Previous: Programming Answer 11, Up: Answers to Exercises [Contents][Index]

#### 2.7.69 Programming Tutorial Exercise 12

This turns out to be a much easier way to solve the problem. Let’s denote Stirling numbers as calls of the function ‘`s`’.

First, we store the rewrite rules corresponding to the definition of Stirling numbers in a convenient variable:

    s e StirlingRules RET
    [ s(n,n) := 1  :: n >= 0,
      s(n,0) := 0  :: n > 0,
      s(n,m) := s(n-1,m-1) - (n-1) s(n-1,m) :: n >= m :: m >= 1 ]
    C-c C-c

Now, it’s just a matter of applying the rules:

    2:  4          1:  s(4, 2)              1:  11
    1:  2              .                        .
        .

      4 RET 2       C-x (  ' s($$,$) RET     a r StirlingRules RET  C-x )

As in the case of the `fib` rules, it would be useful to put these rules in `EvalRules` and to add a ‘`:: remember`’ condition to the last rule.