#13670: Inversion in polynomial quotient rings could give clearer error message
when element is non-invertible
---------------------------------------+------------------------------------
Reporter: Bouillaguet | Owner: malb
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.5
Component: commutative algebra | Resolution:
Keywords: polynomial rings | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Charles Bouillaguet | Merged in:
Dependencies: #13671 | Stopgaps:
---------------------------------------+------------------------------------
Comment (by Bouillaguet):
Replying to [comment:7 mstreng]:
> It's not just a problem of dividing 0 by something. If you try to
compute {{{S(2x)/S(x)}}}, then you have the same problem: the answer is
non-unique, so the univariate case gives a !ZeroDivisionError, while the
multivariate case gives the answer {{{S(2)}}} where {{{S(2+x)}}} is
equally correct.
So, if I understand correctly, division by `f` should only be allowed if
`f` has an inverse in `R/I`. Is that correct?
Thinking about this file more generally : most of the functions in this
file are completely generic and do not depend on what `R` and `I` are.
However there are a few exceptions to this :
* {{{is_unit()}}}. Currently does almost nothing. Could possibly be
improved while staying generic by trying the {{{inverse_mod}}} method of
the parent ring `R`.
* {{{_div_}}}. Currently does something specific when `R` is a polynomial
ring (computing a Gröbner basis, etc.), and something generic in other
cases (multiplying the numerator by the inverse of the denominator, using
the {{{inverse_mod}}} function of `R`).
{{{__invert__}}} is somewhat generic: it tries to use the
{{{inverse_mod}}} function of `R`, and if this is {{{NotImplemented}}},
then it tries {{{_div_}}}. This is bizarre, because in the end it will
also fall back to {{{inverse_mod}}}, except when `R` is a polynomial ring,
but these now have the {{{inverse_mod function}}} thanks to #13675.
So, maybe this ticket could become "Various Small Improvements to
!QuotientRingElement", and could implement:
* the improvement to the error message already discussed above
* small improvement to the {{{is_unit}}} function
* small improvement to the {{{_div_}}} function
I also wonder whether it is the Right Thing to have polynomial-specific
code here...
Ch.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13670#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
