I think that google would expect a link to the actual report
Okay!
- Computation of various subgroups of infinite finitely presented groups
- Computation of Galois groups for a given polynomial
- Finding kernels of homomorphisms with infinite domains
- Extend functionalities of polycyclic groups
- Quotient groups
- Automorphism groups
I also have some Ideas that I want to add such as : - Triple Product Property (https://en.wikipedia.org/wiki/Triple_product_property) we can do it for both groups and sets.
- Normal Groups - While learning about Triple Product Property I also found that currently we do not have Implemented Normal subgroups so maybe this will be a new addition.
- Intersection of subgroups
This is not the final ideas I have just briefed I am still researching and going through code base.(will be able to spend more time once my exams get overed.
I am working in sympy from Jan 2020. Any suggestions are welcome. Please tell if any there are any stalled Pr or where I can start the work from .
@jksuom @divyanshu132 @asmeurer @RavicharanN
Yeah you are right I think we have to select only few ideas out of them that can be possibly completed in a summer.I am still working to narrow down this list (I will come up with much more descriptive and sensible list asap my universities exam gets over).
I was looking for your insight that what do you think about the ideas and what can be improved or removed to make a balanced amount of work for summer.
Computation of various subgroups of infinite finitely presented groups
Can you elaborate on this?Computation of Galois groups for a given polynomial
This is a whole new world, theory of algebraic numbers, not much group theory.Finding kernels of homomorphisms with infinite domains
Do you have some idea of how?Extend functionalities of polycyclic groups
Can you elaborate?Quotient groups
Of what kind of groups?Automorphism groups
Of what kind of structures?Triple Product Property (https://en.wikipedia.org/wiki/Triple_product_property) we can do it for both groups and set
Is there something to implement?Intersection of subgroups
This could be useful though I don't know of algorithms.
Triple Product Property (https://en.wikipedia.org/wiki/Triple_product_property) we can do it for both groups and set.
Is there something to implement?
As Triple Product Property is a property we have to just implement test for this.I have seen the various algorithms for this property here (https://arxiv.org/pdf/1104.5097.pdf) to save your time you can directly head over to page no. 6 and 7 and page 8 to see the efficiency of each algorithms.
I think to implement this it would not take much time except few problems I am having :
- some algorithms are using intersection (groups) to check whether they are trivial or not (obviously we do not need to calculate intersection for this) I have some property but it would only work when group is Normal "Two Normal Subgroups Intersecting Trivially Commute Each Other" (https://yutsumura.com/two-normal-subgroups-intersecting-trivially-commute-each-other/).
I have thoughts like:
- what should we do when groups are not normal ?
- Does Normal group property really be efficient there?