symbolic integtn/diffn of Maxima best of any open source system??

C Y wrote:
> --- seberino@spawar.navy.mil wrote:
> 
>>Is Maxima by far the most powerful and advanced
>>open source computer algebra system out there
>>for symbolic integration and symbolic differentiation???
> 
> 
> Differentiation is actually, if I understand correctly,
> much easier than integrateion - many systems can do it.

This is quite true.  There are some subtle issues about
notation for partial derivatives, and many issues about
simplification to nice forms, but the basic idea of
symbolic differentiation is so simple that a page of
code does most of it in a suitable language. (for example,
lisp).

> Integration is where the real test lies.  Maxima, as far
> as I know, can pretty much hold its own against Maple and
> Mathematica in that department, and for some tasks is better.

Both Maple and Mathematica have improved substantially
and the commercial version of Macsyma has also made many
improvements on the free version, in this area. This is
especially true for definite integration and special
functions.

> I don't know of any other open source program which can
> make that claim.  (Just had a thought - does anyone know
> what Axiom's capabilities are in that department?)

Some of Axiom's capabilities in indefinite symbolic
integration of algebraic functions are, I think, superior.


> 
> 
>>If yes then what is the next best thing that
>>comes closest???
> 
> 
> Um.  Symbolically the only other general purpose systems
> I'm aware of are Yacas and Axiom.  Yacas is a nice system
> but it lacks many of the features of more mature systems.
> IIRC its integration is very lightweight still.  Axiom I
> don't know much about really.  It is also old and mature,
> but I don't know what its integration abilities are like.
> 
> There are programs which focus on specific areas of math
> such as Pari, Gap, Singular and several others.  Comparing
> more focused packages or numerical packages to Maxima is
> kind of pointless, since the purpose of each is different.
> 
> 
>>I believe the web page says this code has been
>>improved since the 1970s??? I nearly fell out
>>of my chair when I read that.
> 
> 
> Most of the code base of Maxima was written in the late 
> sixties/early seventies.  There have been various 
> improvements over the years but most of the true heavy 
> lifting was done then.  I also find that cool - as far as
> I know we've got some of the oldest useful code in the
> open source world. 
> 
> 
>>...And GPL'd too! Someone please thank the person
>>that pulled that off for me. :)
> 
> 
> Dr. Bill Schelter.  Unfortunately he passed away, but his 
> legacy lives on in the Maxima and GCL projects.  He was 
> the sole maintainer of both from 1982 til 2001.  He is 
> the one who obtained permission to distribute the code -
> we wouldn't be here without him.
> 
> CY
> 
>

The GPLing came in 2 phases.  The first was to force
MIT to put a copy in a library run by the Dept. of
Energy.  They were forced to do this in 1982, (on my
insistence).  This did not make it public, since the
DOE required a payment for a copy, and on MIT's insistence
the copy could not be legally re-copied or transferred.
This was so MIT could make money on the technology
transfer to Symbolics, the first "owner" of Macsyma.
The DOE sub-agency running the library "NESC" went
out of business; Bill Schelter was instrumental in
getting a letter out of DOE that made the code free.
Schelter also made many improvements, including putting
the source code into a common lisp framework.
RJF