On 01/05/2018 19:13, David Roe wrote:
On Tue, May 1, 2018 at 1:01 PM, Vincent Delecroix <20100.delecr...@gmail.com
wrote:
On 01/05/2018 18:31, Nils Bruin wrote:
On Tuesday, May 1, 2018 at 9:10:27 AM UTC-7, vdelecroix wrote:
Dear all,
How should be defined division in non-integral domains like Zmod(6)? The
following looks a bit incoherent to me
PPS: people with access to magma are welcome to report!
Magma complains about division by a non-unit. It does allow "div", but it
also allows 5 div 2 in ZZ/6.
I think the problem for "/" is division by a zero-divisor. Otherwise an
answer can be returned in a structure where an inverse has been adjoined.
The ZeroDivisionError is therefore spot-on, if you read it as an
abbreviation of ZeroDivisorDivisionError. Using non-unit as abbreviation
for zero-divisor in Z/nZ is pretty common too. I don't think a change is
necessary.
But there is still something missing in Sage: how do I compute all
possible "quotients" of 5 by 2 in Zmod(6) in my Sage console other than
sage: R = Zmod(6)
sage: a = R(5)
sage: b = R(2)
sage: [c for c in R if c*b == a]
[2, 5]
Such a function would be reasonable to implement, though note that the
actual answer in your example is [], not [2, 5].
I interverted 5 and 4... my bad. I opened
https://trac.sagemath.org/ticket/25278
I agree with Nils that the ZeroDivisionError is correct. If there's
something to be fixed, it's the divides function, which is currently using
a generic implementation from element.pyx that falls back on testing
whether a % b == 0. Indeed:
sage: R = Zmod(6)
sage: R(2).divides(R(4))
True
sage: R(4).divides(R(2))
ArithmeticError: reduction modulo 4 not defined
Indeed
https://trac.sagemath.org/ticket/25277
Vincent
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