@candemirx90 You wrote:

Another question is that is it possible to get a symbolic solution of each variable as well?(x= ...y + ...z +...) In other words can we solve the equations for every variable with another command? or isolate it for every variable?

The command is eliminate, as in

eliminate({eq||(1..3)}, {x});

[{x = 2903/8+(1/8)*y-(1/80)*z}, {6500*y^2-20*y*z+6401*z^2+5593400*y-2351340*z+733056100, 133225*y^2-206250*y*z+198225*z^2+47813600*y-23100000*z+1565019904}]

@Earl There's a little bit of documentation of `?[]` at ?use and more in the Maple Programming Guide. It's essentially equivalent to (A, index::list)-> A[index[]] except that it's built into the kernel and thus it can take a named expression sequence as its first argument. So, for example, if you had a list of lists LoL and you wanted a list of the last elements of each list, you could use map(`?[]`, LoL, [-1]).

What's the discrepancy to which you refer? A higher confidence means a wider interval.

@Don_Caraota DirectSearch must be downloaded from the Maple Applications Centre. See this post of mine.

@Kitonum Vote up.

Something closer to the original matrix notation can be achieved by

A:= Matrix((2,2), symbol= a):
B:= <-1,  2;
           3,  4>:
C:= <-1,  0;
           4, -5>:
seq(eval(A,s), s= evalf(allvalues(solve(convert(A^2+B.A+C, set)))));

or, in the case that there are variables other than those in A, make the last line

seq(eval(A,s), s= evalf(allvalues(solve(convert(A^2+B.A+C, set), convert(A,set)))));

@vv I think that that should be

plots[odeplot](de, [x, diff(y(x),x)^2 - 1], x=0..1);

@stefano91 Your error message is caused by unbalanced parentheses. The right parenthesis at the end has no corresponding left parenthesis. It was intended to be matched with abs(.

You'll need to eliminate the line x:= 0..Xa.

To minimize, don't change maximize to minimize as I suggested earlier. Just remove maximize; the default is to minimize.

A better test of the solution is to plug in the solution on the left, subtract the constant, then simplify. Getting 0 verifies the solution. Maple's simplify is more likely to be able to simplify something to 0 than to some other constant.

@stefano91 I know what "the min and max values of a function" means; there's no need to go into detail. You still need to install the external package DirectSearch because there's no reliable built-in Maple function for computing the global extrema of functions as complicated as yours.

Since you want abs(min(f(x))) and abs(max(f(x))), change the final command to

abs(DirectSearch:-GlobalOptima(Fm(x), [x = a..b], maximize)[1]);

Please note that abs(min(f(x))) is a very different thing than min(abs(f(x))) and that your Question was ambiguous about which you wanted. Indeed, it's possible that abs(min(f(x))) > abs(max(f(x))).

And you want the local extrema also? How many local extrema? And do you want the x-coordinates at which all these extrema are attained? To return these multiple values, I need to know how Excel's =maple(...) command deals with multiple values. Does it expect a list? a Vector? an expression sequence?

@Kitonum The OP's intended expression is sqrt(1-r^2*exp(2*I*theta)). He wrote the expression in LaTeX. The backslashes are not meant as division but rather are the LaTeX escape character.

What do you mean by "simplify"? As far as I can tell, the expression is already in its simplest possible form. So show me the result that you can get by hand, and I'll see if I can get Maple to do it.

@John Fredsted Using a variable is still (somewhat) based on the (temporal) order of execution, not the (spatial) arrangement of commands in the worksheet. It'll only work if you have no intermediate restarts and give unique (and preferably sequential) variable names to the output of every command that you want to refer back to.

See ?Wrightomega.

@Markiyan Hirnyk Yes, but my Answer is based on the exact plot3d command used by plots:-complexplot3d. This can be verified by

subs(plot3d= P, eval(`plots/complexplot3d`))(f(z), z= -2-2*I..2+2*I);

P(abs(f(x+I*y)), x = -2 .. 2, y = -2 .. 2, color = (1/2)*(argument(f(x+I*y))+3.14159265358979312)/Pi, labels = [Re(z), Im(z), ""])

If you make your relevant Reply into an Answer, I'll vote it up.

@mmcdara I just tried in Maple 16, the only other Maple that I have access to right now, and my code works. Try putting restart in its own execution group. A restart should always be in its own execution group; sometimes (and unpredictably) the restart is not fully performed when there are other commands in its execution group.

The following makes no difference to me, as the code already works for me, but try putting the second LinearAlgebra in forward single quotes: 'LinearAlgebra'.

Please let me know how that goes. I want to get to the bottom of this.