Another way can be seen in action in the procedure in that post.

It is done not in a loop though, which makes it (much) more effective (efficient too, but in this particular examle it's not that important).

Now - my this answer was voted down only once - unlike another answer voted down 3 times in this thread? That's a (nice) surprise! Some of "down voters" got scared of my tongue? Nah. Just have to wait for a little bit longer, I guess.

_______________
Alec Mihailovs, PhD
Maplesoft Member

A downside of using that signature is that I've started receiving tons of email (mostly from Asia), requiring immediate assistance to their Maple problems - they think that I am working in Customer Support.

_______________
Alec Mihailovs, PhD
Maplesoft Member

Seems to be working now,

f[1]:=x->x+a: (f[1]@f[1])(x);

                               x + 2 a

_______________
Alec Mihailovs, PhD
Maplesoft Member

Starting from 0,

L:=[2,3,3,3,4,5,5,5,6,7,7,7,8,9,9,9,10,11,11,11,12]:
gfun:-listtorec(L,a(n));

  [{(n + 7) a(n + 1) + (-n - 6) a(n + 2) + (n + 7) a(n + 3)

         + (-n - 6) a(n + 4), a(0) = 2, a(1) = 3, a(2) = 3, a(3) = 3}

        , ogf]

rsolve(%[1],a(n));

seq(%,n=0..20);

  2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12

Subtract 4 from n if you want to start from 4,

expand(eval(%%,n=n-4));

seq(%,n=4..24);

  2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12

_______________
Alec Mihailovs, PhD
Maplesoft Member

For example,

trigsubs(sin(x)+sin(y))[];

eval(%,y=x+Pi/3);

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Alec Mihailovs, PhD
Maplesoft Member

Also, StringTools:-FormatMessage might be useful for formatting the error message in try...catch. For example, with f from the first answer,

for i to 6 do
    try print(f(i))
        catch "bad argument at":
            printf(StringTools:-FormatMessage(
               "%-1 i created a problem", i))
    end
od:

1st i created a problem

                                 g(2)

3rd i created a problem

                                 g(4)

5th i created a problem

                                 g(6)

_______________
Alec Mihailovs, PhD
Maplesoft Member

 ?Statistics package has Select, Remove, SelectNonNumeric, RemoveNonNumeric, SelectInRange, RemoveInRange commands which can be applied to both Arrays and lists.

_______________
Alec Mihailovs, PhD
Maplesoft Member

Sphere point picking article in Mathworld describes several ways of constructing randomly distributed points on a sphere.

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Alec Mihailovs, PhD
Maplesoft Member

I didn't look deep into the code, and it, probably, could be modified to avoid restarting - it is not something that people usually do. But, theoretically speaking, one could use save command to save the variables and then read to retrieve them.

__________________
Alec Mihailovs, PhD
Maplesoft Member

Shortcut keys are available at ?worksheet/reference/shortcutkeys and the package index at  ?index,package .

_______________
Alec Mihailovs, PhD
Maplesoft Member

Your code was correct (well, the posted part of it). It should work. For example,

for i from 100 by -0.01 to 0 do 
    if frem(i,20)=0 then print(i) fi 
od;
                                 100
                                80.00
                                60.00
                                40.00
                                20.00
                                  0.

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Alec Mihailovs, PhD
Maplesoft Member

The list should be in second place, and additional arguments - after that,

L1:=remove(`<>`, L, 3);

                             L1 := [3, 3]

or

select(`=`,L,3);

                                [3, 3]

__________________
Alec Mihailovs, PhD
Maplesoft Member

Also, one could use  ?DifferentialGeometry/ExteriorDerivative (a rather new package, but still useful for some tasks).

with(DifferentialGeometry):
DGsetup([r,theta],M);

                            frame name: M

ExteriorDerivative(r*sin(theta));

_______________
Alec Mihailovs, PhD
Maplesoft Member

The answers (very clever) were submitted by Robert Israel. I came to this page with an intention to mark them up, and wasn't able to, because both of them were classified here as comments.

_______________
Alec Mihailovs
Maplesoft Member

Compare the expression for the composition of 2 rational functions,

collect(normal(eval((a*s+b)/(c*s+d),s=(A*s+B)/(C*s+D))),s);

                      (a A + b C) s + a B + b D
                      -------------------------
                      (c A + d C) s + c B + d D

with the matrix multiplication,

Matrix([[a,b],[c,d]]).Matrix([[A,B],[C,D]]);

                       [a A + b C    a B + b D]
                       [                      ]
                       [c A + d C    c B + d D]

Now, the composition repeated n times can be calculated using the n-th power of matrix

g:=Matrix([[0,1-p],[-p,1]]);

                               [0     1 - p]
                          g := [           ]
                               [-p      1  ]

F:=LinearAlgebra:-MatrixPower(g,n);

  F :=

        [   n    (n + 1)            n
        [  p  - p        - p (1 - p)
        [- -------------------------- , 
        [           -1 + 2 p

                n    n            n    (n + 1)]
        -(1 - p)  + p  + p (1 - p)  - p       ]
        --------------------------------------]
                       -1 + 2 p               ]

        [         n    (n + 1)    (n + 1)          n            n]
        [p (1 - p)  - p          p        - (1 - p)  + p (1 - p) ]
        [--------------------- , --------------------------------]
        [      -1 + 2 p                      -1 + 2 p            ]

_______________
Alec Mihailovs
Maplesoft Member