# This worksheet contains the Maple commands from Chapter 10 of 
# Introduction to Scientific Programming by Joseph L. Zachary.
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# 
# 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;
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# 
# This is the "cow" function from Chapter 9.
# 
> cow := (theta) -> sin(theta) - theta*cos(theta) - evalf(Pi/2);
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# 
# (10.1)  An example of the use of the "bisection" procedure.
# 
> bisection(cow, 2.5, 1.5);\

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>