Hello all,
Please consider voting on the addition of msieve to sage. This
includes an interface file and an .spkg. Msieve, by Jason
Papadopoulos, should increase the integer factorization functionality
of Sage. I'll quote the words of Jason in the Readme file by way of
explanation:
"There are plenty of algorithms for performing integer factorization.
The Msieve library implements most of them from scratch, and relies
on
optional external libraries for the rest of them. Trial division and
Pollard Rho is used on all inputs; if the result is less than 25
digits
in size, tiny custom routines do the factoring. For larger numbers,
the
code
switches to the GMP-ECM library and runs the P-1, P+1 and ECM
algorithms,
expending a user-configurable amount of effort to do so. If these do
not
completely factor the input number, the library switches to the heavy
artillery. Unless told otherwise, Msieve runs the self-initializing
quadratic
sieve algorithm, and if this doesn't factor the input number then
you've
found a library problem. If you know what you're doing, Msieve also
contains
a complete implementation of the number field sieve, that has helped
complete
some of the largest public factorization efforts known."
and
"To be as fast as possible. I claim (without proof) that for
completely factoring general inputs between 40 and 100 digits in size,
Msieve is faster than any other code implementing any other algorithm."
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