MaplePrimes - answers and comments on Question, how do I get sums produced by "add" to immediately evaluate?

I really do want to use evalhf, because we're going to use

webreg2003 — Fri, 08 Mar 2013 07:26:52 Z

I really do want to use evalhf, because we're going to use (a more complicated example than) this to create a sound file using AudioTools, and evalf is too slow. But I do need it to be not-too-complicated, because this is intended to be part of a lab for my calculus students.

How to use evalhf

Carl Love — Fri, 08 Mar 2013 08:55:09 Z

The trick to using evalhf here is that the integration needs to be done at the time h is created, not at the time that h is called. And there's extra complexity that n = 2 needs to be handled as a separate case to avoid division by zero. So, you need to define h this way:

h := subs(J= int(f(x)*sin(n*x), x= -Pi..Pi)/Pi, n-> `if`(n=2, 1, J));

Your f and g can remain the same. If you define h as above, then the call evalhf(g(2)) will work. This is correct usage, not effective usage. To use evalhf effectively, you need to pack as much computation as possible into each invocation of evalhf.

evalhf

Carl Love — Fri, 08 Mar 2013 08:26:46 Z

If I were to rate various aspects of Maple based on the experience level required to use them, on a scale from 0 to 10, I'd say that using evalhf correctly would be level 3, and using it effectively would be level 4.5. If you're doing symbolic integrations inside an add loop, the savings you get from using evalhf are going to be miniscule. Nonetheless, I will post an answer to your question.

Aha! So "subs" will force add to evaluate

webreg2003 — Sun, 10 Mar 2013 22:22:46 Z

Aha! So "subs" will force add to evaluate its operands - that's exactly what I needed!

So, I can leave my f, g and h the same, but then "set" the definition of g with

g:=subs(t=g(x), x->t)

and then evalhf(g(2)) returns a value.

This is a bit eccentric, but seems to work fine. Does it meet your criteria for being effective?