#15381: gens() can mean both module and algebra generators, confusing
morphism.pyx
-------------------------+-------------------------------------------------
Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: | Keywords: categories, gens, morphisms,
categories | modules
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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{{{
sage: D3 = GroupAlgebra(DihedralGroup(3), QQ)
sage: from sage.categories.modules_with_basis import *
sage: g = ModuleMorphismByLinearity(domain=D3, codomain=D3,
on_basis=lambda x: (D3.zero() if list(x) == [] else D3.basis()[x]))
sage: g.is_identity()
True
}}}
Of course, `g` is not the identity. The culprit is here:
{{{
gens = domain.gens()
for x in gens:
if self(x) != x:
return False
return True
}}}
This is part of the `is_identity` method in
`sage/categories/morphism.pyx`. The assumption is that the `gens` method
and the morphism refer to the same category, but here they don't: the
morphism is a module morphism, while `D3.gens()` refers to the generators
as algebra.
Note that the equality check takes the other extreme and seems to only
return `True` if the `on_basis` lambda functions of both morphisms are
identical (i. e., I can add zero to each image and it doesn't return
`True` anymore, even if they are identical).
--
Ticket URL: <http://trac.sagemath.org/ticket/15381>
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