# This worksheet contains the Maple commands from Chapter 10 of
# Introduction to Scientific Programming by Joseph L. Zachary.
# 
# This is the implementation of the bisection function from Figure 9.9.
# 
> bisection := proc (function, positive, negative)
> 
>   local f, avg, pos, neg;
> 
>   f := function;
>   pos := positive;
>   neg := negative;
> 
>   if (f(pos) < 0) then
>     print(`Positive bound to bisection is bad`);
>     RETURN();
>   fi;
>      
>   if (f(neg) > 0) then
>     print(`Negative bound to bisection is bad`);
>     RETURN();
>   fi;
> 
>   avg := pos;
> 
>   while (avg <> (pos+neg)/2.0) do
>     avg := (pos + neg) / 2.0;  
>     if (f(avg) >= 0) then
>       pos := avg;
>     else
>       neg := avg;
>     fi;
>   od;
> 
>   RETURN(avg);
> 
> end;
# 
# This is the cow function from Chapter 9.
# 
> cow := (theta) -> sin(theta) - theta*cos(theta) - evalf(Pi/2);
# 
# (10.1)  An example of the use of the bisection procedure.
# 
> bisection(cow, 2.5, 1.5);
>