id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
32900,implement multiplicative functions for factored integers,gh-maxale,,"Multiplicative functions (such as `number_of_divisors()`, `sigma()`, `divisors()` etc.) can be easily computed for factored integers, but they are not defined for `Factorization` objects. This ticket requests their implementation.
It may be worth to add an optional parameter (eg. `check`) such that `check=True` will instruct to verify `Factorization` object for completeness (i.e. that it's composed of prime powers) and complete it, while `check=False` will just blindly treat `Factorization` elements as prime powers.
Relatedly, it's worth to add `factor()` function for `Factorization` objects, which will complete it when `check=True`, or just return self when `check=False`.
Also, for functions like `divisors()` it is worth to have a parameter `factored` (with default value `False`), which if `True` will instruct to return factorizations of the divisors rather than their numerical values.",enhancement,new,major,sage-9.7,number theory,,,,,,,N/A,,,,,