
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] = ith 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

See
prime.
