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#### 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/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 integer 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 consider 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 algorithm. The -a option indicates the level of sophistication 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
/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

 MATH-MISC(1 ) Rev:  Tue Mar 31 02:42:38 GMT 2015