🚀 go-pugleaf

I need to compute some polynomials of the form p(q1,q2,...,qn)
where p and q1,q2,...,qn are polynomials in several variables.
I am already running into trouble when, e.g. n=5, p has degree 11
and q1,...,q5 have degree 5. I am running this on a PC with 8 MB of
RAM. I don't know whether availability of disk space helps or not.
I expect to deal with much larger examples, for example deg(p))=14
and deg(q1)=...=deg(q5)=13, with n=5.

Since I cannot buy more RAM at this time. Even if I did, the
problems are likely to exceed the available RAM sooner or later.  I would 
like to reformulate the problem somehow. What are some techniques for 
containing the explosion in such computations ?

It is conceivable that I could write p as a sum of polynomials each of
which has only a few terms and that for each summand r the computation
of r(q1,q2,...,qn) is tractable and the answer can be written to a
file. With editing, I could then produce a file that has a polynomial
in it that is the value of p(q1,...,qn), although there might
be multiple occurrences in it of the same monomial with different
coefficients.  In any case, if I tried to read that polynomial back into
REDUCE, it might simply be too large to read in (this happened to me once
about 10 years ago on a UNIVAC).

So I'm wondering what facilities there might be for doing enormous
computations like this in pieces with each piece in a file instead of
expecting REDUCE to keep everything in memory. For example, given
a polynomial in 100 pieces, each in a different file, how can REDUCE
produce a new file containing the actual sum of the pieces, with at most
one occurence of each monomial ?

Allan Adler
ara@altdorf.ai.mit.edu