#3214: [with patch, needs review] gcd needs improved coercion
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Reporter: novoselt | Owner: somebody
Type: defect | Status: reopened
Priority: blocker | Milestone: sage-3.3
Component: basic arithmetic | Resolution:
Keywords: |
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Comment (by cremona):
Hmmm. It seems a real pity to just delete the quick exit line since in
most circumstances as soon as you have a unit you can return 1. This will
result in a lot of calls to vi.gcd(g) where vi is random and g==1, so
those had better be caught efficiently in the member gcd() function.
(Incidentally, there was a reason for putting vi.gcd(g) and not g.gcd(vi),
which I now forget.)
It's another field-of-fractions thing; in the example we are not really
treating the rationals as elements of QQ, but as scaled elements of ZZ,
where x.div(y) means y/x in ZZ even though x,y may be in QQ. Testing for
.is_unit() certainly would not be appropriate. I cannot see a better way
than what the patch does, unless we give up the nice behaviour that the
gcd of a set of rationals is defined to be a generator of the ZZ-module
they span.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3214#comment:7>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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