Mind me jumping in the discussion for this, but I have some comments

The important aspect of DomainMatrix is that the computations should be 
'rational' (which can be generalized up to 'multivariate rational function 
field')
So I don't think that you can implement cholesky or hessenberg or 
householder easily.
I have also though about adjoining the new square roots as algebraic 
extensions,
But I'm afraid that you can't anticipate the speed just like numeric cases 
even if this approach is taken.
On Sunday, March 14, 2021 at 10:16:15 PM UTC+9 kartik...@gmail.com wrote:

> Oscar Benjamin, Have you had a chance to review my GSoC application draft? 
> I've posted it here 
> https://github.com/sympy/sympy/wiki/GSoC-2021-Current-Applications
>
> On Friday, 12 March 2021 at 11:44:49 am UTC+5:30 Kartik Sethi wrote:
>
>> Oscar Benjamin, could you review this first draft of my proposal. Please 
>> let me know if you feel that I should focus 
>> on some other topics/ algorithms in DomainMatrix instead of the ones 
>> chosen by me. 
>>
>> GSoC 2021 Proposal 
>> <https://github.com/ks147/GSoC/wiki/Gsoc_2021_application>
>> On Tuesday, 9 March 2021 at 6:49:29 am UTC+5:30 Oscar wrote:
>>
>>> On Mon, 8 Mar 2021 at 16:00, Kartik Sethi <kartik...@gmail.com> wrote: 
>>> > 
>>> > Oscar Benjamin, what if someone else also puts up this same proposal 
>>> to improve the DomainMatrix module for Gsoc. How does sympy decide which 
>>> person will work on it. 
>>>
>>> There is plenty more work to do on DomainMatrix than one person could 
>>> do in a single GSOC project so there could be two people doing related 
>>> projects on this although we do have limits on how many projects a 
>>> single mentor could supervise. I am not the only person who could 
>>> mentor a project on DomainMatrix though and it's also possible that I 
>>> would mentor a project on something else instead such as ODEs. 
>>>
>>> We will look at all applications and decide which to accept based on a 
>>> number of factors. The two major factors are the priority of the 
>>> project and the quality of the application. I think that DomainMatrix 
>>> is high priority but if there are stronger proposals for other 
>>> projects then it is possible that no proposal for DomainMatrix would 
>>> be accepted. 
>>>
>>> I suggest not to overthink this. The main thing is just to have a good 
>>> application that is well motivated and shows clear understanding of 
>>> the work to be done. 
>>>
>>> -- 
>>> Oscar 
>>>
>>

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