In preparation of the calculation of Gröbner bases we're doing exercises on polynomial division in our Algebraic geometry class. Apparently, Magma 2.11-8 does a 80 variable division in mere (tens of) seconds, while it takes me 15 minutes to do one in 3 variables and 3 divisors... But it sure is clear to me why lexicographical ordering of monomials performs *bad*, every step you see a monomial blowing up and the pain of calculations to come with it.
Now I'm interested in how good a naive implementation in C++ would perform, I feel a little project coming up :). My fingers sure are aching to program a little, it has been a few months since I left computer science and delved headfirst into mathematics. Expect to hear from this in a few days! Not that anyone reads this, but Hey, been trying to meet you.