Opened 2 years ago

Last modified 2 years ago

#23577 new defect

is_squarefree

Reported by: roed Owned by:
Priority: major Milestone: sage-8.1
Component: basic arithmetic Keywords:
Cc: saraedum, caruso, kedlaya, alina Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

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.

Change History (2)

comment:1 Changed 2 years ago by roed

  • Cc saraedum caruso kedlaya added

comment:2 Changed 2 years ago by kedlaya

  • Cc alina added
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