.TH MATH-MISC 1.SH NAMEack, crackerbarrel, factor, fibonacci, fit, genprimes, mersenne, parts, perms, pi, powers, primes, sieve \- miscellaneous mathematical applications.SH SYNOPSIS.B math/ack[.IR m][.IR n].br.B math/crackerbarrel[.IR n].br.B math/factor[.IR n].br.B math/fibonacci.br.B math/fit[.BI -d deg][.B -v][.IR file].br.B math/genprimes[.IR lim].br.B math/mersenne[.IR num].br.B math/parts[.B -a][.IR num ...].br.B math/perms[.IR n].br.B math/pi[.IR dp].br.B math/powers[.B -p num][.B -n num][.B -f num][.B -l num][.B -m num][.B -v].br.B math/primes[.IR m][.IR n].br.B math/sieve[.B -a alg][.IR lim].SH DESCRIPTIONA collection of simple mathematical utilities..PP.TP.B math/ackCalculates and times Ackermann's function A(m, n)..TP.B math/crackerbarrelSolves the crackerbarrel puzzle.B ntimes and outputs the time taken. See the source for details of the puzzle..TP.B math/factorFactors the number n..TP.B math/fibonacciGenerates the first few terms of the Fibonacci series using recursionand user defined exceptions..TP.B math/fitFits a polynomial of degree.I degto 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 spaceand can be real or integer. The values are read from.IR fileor standard input if none is given. The.B -voption prints a table of actual and expected y values..TP.B math/genprimesGenerates primes numbers up to and including.B limusing spawned processes and buffered channels..TP.B math/mersenneTests the primality of the Mersenne numbers ie numbers of the form 2^n-1.The argument.IR numis the power of 2 in the above..TP.B math/partsCalculates the number of partitions of the given number(s). The.B -aoption will print out a table of the number of partitions of all numbers up to  thegiven number(s)..TP.B math/permsPrints out all permutations of.B nelements..TP.B math/piCalculates the value of pi to.B dpdecimal places..TP.B math/powersInvestigates the number of representations of an integer as a sum ofpowers.The.B -poption denotes the power of use (default 2). The.B -noption denotes the number of powers to sum (default 2). The.B -foption denotes the minimum number of such representations found beforereporting them (default 2). The.B -land.B -moptions denote the smallest and largest numbers to consider respectively (defaults 0 and 8192). Finally the.B -voption prints various statistics during the search..TP.B math/primesPrints out all primes between.B mand.B n ..TP.B math/sievePrints out prime numbers up to.B limusing a sieve algorithm. The.B -aoption indicates the level of sophistication of the algorithm (0-4)..PP.SH EXAMPLE.EX 	math/powers -p 3 -m 30000gives	[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**3The number of representations found for each integer is indicated insquare brackets..EE.SH SOURCE.B /appl/math/ack.b.br.B /appl/math/crackerbarrel.b.br.B /appl/math/factor.b.br.B /appl/math/fibonacci.b.br.B /appl/math/fit.b.br.B /appl/math/genprimes.b.br.B /appl/math/mersenne.b.br.B /appl/math/parts.b.br.B /appl/math/perms.b.br.B /appl/math/pi.b.br.B /appl/math/powers.b.br.B /appl/math/primes.b.br.B /appl/math/sieve.b