5.1.113 primefactors

Syntax:

primefactors ( int/bigint/number_expression )
primefactors ( int/bigint/number_expression , int_expression )

Type:

list

Purpose:

returns the prime factorisation up to an optionally given bound, b, on the prime factors
When called with int(s)/bigint(s), no ring needs to be active.
When called with numbers these are assumed to be integers in a polynomial ring over Q.
The method finds all prime factors of an integer n. n' will contain the sign, be zero, or the rest (when a bound is given) respectively. The returned list contains the following information: The returned list contains the following information:
L[1][i] = i-th prime factor (in ascending order),
L[2][i] = multiplicity of L[1][i],
L[3] = n'

Example:

bigint n = bigint(7)^12 * bigint(37)^6 * 121; primefactors(n); ==> [1]: ==> [1]: ==> 7 ==> [2]: ==> 11 ==> [3]: ==> 37 ==> [2]: ==> [1]: ==> 12 ==> [2]: ==> 2 ==> [3]: ==> 6 ==> [3]: ==> 1 primefactors(n,25); ==> [1]: ==> [1]: ==> 7 ==> [2]: ==> 11 ==> [2]: ==> [1]: ==> 12 ==> [2]: ==> 2 ==> [3]: ==> 2565726409