In CoCoA-4 there is some rather inefficient code for multivariate lifting. Can it be made more efficient?
In any case, we need a good (sparse?) multivariate lifter in CoCoALib. Zippel's method needs good (exact) linear algebra. We also want to avoid rational arithmetic.
If I recall well, the multivariate lifter was one of the trickiest piece of code I've ever written.