# IntegerFactorizationPackage I¶

intfact.spad line 311 [edit on github]

This Package contains basic methods for integer factorization. The factor operation employs trial division up to 10, 000. It then tests to see if `n`

is a perfect power before using Pollards rho method. Because Pollards method may fail, the result of factor may contain composite factors. We should also employ Lenstra`'s`

eliptic curve method.

- BasicMethod: I -> Factored I
`BasicMethod(n)`

returns the factorization of integer`n`

by trial division

- factor: I -> Factored I
`factor(n)`

returns the full factorization of integer`n`

- PollardSmallFactor: I -> Union(I, failed)
`PollardSmallFactor(n)`

returns a factor of`n`

or “failed” if no one is found

- squareFree: I -> Factored I
`squareFree(n)`

returns the square free factorization of integer`n`