INTRODUCTION TO MAPLE
Teresa Dern Henson, Lecturer
Department of Mathematics
Naval Postgraduate School
September, 1995
SECTION 4
WRITING DO-LOOPS IN MAPLE
GOALS:
In this section we will learn how to write a do-loop.
DO-LOOPS
do-loops. The Repetition ( for / while / do)
Statement allows you to execute a statement repeatedly either for some
finite number of times (for) or until some condition has been satisfied
(while). The structure for a Repetition Statement which iterates a finite
number of times is
>for k from a by h to b do
>statements to be executed
>od;
where k is the statement variable (the index), a is the initial
value of k, h is the amount by which k is to be incremented
at each iteration, and b is an upper bound for k. The increment
h may be non-integer. The do-loop terminates when k
> b; after the do-loop is executed k will be assigned
the value that it had when the do-loop terminated. The word for
signals the start of the loop while the word od signals the end
of the input. To execute a do-loop all lines must be entered sequentially
starting with the first. No output will be computed or displayed until
the od line is entered.
The statement to be executed must be a valid Maple expression;
the statement line should end in a semicolon. Several statements may be
executed within one do-loop.
If the do-loop ends with a colon, then the output will be computed
but not displayed. You may include a print statement within the do-loop
if you wish to display some part of the output but not all of it.
EXAMPLE: Construct a do-loop which
will evaluate the function f(x) = x2 for
x = 1, x =3/2, x = 2, x = 5/2, ..., x =
5.
Solution: Assign the function f. The initial value for x
is a = 1. The upper bound for x is b = 5. The
increment is h = 1/2.
>f := x^2;
>for k from 1 by 1/2 to 5 do
>subs( x = k, f );
>od;
After executing these lines enter
The statement variable k is now assigned the value 11/2 > 5 = b.
If you wish to reiterate or use k in some other context, you
must first "unassign" k by entering
EXAMPLE: Unassign f before trying
this example
Suppose in the last example we wanted to get output in the form 
where k is an x value. To do this we must "fool" Maple.
>y := x^2;
>for k from 1 by 1/2 to 5 do
>f(k) = subs( x = k, y );
>od;
By assigning the function expression x2 to y,
no functional meaning is attached to the expression f(k)
within the do-loop.
k after executing the do-loop.
EXAMPLE: Unassign y before
trying this example. As an alternative to using functional notation,
you can use subscripted variables. To create a subscripted variable yk
in Maple use a variable name of the form y[k]. This approach
has the advantage of allowing you to assign the output from the do-loop
to a subscripted variable.
>f := x^2;
>for k from 1 by 1/2 to 5 do
>y[k] := subs( x = k, f );
>od;
In this example the right-hand side of each output is assigned to
the left-hand side. Thus the Maple input
will compute 2y3/2 + 1 using the output y3/2
from the do-loop.
EXAMPLE: If you define the function
using function mapping notation, then function evaluation notation may
be used within the do-loop instead of the subs function.
>f := x -> x^2;
>for k from 1 by 1/2 to 5 do
>y[k] := f(k);
>od;
k after executing the do-loop.
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