CoCoA » CoCoALib

I think that if the ideal I is homog then IsInRadical(f,I) is the same as the logical-and of IsInRadical(f_d,I) for all homog components f_d of f. I do not know whether it is faster to compute it this way... or maybe my maths is wrong?

The CoCoA-5 package was translated into C++ by some students at Kassel.
I have cleaned up the resulting code, and checked it in: see files RadicalMembership
I have added doc and a test (but no example).
I have made the fns available via CoCoA-5; the old package is still there, but I have changed the fn names to avoid clashes. Probably the package should simply be deleted (perhaps after a bit more testing?)

I have added a couple of "heuristic tricks" to IsInRadical, as otherwise computation times can be very long (esp, when the polynomial is not in the radical). The trick is just to see if a generator (or RGB element) is not square-free; if so, add as new generator the "radical" of that generator.

Note that SqFreeFactor can be slow when coeffs are in a finite field (since GCD is still via a GBasis computation); so the trick is not applied to "big" polys.