chickadee » chibi-math

chibi-math

Chibi Scheme's math library

Module: (chibi math prime)

Prime and number theoretic utilities.

Original documentation here: https://synthcode.com/scheme/chibi/lib/chibi/math/prime.html

modular-inverse
modular-inverse a bprocedure

Returns the multiplicative inverse of a modulo b.

modular-expt
modular-expt a e mprocedure

Returns (remainder (expt a e) m).

coprime?
coprime? n mprocedure

Returns true iff n and m are coprime.

Exact prime testing

provable-prime?
provable-prime? nprocedure

Returns true iff n is definitely prime. May take an impossibly long time for large values.

Probable primes.

miller-rabin-composite?
miller-rabin-composite? nprocedure

Returns true if we can show n to be composite using the Miller-Rabin test (i.e., finding a witness a where a^(n-1)≠1 mod n or a reveals the existence of a 3rd square root of 1 in Z/(n))

probable-prime?
probable-prime? nprocedure

Returns true if n has a very high probability (enough that you can assume a false positive will never occur in your lifetime) of being prime.

prime?
prime? nprocedure

Returns true iff n is prime. Uses provable-prime? for small n, falling back on probable-prime? for large values.

Prime iteration and factorization

nth-prime
nth-prime iprocedure

Returns the nth prime, with 2 being the 0th prime.

prime-below
prime-below nprocedure

Returns the first prime less than or equal to n, or #f if there are no such primes.

prime-above
prime-above n #!optional (limit #f)procedure

Returns the first prime greater than or equal to n. If the optional limit is given and not false, returns #f if no such primes exist below limit.

factor-alist
factor-alistconstant

Returns the factorization of n as a list of elements of the form (p . k)}, where {{p is a prime factor and k is its multiplicity.

factor
factorconstant

Returns the factorization of n as a monotonically increasing list of primes.

totient
totientconstant

The Euler totient φ(n) is the number of positive integers less than or equal to n that are relatively prime to n.

aliquot
aliquotconstant

The aliquot sum s(n) is the sum of proper divisors of a positive integer n.

perfect?
perfect? nprocedure

Returns true iff n is a perfect number, i.e. the sum of its divisors other than itself equals itself.

Random prime generation

random-prime
random-prime lo hiprocedure

Returns a random prime between lo, inclusive, and hi, exclusive.

random-prime-distinct-from
random-prime-distinct-from lo hi pprocedure

Variant of random-prime which ensures the result is distinct from p.

random-coprime
random-coprime nprocedure

Returns a random integer less than n relatively prime to n.

Maintainer

Diego A. Mundo

Author

Alex Shinn

Version History

0.1.0

License

BSD

Copyright (c) 2009-2021 Alex Shinn 
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