#8800: Doctest coverage of categories
--------------------------+-------------------------------------------------
Reporter: SimonKing | Owner: Simon King
Type: defect | Status: new
Priority: major | Milestone: sage-4.4.2
Component: categories | Keywords: categories doctests
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
--------------------------+-------------------------------------------------
Comment(by SimonKing):
Concerning algebraic extension of algebraically complete fields: sage-
devel expressed the opinion that it is better to do the construction
(namely quotient of a univariate polynomial ring) in any case. So, I leave
it as it is.
Here is another problem:
{{{
sage: R1.<x> = Zp(5)[]
sage: R2 = Qp(5)
sage: R2(1)+x
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/SimonKing/<ipython console> in <module>()
/usr/local/sage/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__add__
(sage/structure/element.c:10830)()
/usr/local/sage/local/lib/python2.6/site-packages/sage/structure/coerce.so
in sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:6966)()
TypeError: unsupported operand parent(s) for '+': '5-adic Field with
capped relative precision 20' and 'Univariate Polynomial Ring in x over
5-adic Ring with capped relative precision 20'
}}}
The reason is
{{{
sage: from sage.categories.pushout import pushout
sage: pushout(R1,R2)
---------------------------------------------------------------------------
CoercionException Traceback (most recent call
last)
/home/SimonKing/<ipython console> in <module>()
/usr/local/sage/local/lib/python2.6/site-
packages/sage/categories/pushout.pyc in pushout(R, S)
1109 # make sense, and in this case simply want to return that
a pushout
1110 # couldn't be found.
-> 1111 raise CoercionException(ex)
1112
1113
CoercionException: 'pAdicFieldCappedRelative' object has no attribute
'completion'
}}}
Rather than implementing a completion of p-adic fields, I suggest to give
the construction functors of fraction fields and of completions the same
rank. This would already suffice (together with the existing merge method
of the completion functor) so that one has
{{{
sage: R1.<x> = Zp(5)[]
sage: R2 = Qp(5)
sage: R2(1) + x
(1 + O(5^20))*x + (1 + O(5^20))
}}}
Note that there is an additional problem, namely that there is no coercion
from a p-adic field of high precision to a p-adic field of lower
precision. I hope sage-devel will answer whether this issue is worth a
separate ticket.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8800#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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