@janhardo 

Don't know how to make from this factorial function suitable for set and list elements

Factorial:= (n::nonnegint)-> local r:= 1, k:= 0; do r*= ++k until k>=n;

-------------------------------------------------------------------
PR:=proc(A,N)   # PR is product
   p:=1;
   for i from 1 to N do p:=p*A[i] end do:
end proc;

A is a list or set or array

example:

@janhardo 

I am looking now at the factorial definition :

Factorial:= (n::nonnegint)-> local r:= 1, k:= 0; do r*= ++k until k>=n;

or as 2D math input makes a big difference in reading!

for example: n::nonnegint is n element of set Z with 0 and positve numbers elements: 2D is showing the symbol notation 

Is it possible to outcomment 2D math too as with Maple input : # and /*..*/

@Carl Love 

An alternative formulation is

SumList:= (L::list(algebraic))-> 
    if L=[] then 0 else local S:= 0, x; for x in L do S:= S+x od fi
:

This is not looking here above anymore on a procedure definition with proc().. end proc;? 
But it seems to be a procedure. 
Its function made by the operator -> then.

Another point about a while clause of the do statement in relation to summing up a list of numbers 

I can take a partial sum of the list,therefore should be needed a while clause  

@acer 

Thanks

Amazing the root finding. 
After such a long time after 2002 (book),  i  could aspect  that fsolve is surpassed by other rootfinding methods  ?

It's specialized knowledge:numeric rootfinding methods.
I can't  go further  in detail for all sort of functions to use in this procedure, right now that's why my attention goes to other things like maplemint.

@Carl Love

Thanks

Get now a good oversight of some loop types

I will study your examples more extensive in Maple   

@acer 

Thanks

Looks great the procedure  when i fill in a function, but by the second one there is a error  message
Error, (in RootFinding:-NextZero) can only handle isolated zeros

It means that there will be limit in what sorts of functions i can enter in the procedure  
example :  sin(x)-x*cos(x)  ..ok and add tan(x) :  sin(x)-x*cos(x)+tan(x)-> error 

I study further with maplemint, because i don't now what rootfinding method to use further ? 

Try to make a procedure from two code examples what are doing the same.
Start first with only as procedure input a function, but that seems to be not working.
The procedure input must be a function , but the points where the tangentlines must occur inthe procedure is not understood. ( see task6 )

---------------------------------------------------------------------

Download betounes_ex_set_2_opg_6.mw

@Carl Love 

Thanks

Indeed i am struggling with the loops and try to improve this
Two forms of the do loop 
- for-from loop
- for -in loop

Your loopexample in the SumList procedure seems to be advanced ( don't know r+)
Tried making the factorial procedure, but make no progress yet.

Yes, the simpler loop example for the procedure SumList you mentioned, is for now easier to understand 
The capital S in the  do loop is a remainder that S is the last executed statement ?

@acer 

Thanks 

I found them back the worksheets from Roger Kraft about programming in Maple 

https://www.maplesoft.com/applications/view.aspx?SID=4744

@dharr 

Thanks

Cannot be shorter :)

@Axel Vogt 

Thanks 

Thereis not much to find about this in the book until now  

@Pascal4QM 

Thanks

@Carl Love 

Thanks

The use of the until statement, why to apply in what code context is yet not clear for me

@Axel Vogt 

Thanks

Yes,but is now by using a procedure for a general case..for all N 

@acer 

Thanks

Interesting books for starting for programming and hopefully i can make some progress

It is not my goal to go very deep in the programming skills, because its probably not neccesary and difficult