TILU and Maxima; tables and copyrights

Dear Professor Fateman,

I am extremely thankful to you for your reply and for all
of your comments below, with which I completely agree.
More explicitly, I could add that

> Wolfram appeared to encourage him in some way to violate
> this contract, but eventually came to some agreement
> with CRC.

The latter seems to be true and today (and about one or
two years ago, I do not remember, but at least one year)
the copyright signs of both CRC Press and Wolfram
Research appear together in several MathWorld pages
such as that devoted on the Hermite orthogonal polynomials

http://mathworld.wolfram.com/HermitePolynomial.html

with the copyright sign (today)

Author: Eric W. Weisstein
© 1999 CRC Press LLC, © 1999-2003 Wolfram Research, Inc.

> I doubt that Wolfram claims he has a
> copyright on the answers produced by Mathematica.

By no means, any answer by Mathematica can be published
anywhere (in a Journal, in a book, on the internet, etc.) with the
copyright having to do with the author and/or the publisher,
by no means by Wolfram Research. They have no such claim.
Their rights are restricted to the Mathematica code sold with
Mathematica, not to the output (even if Mathematica tools
are used) neither to the Mathematica code prepared by a
researcher. (I am a client of Wolfram Research and user
of Mathematica since 1991 and I strongly disagree with
Wolfram Research in several points in their policy, but they
have not asked so much at least so far.) I agree with you.

> I think that the right thing to do is type into a computer
> the integration problems (NOT the solutions) in some suitable
> form, e.g. Mathematica, Macsyma, Maple, Mupad syntax.  Then
> make a table of those inputs and the corresponding outputs
> (with simplifications applied).  This should cover much of
> the usual tables. I doubt that Wolfram claims he has a
> copyright on the answers produced by Mathematica.
>
> The known integration ANSWERS that cannot be done by any of these
> systems will have to be entered by hand. These are mostly
> definite (improper or parametric) integrals with nice compact solutions
> not found by algorithms, or ones where the answers are not in
> closed form (e.g. indefinite summations, limits, other integrals).
>
> The amount of work is really not that much, assuming that many
> of the answers come out in a form that  is good enough for
> further use.

This is a really simple and excellent idea and can rather easily be
implemented. Yet, I would prefer that the computer-derived
integration results could be verified in some way such as by
obtaining them by using two computer algebra systems
simultaneously or if possible (and preferably) through a
direct verification by using differentiation (which uses a totally
different algorithm) and simplification after the integration in
the case of indefinite integrals.

Perhaps, just in few cases, efficient numerical integration could be
used as well for definite integrals even with one or two parameters.
This is completely possible in computer algebra systems such as
Maxima, but rarely used in practice, I do not know why. Perhaps
because of the approximations in numerical integration, but just for
verification tasks they are more or less acceptable.

Does your hybrid approach for the preparation of tables
of integrals, still useful for the reasons you mention below,
has been implemented so far in a book, a CD-ROM or
some other publication?

I am grateful to you for your present reply and precious
comments also hoping that your suggestions will be really
undertaken by a colleague with interests in computer-algebra-
based integration, in our case by using mainly Maxima.

With my kindest regards from Patras,

Nikos

----- Original Message -----
From: "Richard Fateman" <fateman at cs>
To: "Nikolaos I. Ioakimidis" <ioakimidis@otenet.gr>
Cc: <maxima@www.ma.utexas.edu>
Sent: Sunday, February 16, 2003 5:21 PM
Subject: Re: [Maxima] TILU and Maxima; tables and copyrights


> 1. UCB lawyers have other things to worry about than whether
> it is OK for some faculty member to (possibly) violate the
> copyright of some publisher.
>
> 2. CRC Press is not a university press or a professional
> society press.  It is run for profit.  I am reasonably
> certain that if someone approached them to say "we want
> to use your property" that they would not
>   say "go ahead and use it free".
>
> 3. Regarding Weisstein's legal problems: it seems to me
> fairly clear that he sold CRC Press something that he
> didn't intend to sell them.  I think he failed to read the contract
> he signed (or worse, read it and didn't believe it).
> Wolfram appeared to encourage him in some way to violate
> this contract, but eventually came to some agreement
> with CRC.  I find this somewhat amusing since Wolfram
> threatened to sue me when I wrote a Mathematica language
> parser, claiming he owned the "commands" of Mathematica.
> He eventually dropped the matter.
>
>
> I think that the right thing to do is type into a computer
> the integration problems (NOT the solutions) in some suitable
> form, e.g. Mathematica, Macsyma, Maple, Mupad syntax.  Then
> make a table of those inputs and the corresponding outputs
> (with simplifications applied).  This should cover much of
> the usual tables. I doubt that Wolfram claims he has a
> copyright on the answers produced by Mathematica.
>
> The known integration ANSWERS that cannot be done by any of these
> systems will have to be entered by hand. These are mostly
> definite (improper or parametric) integrals with nice compact solutions
> not found by algorithms, or ones where the answers are not in
> closed form (e.g. indefinite summations, limits, other integrals).
>
> The amount of work is really not that much, assuming that many
> of the answers come out in a form that  is good enough for
> further use.
>
> On the other hand one can ask the question: if the algorithm
> can find the result, why bother to put it in a table?
> (a) The table lookup is faster
> (b) The result may be simpler because a human made some
> clever choice of simplification commands
>    and of course
> (c) some entries in the table cannot be done by the computer
> algorithms (yet).