```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 putintegral(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 interms 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 fileThen define something liketest(q,v):=  is (SIMPLIFY( diff(integrate(q,v),v)-q)  = 0);I got 70 confirmations, 15 were not confirmed,  where SIMPLIFY wasin 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)  oras (x^(n+1) +1) / (n+1).  The latter form has the nice property thatlimit 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 operationscan do the necessary reductions, but numerical testing with a modesttolerance seems to confirm them all.RJF>> Detailed comments tomorrow (if feasible, else later).>> Martin.>
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