MATH-MISC(1)                                         MATH-MISC(1)

     NAME
          ack, crackerbarrel, factor, fibonacci, fit, genprimes,
          mersenne, parts, perms, pi, powers, primes, sieve -
          miscellaneous mathematical applications

     SYNOPSIS
          math/ack [ m ] [ n ]
          math/crackerbarrel [ n ]
          math/factor [ n ]
          math/fibonacci
          math/fit [ -ddeg ] [ -v ] [ file ]
          math/genprimes [ lim ]
          math/mersenne [ num ]
          math/parts [ -a ] [ num... ]
          math/perms [ n ]
          math/pi [ dp ]
          math/powers [ -p num ] [ -n num ] [ -f num ] [ -l num ] [ -m
          num ] [ -v ]
          math/primes [ m ] [ n ]
          math/sieve [ -a alg ] [ lim ]

     DESCRIPTION
          A collection of simple mathematical utilities.

          math/ack
               Calculates and times Ackermann's function A(m, n).

          math/crackerbarrel
               Solves the crackerbarrel puzzle n times and outputs the
               time taken. See the source for details of the puzzle.

          math/factor
               Factors the number n.

          math/fibonacci
               Generates the first few terms of the Fibonacci series
               using recursion and user defined exceptions.

          math/fit
               Fits a polynomial of degree deg to a set of points (x,
               y) where x is the independent variable, y the dependent
               one.  All x and y values should be seperated by white
               space and can be real or integer. The values are read
               from file or standard input if none is given. The -v
               option prints a table of actual and expected y values.

          math/genprimes
               Generates primes numbers up to and including lim using
               spawned processes and buffered channels.

     MATH-MISC(1)                                         MATH-MISC(1)

          math/mersenne
               Tests the primality of the Mersenne numbers ie numbers
               of the form 2^n-1.  The argument num is the power of 2
               in the above.

          math/parts
               Calculates the number of partitions of the given
               number(s). The -a option will print out a table of the
               number of partitions of all numbers up to  the given
               number(s).

          math/perms
               Prints out all permutations of n elements.

          math/pi
               Calculates the value of pi to dp decimal places.

          math/powers
               Investigates the number of representations of an inte-
               ger as a sum of powers.  The -p option denotes the
               power of use (default 2). The -n option denotes the
               number of powers to sum (default 2). The -f option
               denotes the minimum number of such representations
               found before reporting them (default 2). The -l and -m
               options denote the smallest and largest numbers to con-
               sider respectively (defaults 0 and 8192). Finally the
               -v option prints various statistics during the search.

          math/primes
               Prints out all primes between m and n .

          math/sieve
               Prints out prime numbers up to lim using a sieve algo-
               rithm. The -a option indicates the level of sophistica-
               tion of the algorithm (0-4).

     EXAMPLE
               math/powers -p 3 -m 30000
          gives
               [2] 1729 = 1**3 + 12**3 = 9**3 + 10**3
               [2] 4104 = 2**3 + 16**3 = 9**3 + 15**3
               [2] 20683 = 10**3 + 27**3 = 19**3 + 24**3
          The number of representations found for each integer is indicated in
          square brackets.

     SOURCE
          /appl/math/ack.b
          /appl/math/crackerbarrel.b
          /appl/math/factor.b
          /appl/math/fibonacci.b
          /appl/math/fit.b
          /appl/math/genprimes.b

     MATH-MISC(1)                                         MATH-MISC(1)

          /appl/math/mersenne.b
          /appl/math/parts.b
          /appl/math/perms.b
          /appl/math/pi.b
          /appl/math/powers.b
          /appl/math/primes.b
          /appl/math/sieve.b