@love maths Here's an example. I couldn't upload an executed example (some bug in MaplePrimes), so you'll have to execute this yourself.

Eigen:= proc(A::'Matrix'(2,2))
local
     a:= A[1,1], b:= A[2,1], c:= A[1,2], d:= A[2,2],
     s:= sqrt((a-d)^2+4*b*c)/2,
     e1:= (a+d)/2 + s, e2:= (a+d)/2 - s,
     ev1:= < c, (d-a)/2+s >, ev2:= < c, (d-a)/2-s >
;
     if s=0 then [] else [e1, e2, ev1, ev2] end if
end proc:

A:= LinearAlgebra:-RandomMatrix(2,2) + I*LinearAlgebra:-RandomMatrix(2,2);
Sol:= Eigen(A);
A.Sol[3] - Sol[1].Sol[3];
simplify(%);

@sarra There is no mistake. You can ignore the higher-order terms. The expression is still O(h^4) (as h-> 0). The purpose of big-O notation is to let you ignore higher-order terms.

@Preben Alsholm Thanks. I corrected the Answer.

@YasH See ?emptysymbol . Using `` as a function name has the same effect as using f or any other undefined symbol, except that `` does not print as anything.

I just answered that two days ago, here.

Is your primary objective to get the answers, or to do it by the Newton-Raphson method?

I can confirm all three of your observations on Windows 8.1/64 using Maple 17.02/64:

1. That there is a memory leak; indeed it is some of the fastest memory consumption that I've ever seen. The memory usage is not reported on the Maple status line.
2. That restart does not release the memory, even when followed by gc();
3. That the difference of the two integrals that should be zero is not even close.

Since your code executes without any explicit error message, you'll need to explain why you think that there is a problem.

@mkharban Pi is capitalized in Maple. Also, after you execute restart, you need to re-execute the other lines also. It looks like you did not re-execute the lines defining the ranges X and Y.

And please read your email, at whatever email address you used to sign up for MaplePrimes.

@Axel Vogt wrote:

So users say "please set 'by time' as default" and Maple's answer is "do it yourself".

Note that the option to "do it yourself", i.e., to set the order, applies only to Answers. There is no way to set the order for the Replies (aka Comments) to the Answers. That order may even change between reloads of the same page.

Describe the algorithm, and I'll implement it in Maple.

@Kitonum Which goes to show that you'll need some variation in your X values if you want to get a meaningful answer. Otherwise, the answer is going to be a = X[1], b=0, c=0, regardless of the Y or Z values.

@Kitonum Can you explain why you used the divisor 7 rather than 8 in procedure P?

@Christopher2222 I think that Maple should detect the case where the weights are all positive integers and, in that case, use the standard formula.

@pepegna90 Replace RowDimension with LinearAlgebra:-RowDimension and likewise for ColumnDimension.

If you have further questions, please upload a worksheet, not a screenshot. If the worksheet depends on a data file for the Matrix, then upload the datafile also.