differ.mac")$
>
>(%i6) difference(u[n]=2*u[n-1], u[n]);
>difference: no u[n+1] term -- u[n] = 2*u[n-1]
>(%o6) DONE
>
>Okay, this doesn't seem to be the correct form for the input.....try
>again.
>
>(%i7) difference(u[n+1]=2*u[n], u[n]);
>(%o7) u[n] = u[0]*2^n
>
>Barton
>
>
>
>
>
>Eric Delevaux <ericd@telefonica.net>
>Sent by: maxima-admin@math.utexas.edu
>09/07/2004 02:46 PM
>
>
> To: maxima@math.utexas.edu
> cc:
> Subject: Re: [Maxima] define a sequence
>
>
>Now i got my sequence u[n]=2*u[n-1]+1, no problem for the limit,
>I tried
>makelist(u[n],n,1,9);
>to obtain u_1 to u_9. It does work. Is there another way? With map?
>Is there a way to obtain the expression of u[n] in function of n with an
>defintion by recurrance?
>example :
>u_0=3
>u_n=2*u_{n-1}
>
><verynycemaxymafunctioninordertoobtain:>
>
>u_n=3*2^n
>Bye
>Eric
>
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