#9819: Add a default gcd and lcm methods for fields
---------------------------+------------------------------------------------
Reporter: lftabera | Owner: AlexGhitza
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-duplicate/invalid/wontfix
Component: algebra | Keywords: lcm, gcd, fields
Work_issues: | Upstream: N/A
Reviewer: | Author: Luis Felipe Taberea
Merged: | Dependencies:
---------------------------+------------------------------------------------
Changes (by mstreng):
* status: needs_review => positive_review
Old description:
> For the case of field elements gcd and lcm methods are not of great
> interest. However, they can be addecuated for some reasons.
>
> - Some algorithms may accept as input either polynomials or rational
> functions. In these algorithms we may reduce a list of polynomials and
> rational functions to a common denominator. If all the inputs are
> polynomials, the denominators are the one element of the base field. In
> this case, lcm would fail.
>
> See #9063 for a case of this problem.
>
> - Rational numbers already have custom gcd and lcm methods.
>
> -It would erase the following problem. Currently, if we are dealing with
> elements in a finite field, the gcd of the elements can be computed
> sometimes coercing to the integers and doing computations. This lead to
> inconsistencies.
>
> {{{
> sage: a=F(2)
> sage: gcd(a,a)
> 2
> sage: gcd(a,p)
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /home/luisfe/Varios/Comprobantes-gastos/<ipython console> in <module>()
>
> /opt/SAGE/sage-4.5.2/local/lib/python2.6/site-
> packages/sage/rings/arith.pyc in gcd(a, b, **kwargs)
> 1423 return ZZ(a).gcd(ZZ(b))
> 1424 except TypeError:
> -> 1425 raise TypeError, "unable to find gcd of %s and
> %s"%(a,b)
> 1426
> 1427 from sage.structure.sequence import Sequence
>
> TypeError: unable to find gcd of 2 and p
> }}}
>
> I propose the following:
>
> - For gcd, follow the convention of the rational cesa. If both elements
> are 0, return 0 (on the appropriate field). Otherwise return 1
>
> - For lcm, if one of the elements is zero, return zero. Otherwise return
> 1.
>
> #9063 depends on this bug to be merged.
New description:
'''This ticket should be closed as fixed by #10771'''
For the case of field elements gcd and lcm methods are not of great
interest. However, they can be addecuated for some reasons.
- Some algorithms may accept as input either polynomials or rational
functions. In these algorithms we may reduce a list of polynomials and
rational functions to a common denominator. If all the inputs are
polynomials, the denominators are the one element of the base field. In
this case, lcm would fail.
See #9063 for a case of this problem.
- Rational numbers already have custom gcd and lcm methods.
-It would erase the following problem. Currently, if we are dealing with
elements in a finite field, the gcd of the elements can be computed
sometimes coercing to the integers and doing computations. This lead to
inconsistencies.
{{{
sage: a=F(2)
sage: gcd(a,a)
2
sage: gcd(a,p)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/luisfe/Varios/Comprobantes-gastos/<ipython console> in <module>()
/opt/SAGE/sage-4.5.2/local/lib/python2.6/site-
packages/sage/rings/arith.pyc in gcd(a, b, **kwargs)
1423 return ZZ(a).gcd(ZZ(b))
1424 except TypeError:
-> 1425 raise TypeError, "unable to find gcd of %s and
%s"%(a,b)
1426
1427 from sage.structure.sequence import Sequence
TypeError: unable to find gcd of 2 and p
}}}
I propose the following:
- For gcd, follow the convention of the rational cesa. If both elements
are 0, return 0 (on the appropriate field). Otherwise return 1
- For lcm, if one of the elements is zero, return zero. Otherwise return
1.
#9063 depends on this bug to be merged.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9819#comment:8>
Sage <http://www.sagemath.org>
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