In this directory (peoplesparc.Berkeley.EDU: ~ftp:pub/mma.src)
accessible by anonymous ftp, 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).

The meaning of coefficients in the canonical form package (poly.lisp
can be altered (see definition of coefp) to any numeric type (or all
numeric types)or something else (though there should be
 redefinition of coefficient operations like * + ^ zerop etc.)

Non-portable CL stuff: We believe that by using the loading file
init2.lisp, other CLs other than the one we used, can work.  In
particular, Lucid and KCL.  Here are some notes though.

1. we use both cases, but not usually in an essential way, if
   you don't MIND YOUR COMPUTER SHOUTING AT YOU. This affects the
   definition of Set in eval.lisp which had better be distinct (i.e.
   mma::Set and not LISP:SET.)  2. we use errorset (excl:errorset) in
   file eval.lisp. You could
   change it for something else in your lisp. See the import statement
   near the top.  3. hcons is allegro-CL specific although
   machine-independent in
   that dialect. If you get stuck on this, try renaming the file
   uconsalt.lisp to ucons1.lisp, and running that way

For some people the major or only item of interest here is the parser,
which parses the Mathematica (tm of WRI) language.  The parser for
mathematica is in file parser.lisp.  To use it, do (in Allegro CL)
(set-case-mode :case-sensitive-lower) :ld mma :ld parser (use-package
"math-parser"), then use the parser (p).

The top level for a simple mathematica-like system is very
incompletely programmed in eval.lisp.  To use it, 
:ld init (in-package :mma)
 (tl)

hcons is a hashing cons package for allegro CL.  ucons.lisp is a
unique-ification package using hcons that should make the simp stuff,
as well as the polynomial stuff, work better if the kernels are other
than atoms.  Non-allegro CL systems can either define hcons in some
other way, or intercept all calls on it by redefining ucons, uappend,
ulist, umapcar.  as their corresponding programs cons, append, list,
mapcar; or uniq-ify their results (see paper on this..)

index to files

README - this file 
mma.lisp - symbols used by mma, put in a common package 
pf.lisp - print formatting programs used by display
disp1.lisp - display of formatted expressions parser.
lisp - Mma to Lisp parser
eval.lisp - top-level, evaluator 
simp1.lisp - interchange between
Lisp-prefix form and rational simplification 
rat1.lisp - rational function factored form 
poly.lisp - polynomial form 
match.lisp -(partial) implementation of Mma pattern matching 
lucid.readme, kcl.readme - note on portability

hcons.fasl - allegro CL hashing cons used by ucons only.  
ucons1.lisp- unique cons 
uconsalt.lisp - if you can't run ucons/hcons 
stack1.lisp - implementation of stack used by match and eval

init.lisp - file to load all the stuff that is in this directory
init2.lisp - file to load into a non-allegro system 
diffrat.lisp - differentiation, derivative-divides Integration
copyright - copyright and warranties notice

the subdirectory ../mma.sparc.bin if present
has "fasl" object files for the allegro CL sun4 (sparc) version.  to
be of interest.  not included in the distribution yet: factorization,
rational integration, bigfloat arithmetic & elem. funs.

Other hints.

Try the commands D[Log[x],x], Int[Log[x],x], Simp[(a+b)^2+1],
Expand[(a+b)^2], sin[I], 4atan[1],

Warranty: See the file, copyright in this directory.

the author for other uses.  SEE copyright file.

11 January, 1991 last modified 13 September, 1991 4 October, 1991 (to
remove the joke "L-mathematica" name on the
		   header, primarily) 21 April, 1992 minor changes
here and there to the parser and elsewhere 14 August, 1992 copyright
notice Richard J. Fateman, fateman@cs.berkeley.edu

Berkeley CA.