Dear Travis,
I opened the ticket for twisting in tensor product
(https://trac.sagemath.org/ticket/21363#ticket)
renaming displayed variables is more on the cosmetic side, should I open
another one just for this?
git trac checkout 21363 ends in an error:
Loading ticket #21363...
> Traceback (most recent call last):
> File "/usr/local/bin/git-trac", line 18, in <module>
> cmdline.launch()
>
> File "/usr/local/lib/python2.7/dist-packages/git_trac/cmdline.py", line
> 209, in launch
> app.checkout(args.ticket_or_branch, args.branch_name)
>
> File "/usr/local/lib/python2.7/dist-packages/git_trac/app.py", line 115, in
> checkout
> self._checkout_ticket(int(ticket_or_branch), branch_name)
>
> File "/usr/local/lib/python2.7/dist-packages/git_trac/app.py", line 122, in
> _checkout_ticket
> ticket = self.trac.load(ticket_number)
>
> File "/usr/local/lib/python2.7/dist-packages/git_trac/trac_server.py", line
> 101, in load
> ticket = TracTicket(ticket_number, self.anonymous_proxy)
>
> File "/usr/local/lib/python2.7/dist-packages/git_trac/trac_ticket.py", line
> 155, in TracTicket
> change_log = server_proxy.ticket.changeLog(ticket_number)
> File "/usr/lib/python2.7/xmlrpclib.py", line 1240, in __call__
> return self.__send(self.__name, args)
> File "/usr/lib/python2.7/xmlrpclib.py", line 1599, in __request
> verbose=self.__verbose
> File "/usr/lib/python2.7/xmlrpclib.py", line 1280, in request
> return self.single_request(host, handler, request_body, verbose)
>
> File
> "/usr/local/lib/python2.7/dist-packages/git_trac/digest_transport_py2.py",
> line 129, in single_request
> return self.parse_response(response)
> File "/usr/lib/python2.7/xmlrpclib.py", line 1490, in parse_response
> return u.close()
> File "/usr/lib/python2.7/xmlrpclib.py", line 797, in close
> raise ResponseError()
> xmlrpclib.ResponseError: ResponseError()
>
did I do something wrong?
m
On Monday, 29 August 2016 16:23:01 UTC+2, Travis Scrimshaw wrote:
>
> Hey Marek,
>
>>
>> I have two questions regarding cohomology ring of (delta/simplicial)
>> complexes.
>>
>> First:
>> How to change the way the generators are displayed?
>> (currently it's h^{i,j}, where i is the degree/gradation and j is the
>> index of generator in its gradation)
>> It would be much nicer to be able to name them (actually: display) with
>> more human readable names.
>>
>> e.g. for the cohomology ring You could do
>>
>> >S_2 = delta_complexes.SurfaceOfGenus(2)
>>> >H = S_2.cohomology_ring(QQ); H
>>> Cohomology ring of Delta complex with 3 vertices and 29 simplices over
>>> Rational Field
>>> >H.__custom_name= 'H*(S_2)'; H
>>> H*(S_2)
>>>
>>
>> But I was not able to change how x_1 = H.basis(1)[0] is displayed.
>> This is probably trivial, it's just me not beeing able to find an option
>> to do this. I tried things around Indexed generators
>>
>
> IndexedGenerators has some control over the print representation when
> allowed access. However, it is just coming along for the ride with
> CombinatorialFreeModule, which the class HomologyVectorSpaceWithBasis is
> based off of. HomologyVectorSpaceWithBasis explicitly sets its
> representation behavior with _repr_term.
>
> It's not too hard to add options; in particular, there is the class
> GlobalOptions (see, e.g,, Partitions or Tableaux for examples) that we can
> add to include options.
>
>>
>> Second: Consider cartesian product:
>>
>> >SxS = S_2.product(S_2); SxS
>>>
>>> Delta complex with 9 vertices and 3635 simplices
>>>
>>>
>> This doesn't seem prohibitively large, yet computation of
>> SxS.cohomology_ring(QQ) takes a lot of time.
>> So I decided to play smart and set:
>>
>> H2 = tensor([H,H])
>>>
>>
>> However the product in the tensor product is twisted (see e.g. A.
>> Hatcher, Algebraic Topology, Section 3.2 on the cup product, p. 219):
>>
>> (a \otimes b) \cup (c \otimes d) = (-1)^{|b||c|} (a \cup c) \otimes (b
>>> \cup d)
>>>
>>
>> yet I don't see a way to ask sage to respect that? maybe tensor([H,H],
>> twisted=True) could be introduced
>>
>> I'd be willing to address both issues in code if someone would be willing
>> to guide me.
>>
>> Great! I would be happy to help. Please cc me on the ticket (tscrim), and
> we can discuss details there. You should all cc John Palmieri (jhpalmieri),
> who should also be interested in this.
>
> Best,
> Travis
>
>
>
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