#6101: computation of induced morphism on homology and cohomology of simplicial
complex morphisms
-------------------------------------+-------------------------------------
Reporter: bantieau | Owner: bantieau
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: u/jhpalmieri | 698ba79f9837c3c2e83bd358441b4cd4a4073392
/induced-maps | Stopgaps:
Dependencies: #19179, #6102 |
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Comment (by cnassau):
Hi John,
This seems pretty interesting. I just started to play around with it and
was struck by a couple of minor usability issues:
{{{
sage: X=simplicial_complexes.BrucknerGrunbaumSphere()
sage: phi, M = algebraic_topological_model(X, GF(2))
sage: phi
Chain homotopy between Chain complex morphism from Chain complex with at
most 4 nonzero terms over Finite Field of size 2 to Chain complex with at
most 4 nonzero terms over Finite Field of size 2 and Chain complex
morphism from Chain complex with at most 4 nonzero terms over Finite Field
of size 2 to Chain complex with at most 4 nonzero terms over Finite Field
of size 2
sage: phi._codomain()
Trivial chain
sage: phi._domain()
Trivial chain
sage: phi._codomain() is phi._domain()
False
}}}
As you can see, I made the basic mistake of thinking of "phi._domain" as
private functions, when they are in fact just attributes:
{{{
sage: phi._domain
Chain complex with at most 4 nonzero terms over Finite Field of size 2
sage: phi._domain is phi._f._domain
True
}}}
The Sage maps that I'm used to (mainly morphisms between
CombinatorialFreeModules) have public "domain" and "codomain" methods;
this might have spared me a 5 minute detour in this case. I have no good
idea, though, what to call the $H_0$ and $H_1$ of a homotopy $H_t$...
Also, I wonder if phi shouldn't better be printed like
{{{
sage: phi
Chain homotopy between
Chain complex morphism
From: Chain complex with at most 4 nonzero terms over Finite Field
of size 2
To: Chain complex with at most 4 nonzero terms over Finite Field
of size 2
and Chain complex morphism
From: Chain complex with at most 4 nonzero terms over Finite Field
of size 2
To: Chain complex with at most 4 nonzero terms over Finite Field
of size 2
}}}
At least this is the way morphisms between combinatorial free modules are
printed:
{{{
sage: A,B=[CombinatorialFreeModule(GF(2),x) for x in [(1,2,3),(2,3,4)]]
sage: f=A.module_morphism(codomain=B,on_basis = lambda x:x+1) ; f
Generic morphism:
From: Free module generated by {1, 2, 3} over Finite Field of size 2
To: Free module generated by {2, 3, 4} over Finite Field of size 2
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/6101#comment:10>
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