IntegerFactorization objects - Parents and Elements

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# IntegerFactorization objects

class sage.structure.factorization_integer.IntegerFactorization(x, unit=None, cr=False, sort=True, simplify=True, unsafe=False)

  Bases: `Factorization`

  A lightweight class for an `IntegerFactorization` object, inheriting from the more general `Factorization` class.

  In the `Factorization` class the user has to create a list containing the factorization data, which is then passed to the actual `Factorization` object upon initialization.

  However, for the typical use of integer factorization via the `Integer.factor()` method in `sage.rings.integer` this is noticeably too much overhead, slowing down the factorization of integers of up to about 40 bits by a factor of around 10. Moreover, the initialization done in the `Factorization` class is typically unnecessary: the caller can guarantee that the list contains pairs of an `Integer` and an `int`, as well as that the list is sorted.

  AUTHOR:

  - Sebastian Pancratz (2010-01-10)