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Generators of infinite bars

이덕재
 

Hi,


Dionysus does not compute the generators of infinite bars as mentioned at [https://groups.io/g/dionysus/message/75] and also does not show such bars in the barcode diagram.

Is there a way to compute the generators of infinite bars and also show the bars in the diagram?

For small complexes I added artificial simplexes at the end of the filtration to kill all the bars, but this adhoc method is not scalable at all.

Thanks.


Deokjae Lee

Dmitriy Morozov
 

I'm not sure what you mean by scalable. You can always cone off the complex, then all homology will eventually die, and you can get the generators of the previously infinite bars. The computation will take longer, but in terms of code, it's extra 5-10 lines.


On Wed, Feb 13, 2019 at 6:43 AM 이덕재 <lee.deokjae@...> wrote:

Hi,


Dionysus does not compute the generators of infinite bars as mentioned at [https://groups.io/g/dionysus/message/75] and also does not show such bars in the barcode diagram.

Is there a way to compute the generators of infinite bars and also show the bars in the diagram?

For small complexes I added artificial simplexes at the end of the filtration to kill all the bars, but this adhoc method is not scalable at all.

Thanks.


Deokjae Lee

이덕재
 

The problem is the computing time. The number of simplices may be doubled by constructing the cone and the computation takes longer time as you said. I wondered if there is a way to reduce the extra time consumption. If there is no way, then it's just ok. Thanks.

Dmitriy Morozov
 

There are algorithms to do it, but they are not implemented in Dionysus. Well, not for homology. For cohomology, you get generators of the infinite bars with what's already implemented.


On Wed, Feb 13, 2019 at 6:03 PM 이덕재 <lee.deokjae@...> wrote:
The problem is the computing time. The number of simplices may be doubled by constructing the cone and the computation takes longer time as you said. I wondered if there is a way to reduce the extra time consumption. If there is no way, then it's just ok. Thanks.