#16507: Better handling of subspace construction in pushout
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.3
Component: categories | Keywords: pushout subspace
Merged in: | Authors: Peter Bruin
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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When taking a pushout of two modules in the case where the construction of
exactly one of them involves a subspace construction, the result does not
have a coercion map from the other object:
{{{
sage: A = ZZ^2
sage: V = span([[1, 2]], QQ)
sage: P = sage.categories.pushout.pushout(A, V)
sage: P
Vector space of degree 2 and dimension 1 over Rational Field
User basis matrix:
[1 2]
sage: P.has_coerce_map_from(A)
False
}}}
The explanation is that for the other currently existing constructions
`F`, the result `F(X)` of applying the construction to `X` has a coercion
map ''from'' `X`, but for the subspace construction, `F(X)` only has a
coercion map ''to'' `X`.
This ticket addresses this by equipping the class `ConstructionFunctor`
with an attribute `coercion_reversed`, which is `False` by default; if it
is `True` for a construction `F`, then the pushout of two objects omits
`F` in the case where (at a given step of constructing the pushout)
exactly one of the two constructions is `F`. Of course, we set
`coercion_reversed = True` for the subspace construction.
No change is necessary in the case where both constructions involve `F`,
since this situation should be taken care of by `F.merge()`. This is
indeed true for the subspace construction, where `F.merge()` takes the sum
of the two subspaces.
The situation described above can be viewed as the case where one of the
two constructions involves a "trivial" application of `F`, i.e. with the
subspace equal to the whole space. Hence we should interpret our
situation as a case where the effect of `merge()` with one trivial
argument is desired.
In the above example, this strategy will cause `P` to be equal to `QQ^2`,
as might be expected.
--
Ticket URL: <http://trac.sagemath.org/ticket/16507>
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