you have c ~ d for the 6 leading decimal, so you plot 0 ... 1e-6/1000 = 0 ... 1e-9

at least you may want to increase Digits to ~ 18

I do not have Maple here. But some thoughts:

1. write exp(x), not e^x

2. do you mean 20 * x * exp(x) - 1 or 20 * x * exp(x-1) or what ? And the first multiplication sign is missing ...

3. define the function correctly, if you use it like in your picture as f:= x -> 20 * x * exp(x) - 1

4. read the help: solve is for symbolic solutions, fsolve for numerical ones

sin(x) = 1/2; RootOf(%,x); [allvalues(%)];

                   [1/6 Pi + 2/3 Pi _B1 + 2 Pi _Z1]

cos(4*x) = sin(x); RootOf(%,x); [allvalues(%)]: simplify(%);


  [1/2 Pi + 2 Pi _Z2, 1/2 Pi + 2 Pi _Z3, -1/6 Pi + 2 Pi _Z4,

                                        1/2
                                       5    - 1
        -5/6 Pi + 2 Pi _Z4, arctan(----------------) + 2 Pi _Z5,
                                            1/2 1/2
                                   (10 + 2 5   )

                     1/2
                    5    - 1
        -arctan(----------------) + Pi + 2 Pi _Z5,
                         1/2 1/2
                (10 + 2 5   )

                     1/2
                    5    + 1
        -arctan(----------------) + 2 Pi _Z6,
                         1/2 1/2
                (10 - 2 5   )

                    1/2
                   5    + 1
        arctan(----------------) - Pi + 2 Pi _Z6]
                        1/2 1/2
               (10 - 2 5   )

x^4+1 = 0; RootOf(%,x): [allvalues(%)]: 
map( 't -> x - t', %): # write all as x - root
 `*`(op(%)); # multiply together
                               4
                              x  + 1 = 0


  /     1/2             \ /     1/2             \
  |    2             1/2| |    2             1/2|
  |x - ---- - 1/2 I 2   | |x + ---- - 1/2 I 2   |
  \     2               / \     2               /

        /     1/2             \ /     1/2             \
        |    2             1/2| |    2             1/2|
        |x + ---- + 1/2 I 2   | |x - ---- + 1/2 I 2   |
        \     2               / \     2               /

_Z stands for any integer

Download 102_Garch_estimation_using_Compile.mws
View file details

For more see my link posted above.

It is a bit strange, that the Optimizer does not want to compute gradients himself ...
it even does not like to be provided with them through 'fdiff'

www.mapleprimes.com/blog/axelvogt/financialnumericsestimatinggarch11

look up 'mod' in the help and more generally 'modulo' at Wikipedia or a Math book

edited: and if you want a funny way for that homework, than recall Erathostenes'
sieve for primes. Up to 100 you only miss 5 as prime in sqrt(100). So you need
all primes plus multiples of 5 except those bad for 2,3,7

Gustl,

please make it more clear by uploading a sheet (or txt file) ...

It is a piecewise function defined through polyniomial of degree = 3. You either use convert(%, rational) to get a symbolic solution. Or more generally split integration at the 'piecewise' points (you have to code a bit), since 'int' is for symbolic integration and that assumes analytic (in most cases)

Edited to add:

Digits:= 18
S:=convert(s, rational):
int(S, y): evalf(%): 
J:=convert(%, rational):
eval(J, y=2.338412729)- eval(J, y=-Pi);
evalf(%);

                         4.93149865258361510

Sometimes I have difficulties to understand what you are saying.

But my (personal) suggestion is: do not use palettes, except if  you really need them.
And it is much more 'safe' to use the classical interface in most cases (even if it does
not look that nice).

b:=(1+1/n)^((1/8)*(n^(1/3)+(n+1)^(1/3))^3):
'limit(b, n=infinity)': '%'=%;

                           lim       b = exp(1)
                      n -> infinity

Then you have to show, that b is decreasing

You may look at the thread, where users replied - but it is naive to expect an answer from Maple stuff beyond a political reply.

However you can look at the new owner, may guess whether it is an investor, check its quotations at stock exchange and try to find out what happens with other companies in its portfolio (concurrent and past).

There is an extra command LinearAlgebra[Eigenvalues] . However what you want is: the (10 smallest) zeros of a polynomial of degree > 1000. And I am not astonished that it takes time ...

I must admit, that I was too hasty and ignored, that you 'only' want to simulate.

The thing I had in mind was 'real data' and  www.wilmott.com/messageview.cfm will give you references.

@Alex: nice finding :-)

Don't you want it to be symmetric?

  C := Matrix(n, n, xx):
  C:=C.Transpose(C):
  Eigenvalues(C);
  IsDefinite(C);
                                 true

solve is not the right thing, fsolve may find only few or only 1 solution, but your task may have many solutions

if you use Groebner, an algebraic method, you may wish to pass from floating values to 'exact' values by 'convert( ..., rational)' as first step

exp(2*Pi*I*t);
plot( [Re(%), Im(%)], t = 0 .. 1, color=[red,blue]);