Some Number Theoretic Functions
Axiom provides several number theoretic operations for integers.
More examples are in
IntegerNumberTheoryFunctions,
The operation fibonacci computes the
Fibonacci numbers. The algorithm has a running time O(log(n)**3) for
argument n.
The operation legendre computes the
Legendre symbol for its two integer arguments where the second one is
prime. If you know the second argument to be prime, use
jacobi instead where no check is made.
The operation jacobi computes the Jacobi symbol
for its two integer arguments. By convention, 0 is returned if the greatest
common divisor of the numerator and denominator is not 1.
The operation eulerPhi compute the values
of Euler's φ-function where φ(n) equals the number of
positive integers less than or equal to n that are relatively prime to the
positive integer n.
The operation moebiusMu computes the
Moebius μ function.
Although they have somewhat limited utility, Axiom provides Roman numerals.
