[Jprogramming] Tacit series

[Roger Hui]

I expect Kip knows all that, but is interested in exactly what he said,
tacitly computing a function by a series.

I have an example of doing what you said, which is deciding how many terms
are needed and then only computing those terms.  See:

http://www.jsoftware.com/jwiki/Essays/Extended_Precision_Functions#Exponential

Other functions on the page also do the same.  The idea is to compute
various functions to any specified but finite precision using rational
numbers.  A direct computation on rationals does not terminate, of course,
so the approach of computing the number of required terms is needed.



On Sun, Dec 22, 2013 at 2:48 AM, Bo Jacoby <bojacoby at yahoo.dk> wrote:

> Don't be interested in terminating a series when its partial sums stop
> changing. If the partial sums never stop changing, then the program cycles,
> which you don't want. Make up your mind how many terms you want to include
> in the worst case, and then use that number of terms in any case.  That
> leads to simpler programming and fewer programming errors. Noone cares
> about a little waste of cpu-time.
>