Re: [Maxima-discuss] ((MPLUS SIMP FACTORED) 2 3) -> 3 + 2

[Stavros M. <mac...@gm...>]

*great *has one function ("hat") -- providing a standard *internal*
ordering.

By far the most important use of *great* is in ordering
commutative/associative operators, namely *mplus* and *mtimes. *The
*great* ordering
is designed to make that efficient, so that terms that can be combined are
adjacent, for example. Similarly for* diff(f(a,b),b,1,a,1,b,1) =>
'diff(f(a,b),a,1,b,2) *and *{b,a,b} => {a,b}*. Another case is where some
consistent syntactic ordering is wanted for canonicalization, namely
normalizing the sign of even function arguments: *abs/signum/cos/...(a-z)
=> f(z-a).* But for some reason this doesn't apply to *(z-a)^2 ==
(a-z)^2, *although
*factor *does canonicalize it. I haven't thought enough about it to have an
opinion on whether it should.

Using *great *ordering for displaying products and reversed *great *ordering
for sums is, as I said, "a crude heuristic, but it produces pretty good
results". To improve on that, *great *should not be modified -- that should
be done in *nformat*, which already does things like
*a*b^-1*c*q^-1*w*x^-1*y*z^-1
*(internal format) *=> (a*c*w*y)/(b*q*x*z) *(external format), *rat(2,3)*x
=> (2*x)/3, x^rat(-1,2) => 1/sqrt(x), *etc.

Maybe you could start by making a list of cases where you think Maxima is
producing suboptimal display orderings. Keep in mind that the ordering
often depends on what is considered a "variable" and what is considered a
"parameter".

            -s