Date: Apr 25, 2013 12:33 PM
Author: Richard Fateman
Subject: Re: An independent integration test suite
On 4/24/2013 1:42 PM, clicliclic@freenet.de wrote:

....

>> integrate(1/(a^2+b^2*x^2),x);

>> [...]

>

> Some quick remarks on your converted suite: You have 85 entries. The

> original (like Chapter 1 of the book) has 81 items where items 14 and 15

> are vectors holding two integrals each, item 30 again holds two

> integrals, and item 48 holds three integrals. This makes a total of 86

> integrals.

yes, I found that Macsyma was unhappy with vectors that looked like

[ integral(a,x)=b=c , integral(f,x) = g = h]

and so I just put

integral(a,x)

integral(f,x)

on separate lines.

>

> Derive's #e seems to have been converted to %w (there is no %e in your

> suite).

oops. the W key is right next to the E key. I re-edited. No change in

terms of integrability. Presumably a factor of log(w) was inserted

where needed.

If we replace the string "integrate" with the string "test" in the test

file

Then define something like

test(q,v):= is (SIMPLIFY( diff(integrate(q,v),v)-q) = 0);

I got 70 confirmations, 15 were not confirmed, where SIMPLIFY was

in Maxima, a selection of transformations like ratsimp, trigsimp, and

evaluation to 0.0 at x=1.234.

This does not measure whether the form of the integral was particularly

nice, or continuous, etc. Just that it has the property of being an

antiderivative. This can matter. e.g.

integrate(x^n,x) can be expressed as (x^(n+1))/ (n+1) or

as (x^(n+1) +1) / (n+1). The latter form has the nice property that

limit as n-> -1 goes to log(x). not Infinity. (uh, plus a constant..)

I have also not tested to see if a sequence of simplification operations

can do the necessary reductions, but numerical testing with a modest

tolerance seems to confirm them all.

RJF

>

> Detailed comments tomorrow (if feasible, else later).

>

> Martin.

>