# This worksheet contains the Maple commands from Chapter 4 of
# Introduction to Scientific Programming by Joseph L. Zachary.
# 
# (4.2)  We use rational arithmetic to add up the reciprocals of the
# first ten even numbers.  The answer is exact. 
# 
> rat10 := 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 +
> 1/20;
# 
# (4.3)  This is a ten-digit floating-point approximation to the
# rational sum computed in (4.2).
# 
> evalf(rat10);
# 
# (4.4)  We use floating-point arithmetic to add up the recriprocals of
# the first ten even numbers.  We get the same answer as in (4.3).
# 
> float10 := 1/2. + 1/4. + 1/6. + 1/8. + 1/10. + 1/12. + 1/14. + 1/16. +
> 1/18. + 1/20.;
# 
# We change over to two-digit mantissas.
# 
> Digits := 2;
# 
# (4.5)  We repeat (4.4) using two-digit floating-point numbers.  The
# answer is significantly different.
# 
> float10 := 1/2. + 1/4. + 1/6. + 1/8. + 1/10. + 1/12. + 1/14. + 1/16. +
> 1/18. + 1/20.;
# 
# (4.6)  Adding an 11th term onto the sum from (4.5) has no effect.
# 
> float11 := float10 + 1/22.;
# 
# (4.7)  We load the blocks package from the custom Maple library that
# accompanies this book.
# 
> with(blocks);
# 
# We switch back to ten-digit mantissas.
# 
> Digits := 10;
# 
# (4.8)  We use two functions from the blocks package to repeat the sums
# from (4.4) and (4.2).
# 
> blockFloat(10); blockRat(10);
# 
# (4.9)  We display the number of seconds of computer time that Maple
# has consumed since it was started.
# 
> time();
# 
# (4.10)  We display the elapsed time before and after the evaluation of
# a call to blockFloat.  The difference is the number of seconds of
# computer time used by blockFloat to do its calculations. 
# 
> time(); blockFloat(100); time();
# 
# (4.11)  We time blockFloat in a different way so that the third value
# displayed in the actual elapsed time.
# 
> start := time(); blockFloat(100); time() - start;
# 
# (4.12)  We follow the first two commands from (4.11) with colons
# instead of semicolons to suppress the display of their results.  Only
# the time required to run blockFloat is shown now.
# 
> start := time(): blockFloat(100): time() - start;
# 
# (4.16)  We exploit a much better method for computing the sum of the
# first trillion even terms of the harmonic series.
# 
> evalf(1/2 * (Psi(1e12 + 1) + gamma));
# 
# (4.17)  The ! operator computes the factorial function.
# 
> 5!;
>