#10771: gcd and lcm for fraction fields
--------------------------------+-------------------------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: basic arithmetic | Keywords: gcd lcm fraction fields
Author: Simon King | Upstream: N/A
Reviewer: Marco Streng | Merged:
Work_issues: |
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Changes (by mstreng):
* status: needs_review => needs_work
Comment:
New complaints, sorry.
* I don't really like this:
{{{
sage: M = Matrix(GF(3),2,2,[1,2,0,1]); M
[1 2]
[0 1]
sage: GF(2)(1).lcm(M)
1
}}}
I think you should first try to coerce other to self.parent() in gcd
and lcm for Field elements.
* Line 64 of quotient_fields.py "{{{both GCD and LCM, it is possible to
be a bit more specific}}}"
uses capital letters GCD and LCM, while the methods that it
(quasi-)refers to are lower case:
{{{AttributeError: 'sage.rings.rational.Rational' object has no
attribute 'GCD'}}}
* Next line: "define the GCD uniquely up to a unit in the base ring".
Write "of" instead of "in"
so that it is clear that you are not saying that the GCD is in the base
ring.
* Your tests with {{{R.<q> = ZZ.extension(x^2+5)}}} is unrelated to
fraction field: q is 1
{{{
sage: R.<q> = ZZ.extension(x^2+5)
sage: g = R.gens(); g
[1, q]
sage: q
1
sage: g[1]
q
sage: g[1] == q
False
}}}
All your examples involving q get coerced to ZZ by the global GCD and
LCM, so you should
find other examples. This seems to work:
{{{
sage: gcd(g[1],1)
TypeError: unable to find gcd of q and 1
sage: gcd(g[1]/1,1)
1
}}}
(Correct behaviour both times)
Time to catch a bus, may have more comments later.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10771#comment:10>
Sage <http://www.sagemath.org>
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