Since this topic raises more interest than the giac topic raised by Frederic yesterday, I will pollute it a little by pointing to the ticket (http://www.google.com/url?q=http%3A%2F%2Ftrac.sagemath.org%2Fticket%2F18749&sa=D&sntz=1&usg=AFQjCNG_L1Fc90KhKpiCCnDCggjiG5LfVg) where I made a few comparisons f4/giac. I believe f4 is a really nice package, it is to my knowledge the first open-source package computing Groebner basis that really competes with giac :-) Both are complementary, giac modular GB computations are mostly there for GB computations over the rationals and rational univariate representations computations.
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