CharSets is a program which I translated from the Maple package CharSets,
written by Dr. Dongming Wang.  His homepage is  http://calfor.lip6.fr/~wang.
A good reference for Characteristic sets is his book Elimination Methods.

I wish to thank Dr. Wang for making this code available to the maxima
project.  I also wish to thank Dr. Willis, Dr. Fateman and Mr. Dotson for
their assistance with this project.
Finally, I wish to dedicate this work to the late Dr. Paul Karmel.
Dan Stanger
11/28/02

The CharSets package depends on the set functions in set.lisp, which was
previously in maxima/src/ and is now in maxima/share/algebra/charsets/.
To use CharSets, set.lisp must be loaded first, as it is no longer part
of the compiled Maxima code. For general use, nset.lisp in
maxima/share/contrib/nset/ supersedes set.lisp.

Robert Dodier
2005/02/07

src/flatten.lisp has also been moved to share/algebra/charsets/,
with $every cut from src/mutils.lisp and pasted into flatten.lisp.
$flatten and $every have been renamed to $charsets_flatten and
$charsets_every, and every function in set.lisp has been renamed
from $foo to $charsets_foo. Function calls in charsets.mac and
rtestflatten.mac have been fixed up from foo to charsets_foo to
match set.lisp and flatten.lisp.

Robert Dodier
2005/02/23

charsets appears to be broken, and I don't see how it ever worked. I've
made some recent commits to fix some things, but there are still some
references to undefined functions, and maybe other problems. The
undefined functions are some subset of:

[Gcd, RootOf, charsets_die, charsets_dieA, coeffs, complexity,
das, eval, evala, fmedset, gbasis, lcm, leadmon, medset, ml2, ml3,
normalf, numer, prem, rand, readstat, simplify, sprem, theRankFunction,
tn, variablep]

which are the symbols which appear in function calls in functions
defined in charset.mac, which are apparently not defined functions
(i.e., neither a Lisp function, nor a Maxima := function, nor a
Maxima defmspec, nor a Maxima autoloading function). Some of those
symbols are local names of functions which are arguments, so it is
expected that there will be no function definitions for those
symbols. I haven't tried to sort out which are the local names and
which are honest-to-goodness undefined functions.

Some fragmentary notes about the undefined functions.

 * Gcd and RootOf are only referenced in charsets_Malgcd which is
   not called anywhere.
 * charsets_die and charsets_dieA are used as variables but then
   as functions. The value of the variables doesn't appear to be
   a lambda expression. Is the variable supposed to be assigned
   lambda([], foo) where foo is the value now assigned? In both
   cases, the value is a random number, so it's meaningful to
   call it (to get a different number each time).
 * gbasis, leadmon, and normalf appear to be functions from an old
   Maple package for computing Groebner bases.
 * theRankFunction and tn are function arguments which are, I believe,
   supposed to be function names.
 * rand maybe is supposed to be random.

Robert Dodier
2016-01-04