Check your constraints as a first step. It looks like Maple's Optimization routines can't find any values which satisfy those (even with integer and non-negative assumptions removed).

@Zeineb Even if you install the third-party DirectSearch package, I doubt it will be able to solve your n=100 problem (10,000 equations!).  I suspect you need to reformulate to something that can be handled by a specialty numerical library.

@mehdibaghaee I would have to see your full problem to say for sure, but if you are doing assignments in a loop, you could instead do evaluations in the loop -- but in that case you should use map[inplace](eval, M, {a=0}) (e.g.) to avoid copying at matrix at each evaluation.  Another option might to use rtable_eval(Mm__11, inplace) to force evaluation of the assigned symbols to modify the Matrix.

@tomleslie If you read more carefully, you'll see it's only four unknowns.  The @bogus5331 has just not provided us with those values explicitly (you can see that only the four unknowns in the fsolve command appear in the pasted ascii 2D-output)

PolynomialTools:-Splits will get you part of the way there, but then you're faced with the problem of identifying real linear factors, and combining the complex ones.   I don't, right off, know an out of the box solution that gives a purely real factorization.

Something to be aware of.  For each value of epsilon, your system has (generically) has four solutions.  fsolve by default only returns one of the solutions to a system. See with:

sol := solve({eq3, eq4, eq5, eq6}, {d[0], d[1], d[2], d[3]});
sols := allvalues(sol):
evalf(eval([sols], epsilon = -1/10));

It is possible to call Matlab solvers, but in fact Matlab mostly uses all the same numerical numerical solvers that Maple does ( ATLAS / MLK / LAPACK ).   The key to getting at the speed in Maple is making sure your matrix is stored as a hardware floating point (datatype=float[8]) array so that you avoid expensive copy and conversion overhead when you call linear algebra routines.

@AmusingYeti creating a function f as a procedure and then plotting it as a function call  plot(f(x), x=0..5) is a classic anti-pattern in Maple, it works OK in many cases, but you are almost always better off plotting the procedure directly:

plot(f, x=0..5);
plot(2*f, x=0..5);

etc

hellohihihi,

I would be interested to see your system of equations (and inequations), since solve will almost always call SolveTools:-PolynomialSystem directly on problems that are purely polynomial and so it should not usually be slower to use solve instead.

John

This seems to be hard one.   I stopped it after 17 hours on my i7.

memory used=7230230.4MB, alloc=5588.3MB, time=62626.80

John

This seems to be hard one.   I stopped it after 17 hours on my i7.

memory used=7230230.4MB, alloc=5588.3MB, time=62626.80

John

I am unable to view the file in the link (I get a login screen).  Is it possible to host it somewhere else?

John

http://en.wikipedia.org/wiki/Poplar

Talking about trees all the time does not always make one very poplar.

John

The easiest option is to build your expression using the 2D math palettes and when done highlight the whole thing and select the context menu: 2-D Math > Convert To > Atomic Identifier

If you lprint() the result, and play around a little bit, you will see that something similar could also be entered programmaticly in Maple's typsetting markup:

`#msubsup(mi("σ"),mrow(mi("θ"),mi("θ")),mi("S"))`

Displayed as: 

John