🚀 go-pugleaf

The correct way to expand polynomials in macsyma is to use rat( ), not
expand( ).  The latter command is far more general and is probably not
comparable to commands of the same name in other systems.  This lack
of comparability is unfortunate and has lead to lots of bogus
comparisons of speed.  There is also an issue of data representation
-- the right way to represent polynomials (especially large ones) in
Macsyma is to use the rational function "CRE" form.  Since REDUCE's
principal (only?) representation is more like CRE form, that would be
the more logical comparison. In any case, I tried the computation of
rat(p^6) on a version of macsyma (not the official symbolics version
but a DOE version) (on a MIPS M/120 computer) and it took 86.45 CPU
seconds. This used Allegro common lisp.  Another version took 69
seconds -- an HP 9000/720 workstation in AKCL.  Exact times would
vary depending on debugging / optimization switches in compilers etc.
But it is not 172+ minutes if done right.



There are ways of reordering the polynomial variables by the
ordergreat command in macsyma, (or ratvars, within the rational
function system), but I don't know offhand of a built-in way of seeing
the results in (say) total-degree-order. This could be programmed of
course (and most likely already has been programmed, internally, for
Grobner basis computations). 

Richard Fateman