#8972: Inversion and fraction fields for power series rings
-----------------------------------------------+----------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.4.4
Component: algebra | Resolution: fixed
Keywords: power series ring, fraction field | Author: Simon King
Upstream: N/A | Reviewer: Robert
Bradshaw
Merged: | Work_issues: fix division
if no fraction field exists; use ~ instead of / in elliptic curve code
-----------------------------------------------+----------------------------
Changes (by SimonKing):
* work_issues: trouble with schemes/elliptic_curves => fix division if
no fraction field exists; use ~ instead
of / in elliptic curve code
Comment:
After fixing what I mentioned above, I get for {{{sage -testall}}}:
{{{
The following tests failed:
sage -t "devel/sage/sage/crypto/lfsr.py"
sage -t "devel/sage/sage/modular/modform/find_generators.py"
sage -t
"devel/sage/sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field.py"
}}}
This seems doable.
Perhaps I was too strict when I implemented {{{_div_}}}: I wanted that the
result ''always'' lives in the fraction field, and I wanted that an error
is raised if no fraction field exists. But I guess it is better to proceed
as it is known from other rings that are no integral domains:
{{{
sage: K = ZZ.quo(15)
sage: parent(K(3)/K(4))
Ring of integers modulo 15
sage: parent(K(4)/K(3))
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call
last)
...
ZeroDivisionError: Inverse does not exist.
}}}
So, rule:
1. ''If'' a fraction field exists then the result of a division must live
in it (example: 1/1 is a rational, not an integer).
2. If no fraction field exists, then devision shall yield an element of
the original ring, if that's possible, and raise a {{{ZeroDivisionError}}}
otherwise.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8972#comment:30>
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