is_squarefree

[roed314]

sage: is_squarefree(6/1)
True
sage: is_squarefree(12/1)
False
sage: is_squarefree(2/3)
False
sage: (2/3).is_squarefree()
Traceback (most recent call last):
...
AttributeError: 'sage.rings.rational.Rational' object has no attribute 'is_squarefree'

The implementation of the global is_squarefree method eventually uses return all(r[1] == 1 for r in factor(n)). A more mathematically sensible definition is that x is squarefree if and only if it is not divisible by the square of any non-unit. For fields, this means that 0 is not squarefree and everything else is squarefree.

Of course, this can be confusing for beginners who now have to deal with (4/1).is_squarefree() returning True.

See also #23510.

CC: @saraedum @xcaruso @kedlaya @sagetrac-alina

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/23577