#12969: Coercion failures in symmetric functions
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Reporter: aschilling | Owner: sage-combinat
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.3
Component: combinatorics | Resolution:
Keywords: symmetric functions, coercion | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: | Stopgaps:
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Comment (by SimonKing):
The patch seems to work. But meanwhile I wonder whether my fix is really
correct.
The aim is: Find a coercion from X to Y.
Backtracking means: We know some B1,B2,... that coerce into Y. Hence, we
try to find a coercion from X to B1,B2,... but avoiding Y, so that there
is no infinite loop. That's why the pair (X,Y) is temporarily disregarded
when searching for a coerce path.
In particular, the recursive search will always start at X.
Hence, it was my understanding that all temporarily disregarded paths
start at X. That's why I wrote
{{{
#!python
cdef bint _may_cache_none(x, y, tag) except -1:
# Are we allowed to cache the absence of a coercion
# from y to x? We are only allowed, if y is *not*
# part of any coerce path that is temporarily disregarded,
# with the only exception of the path from y to x.
# See #12969.
cdef EltPair P
for P in _coerce_test_dict.iterkeys():
if (P.y is y) and (P.x is not x) and (P.tag is tag):
return 0
return 1
}}}
However, to be on the safe side, I tested whether I drew the correct
conclusion. Apparently I didn't.
Namely, when Sage starts and a coercion from the complex double field
into, say, the integer ring is sought, then the path from the complex lazy
field to the complex double field is disregarded. Also, while trying to
find a coercion from the complex lazy field to the integers, the search
path from "Number Field in I with defining polynomial x^2^ + 1" to the
rational field is temporarily disregarded.
Even weirder: When doing `m(P.one())` in the example from the ticket
description, the coercion from "<type 'str'>" to Fraction Field of
Multivariate Polynomial Ring in q, t over Rational Field is disregarded,
while searching for a coerce path from None (sic!) to the ring of
integers.
I wonder how this can possibly happen, given how backtracking works. And
what does that mean for the patch? I guess the cleanest solution would be
to find out why the wrong paths are temporarily disregarded, and why the
heck a coercion from None to anything is requested.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12969#comment:31>
Sage <http://www.sagemath.org>
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