# This worksheet implements the blocks package used in Chapter 4 of
# Introduction to Scientific Programming by Joseph L. Zachary.
# 
# Create an empty package.
# 
> blocks := table();
# 
# 
# Compute maximum extension for "n" blocks using floating-point
# arithmetic.
# 
> blocks[blockFloat] := proc (n)
>   local total, i;
>   total := 0.0;
>   for i from 1 to n do
>     total := total + 1.0/(2.0*i);
>   od;
>   RETURN(total);
> end;
# 
# Compute maximum extension for "n" blocks using rational arithmetic.
# 
> blocks[blockRat] := proc (n)
>   local total, i;
>   total := 0;
>   for i from 1 to n do
>     total := total + 1/(2*i);
>   od;
>   RETURN(total);
> end;
# 
# Compute maximum extension for "n" blocks using Psi function and gamma
# constant.
# 
> blocks[blockFast] := proc (n)
>   RETURN(.5 * evalf(Psi(n+1)+gamma));
> end;
>