9 years, 6 days

## Evalf precision incorrect...

In the following code, the evalf prints -32.16...

restart; S := 8;

sigma := 8/sqrt(2*Pi);

iprec := 151;

evalf(log[2](-(sum(log(round(2^iprec*exp(-j^2/(2*sigma^2)))/2^iprec*exp(-j^2/(2*sigma^2))))*round(2^iprec*exp(-j^2/(2*sigma^2)))/2^iprec, j = 0 .. 7))));

Change the last line to evalf[20](log[2](....)), and re-run *just that line*. It now prints -66.67...

Change the last line to evalf[200](log[2](...)) and re-run *just that line* again. It now prints -151.24... (I have strong evidence to support that the true value is near -151, so I believe this answer.)

Now remove the precision indicator from the command completely and re-run just the last line. It *still* prints -151.24...!

My two questions are: why do I need evalf[200] to get the first three digits of the answer to be correct? and why does setting the evalf precision and then removing it cause the previous precision to persist?

## Broken Summation Notation...

Below is a Maple ws describing the problem. I have some fixed values pr0 and pr1, and a four variations of a function "pdf". The problem is that when I use the function in a sum (either the "sum" function or the sigma notation), the result is different than if I write out the sum explicitly. It's very puzzling as to why they woudl be different in the first place, but even more strange is that the different versions have *different* deltas. Even version 3, with a delta of 10^-100 is too much for my application (moreover the delta gets larger when I sum over more terms).

In the worksheet below, I compare "sum(f(x),x=3..3)" to "f(3)". I expect this should always be identically 0, but that is not true for any of the four versions of my function. (The same is true for "Sum(f(x),x=3..3)".) However, "sum(f(3),x=3..3)" *is* (blessedly) identically "f(3)". What gives?

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Maple doesn't always like subscripted variables. Is that the problem?

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Maybe it's the binary expansion that's the issue

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No procedures, no arrays

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Download maple_bug.mw

## How get numerical result when evalf fail...

In the following worksheet, I can evaluate , but not . As a result, I can't use any value that depends on  (or any ), for example, the graph is incomplete. How can I get Maple to evaluate ?

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Expected result of :

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All told, S(i) fails for i in [0..31], i = 115,116, and 221. S(i) succeeds for all other i < 3500.

Download test.mw

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