You can find MMA at ftp://carnet.hr:/pub/misc/math/mma15c09.tgz
WHAT IS MMA?
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MMA are the underpinnings of a common-lisp implementation of a small
and efficient algebra system. The intention is to be as fast as possible
without making major concessions to usefulness. Absolute brevity in
code is not a goal, nor is complete perspicuity, if it is inconsistent
with efficiency.
As far as efficiency goes, it is expected that for similar problems,
the code would be faster than Macsyma's rational function package,
Reduce, or Maple, and generally much faster than Mathematica and
much^2 faster than Macsyma's general representation.
It is our intention that no one would have any reasonable hope of
making a package that was much faster, at least while coding in Lisp,
and that there would be no need to look inside the package for most
users. It is also our hope that even by going to C or assembly
language, not much of a speedup could be expected. Of course
eliminating some features (e.g., going to fixed precision rather than
arbitrary precision integers), can result in savings.
How general a set of features do we need? For example, I consider
multi-variate polynomial arithmetic essential, as well as arbitrary
precision integer coefficients. By contrast, computation in
non-commutative variables is not supported. Although only a simple
polynomial GCD is used, more elaborate and faster versions have been
written (not debugged).
Try the commands D[Log[x],x], Int[Log[x],x], Simp[(a+b)^2+1],
RatExpand[(a+b)^2], sin[I], 4atan[1],
IS MMA READY FOR FREE LISPS?
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********************
* *
* Hello Math fans! *
* *
********************
Prof Richard J. Fateman made a great Mathematica(tm)-like program
in lisp. Now it is small and has only basic functions, it certainly
needs to grow... But that's probably a beginning of a long mathfree
story.
MMA has implemented just a small portion of the functions that real
Mathematica(TM) offers.
There are 4 different views of MMA:
1. What works on free lisps
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(Mathematica(TM) script parser and nice formatted output,
polynomial handling, basic database for integration and
differentation; basic pattern matching, arithmetic simplification,
other odds and ends.)
2. What works for Allegro lisp (Not free) and needs porting to free lisps
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(hashing table for the algebra for more efficent common subexpression
sharing.)
3. What requires small effort to be done
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(adding new command-style functions, extending integration/derivation
database written in lisp)
4. What requires greater effort to be done
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(Implementation of Mathematica(TM) control structure semantics
evaluator should be programmed to understand it;
Some advanced details in the pattern matcher.)
Up to now, MMA works on following LISPs:
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1. Allegro LISP (MMA's was first written using this)
2. KCL (AKCL) (ported a few years ago to KCL, recently adapted for new AKCL)
3. LUCID (I haven't tried)
4. CLISP (recently done)
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_______________________ COMMENTS ON SPEED ________________________
Now, the situation looks like this: Let's try to put WRI down from
the 1st place by beating it with the freely redistributable LISPs!!
Machine: 486dx2-50 with few wait states, 8M RAM 256K cache.
Test sample: Timing[RatExpand[(x+y+z)^15];done]
1. Mathematica 2.0 (DOS) for 386/387 0.6 seconds
2. CLISP compiled (Linux) 1.12 seconds
3. AKCL compiled (Linux) 1.55 seconds
4. CLISP interpreted (Linux) 13.8 seconds
5. AKCL interpreted (Linux) 66.7 seconds
Allegro LISP (not free) already beats Mathematica(TM) on the same
machine. This is probably because of more optimized compiling and
an efficient representation of integers, but perhaps the use of
unique-consing by hash-table storage of parts of the data also
contributes to speed. Our free domain LISPs can be faster than
that if we port the hashing algorithm or (more likely) produce more
optimized code that could run the code 2x faster :>.
"Native lisp" of MMA is Allegro CL, and for it a highly optimized
hcons1.lisp is written. For others (and CLISP) we use hconsalt.lisp
which is common-lisp compatible but much slower.
If there is some CLISP/KCL expert, it would be good that he/she :)
writes a CLISP version of hcons1.lisp.
______________________________ * * * ________________________________
There is some more documentation at peoplesparc.berkeley.edu, on
polynomial arithmetic and display at .../pub/papers/[lai.tex, tak.tex]
Send your patches, bug reports, new whole routines, documentation or
whatever about MMA to me. If, after studying the code for a while
(there are many comments in it), you have specific questions about
the MMA insides you can contact
Professor Richard J. Fateman, <fateman@cs.berkeley.edu>.
Have a nice math meditation.
Davor.
--
Davor , Dept of FEP, IRB | Physics, Energetics, Application
Jadrijevic POB 1016 | Institute "Rudjer Boskovic"
Bijenicka 54a | Tel: +385 41 461079 => <davj@apoirb.irb.hr>
HR-41001 Zagreb | Croatia | <davor%emard.uucp@ds5000.irb.hr>
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