#19179: Chain homotopies
-------------------------------------+-------------------------------------
Reporter: jhpalmieri | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers:
Authors: John Palmieri | Work issues:
Report Upstream: N/A | Commit:
Branch: | 07c9c4258f68999ecf4e2659890a3385c8f8aa0e
u/jhpalmieri/chains | Stopgaps:
Dependencies: #6102 |
-------------------------------------+-------------------------------------
Comment (by cnassau):
I've been playing around with this for the last week and I'm essentially
ready to give the ticket a positive review. I can think of a couple of
very minor improvements that might be better addressed in a follow-up
ticket:
- add syntactic sugar to replace `H._g` with something like `H[1]`, or
`H.endpoint(1)` or whatever
- create a parent for chain homotopies so that linear combinations can
be taken easily
I encountered one more serious surprise in my experiments, and I'm not
quite sure how to address this: I was starting with a chain complex `C`
over the integers, and I wanted to work with its reduction modulo 2. The
code that I came up with actually messed up the original complex:
{{{
sage: d1 = matrix([[-1,1,0],[1,-1,0],[-1,0,1],[1,0,-1]]).transpose()
sage: d2 = matrix([[-1,-1,+1,+1],[1,1,1,1]]).transpose()
sage: C=ChainComplex({2:d2,1:d1},degree_of_differential=-1,base_ring=ZZ)
sage: ascii_art(C)
[-1 1]
[-1 1 -1 1] [-1 1]
[ 1 -1 0 0] [ 1 1]
[ 0 0 1 -1] [ 1 1]
0 <-- C_0 <-------------- C_1 <-------- C_2 <-- 0
sage:
D=ChainComplex(C._diff,degree_of_differential=C.degree_of_differential(),base_ring=GF(2))
sage: ascii_art(C)
[1 1]
[1 1 1 1] [1 1]
[1 1 0 0] [1 1]
[0 0 1 1] [1 1]
0 <-- C_0 <---------- C_1 <------ C_2 <-- 0
}}}
I would have expected an error here, and possibly a more convenient way to
carry out the base change.
As for the patchbot errors: these are a bit confusing; I think they're all
due to the fact that the dependencies of the ticket have not been properly
merged for the test. Given the dependencies with #6101, #6102 I wonder if
it isn't the best approach to approve them all at once, eventually.... (?)
--
Ticket URL: <http://trac.sagemath.org/ticket/19179#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
