#12969: Coercion failures in symmetric functions
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Reporter: aschilling | Owner: sage-combinat
Type: defect | Status: new
Priority: major | Milestone: sage-5.3
Component: combinatorics | Resolution:
Keywords: symmetric functions, coercion | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by SimonKing):
I think I can explain (and thus, solve) the problem!
The bug is in the backtracking algorithm for finding a coercion path.
Every parent A has a list of other parents B1, B2, ... such that a
coercion from B1, B2 to A is registered. When searching for a coercion
from parent X to A, and a direct coercion is not registered, then a
coercion from X to B1, B2, ... is (in that order!) is searched. But of
course one must avoid infinite recursions, and thus any coercion path from
X to B1, B2, via X is disregarded. Disregarding one node in the
backtracking algorithm is the purpose of _register_pair in
sage.structure.parent.
Now consider the following situation, where arrows denote registered
coercions (partially the coercions are registered in ''both'' directions -
that's what happening in the symmetric functions code):
{{{
X -> B2 <-> A <-> B1
}}}
We first ask for a coercion from X to A.
There is no coercion from X to A found in the cache. Thus, we disregard
(X,A) in our backtracking algorithm, and search for a coercion from X to
B1. The only coercion path from X to B1 would be via A, but that is
disregarded in the backtracking algorithm. The absence of a coercion from
X to B1 is cached. In the next step, a coercion from X to A via B2 is
found, cached and returned.
But when later asking for a coercion from X to B1, the cache states that
there is no coercion!
Here's the bug: The absence of a coercion from X to B1 must ''only'' be
cached if X is not the starting point of any disregarded search path (such
as (X,A) in the example above), with the only exception of (X,B1).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12969#comment:18>
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