1. almost regardless of f, f^K for sufficiently large K is likely to be fairly dense. 2. You could encode f more tightly as a univariate polynomial by using different N, depending on the degree of x,y,z, etc. 3. (most plausible) you could use a recursive representation for f, which could, I think, also solve your 100-variable problem by suitable ordering of variables. 4. my experience is that you can multiply polynomials that are not too large or too sparse lots of ways that are faster than the heapmul by Monagan and Pearce, but your implementation experience may differ. 5. Maxima's CRE form is already in Sage, and does (3). RJF
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