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You guys might find this article interesting.

It presents a linear algebra problem, then writes a program to solve it in Maple, Mathematica, and Maxima to see which one is better. What do you think?

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I would like to pay attention to a series of applications by Samir Khanhttp://www.maplesoft.com/applications/view.aspx?SID=153600http://www.maplesoft.com/applications/view.aspx?SID=153599http://www.maplesoft.com/applications/view.aspx?SID=153596http://www.maplesoft.com/applications/view.aspx?SID=153598My congratulations to the author on his work well done. New capacities of Global Optimization Toolbox are spectacular. For example, in the first application an optimization problem in 101 variables under 5050 nonlinear constraints(other than 202 bounds) is solved. I think it requires a very powerful comp and much time.I tried that problem for n=20 with the good old DirectSearch on my comp (4 GB RAM, Pentium Dual-Core CPU E5700@3GHz) bysoln2 := DirectSearch:-GlobalSearch(rc, {cons1, cons2, rc >= 0, seq(`and`(vars[i] >= -70, vars[i] <= 70), i = 1 .. 2*n), rc <= 70}, variables = vars, method = quadratic, number = 140, solutions = 1, evaluationlimit = 20000)and obtained not so bad rc=69.9609360106765 (whereas www.packomania.com gives rc=58.4005674790451137175957) in about one hour.

Packing_by_DS.mwFor n=50 the memory of my comp cannot allocate calculations or the obtained result by the Search command is far away from the one in packomania.

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