#9463: Integer factorization should handle perfect powers efficiently
---------------------------------+------------------------------------------
Reporter: fredrik.johansson | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone:
Component: basic arithmetic | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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factor() is extremely slow at factoring large perfect powers (with a
nontrivial base).
{{{
sage: %time factor(next_prime(10^20)^150)
CPU times: user 0.75 s, sys: 0.00 s, total: 0.75 s
Wall time: 0.75 s
100000000000000000039^150
sage: %time factor(next_prime(10^20)^250)
CPU times: user 2.68 s, sys: 0.00 s, total: 2.68 s
Wall time: 2.69 s
100000000000000000039^250
sage: %time factor(next_prime(10^20)^500)
CPU times: user 13.19 s, sys: 0.00 s, total: 13.19 s
Wall time: 13.20 s
100000000000000000039^500
}}}
For comparison, !SymPy handles such numbers in an instant:
{{{
sage: from sympy import factorint
sage: %time factorint(next_prime(10^20)^150)
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
{100000000000000000039L: 150}
sage: %time factorint(next_prime(10^20)^250)
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.01 s
{100000000000000000039L: 250}
sage: %time factorint(next_prime(10^20)^500)
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.02 s
{100000000000000000039L: 500}
}}}
Perfect power testing is very cheap, so it should be attempted early on
for large numbers.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9463>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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