#10771: gcd and lcm for fraction fields
--------------------------------+-------------------------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_review
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: |
--------------------------------+-------------------------------------------
Changes (by SimonKing):
* cc: burcin (added)
* status: needs_work => needs_review
Comment:
With the new patch, all tests pass for me. The behaviour is now (mutatis
mutandis for lcm):
* If `ZZ` is a subring of a field F that is not a fraction field then
`a.gcd(b)` first tests if a and b can be converted into `ZZ`. If it is the
case, their gcd in `ZZ` ''as element of `ZZ`'' is returned. This is not
nice, but it is compatible with the "unpatched" behaviour of Sage and is
assumed in some other parts of Sage:
{{{
# unpatched!
sage: gcd(RR(1),RR(1))
1
sage: _.parent()
Integer Ring
}}}
* If `ZZ` is no subring of F or conversion fails then `a.gcd(b)` returns
`F(0)` or `F(1)`. This is, e.g., the case for `gcd(CC(2),CC(2))`, since
`CC(2)` can not be converted into `ZZ`.
* a.gcd(b) only raises an error if `b` can not be converted into
`a.parent()`.
* gcd and lcm in fraction fields of a unique factorization domain R
restrict to R, and moreover they satisfy `gcd(a,b)*lcm(a,b)==a*b` up to
multiplication with a unit of R.
There is a price to pay, and that's why I put Burcin on Cc:
The distribution of minus signs in symbolic expression changes, apparently
since now gcd raises no errors in examples like the following:
{{{
sage: (I - 1/3*sqrt(2))^2
1/9*(-sqrt(2) + 3*I)^2
# Without patch, we would get
# 1/9*(sqrt(2) - 3*I)^2
}}}
The question is whether a changed minus sign distribution is such a
serious thing.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10771#comment:21>
Sage <http://www.sagemath.org>
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