Hello Vincent, Thank you for the feedback. Sorry I didn't take into account exact fields while writing about Task-1, but I am also a bit confused since I am also exploring Krylov subspaces for the first time only. When I searched to do so for exact fields, what I understood was that after building up the block-krylov subspace I could use rank-revealing decompositions such as QR/SVD modified for exact linear algebra to extract kernel or we could first orthogonalise it using projections and then use QR to extract kernel. Other method was directly solving the system Av=0. I did see that Arnoldi and other methods are used generally though not sure about exact linear algebra. One more I can think of that after finding the characteristic polynomial using Keller-Gehrig's algorithm, I can from there find kernel, cokernel and the invariant factors. Though I will admit I am not sure about this.
Can you please just check if I am thinking I am in the right direction. If yes, I will incorporate this into my proposal. On Thursday, April 3, 2025 at 12:16:05 PM UTC+5:30 Vincent Neiger wrote: > Dear Pawani Agarwal, > > I have quickly reviewed your proposal --- please note that I might not > have time to do it again before deadline. It is well organized and > complete, yet on the core of the project, a large part of the detailed > project (basically all of Task 1) concerns things that are unrelated to > exact fields. The suggested idea of project was about exact computations > (e.g. over finite fields, over the rationals, ...). It is absolutely fine > if you propose another project, but I think you should then stick to it and > define it clearly. For the moment, your project mixes both aspects and it > makes it both difficult to understand and too ambitious for 3 months. Your > Task 2 is vague on what problems/algorithms it will tackle: what are "block > Krylov sequences for a structured subspace", and what "structured > matrix-vector products" do you have in mind? Your Task 3 seems to target > a method indeed relevant for the exact case (unlike Task 1). > > Best regards, > > Vincent Neiger > Le mardi 1 avril 2025 à 23:50:15 UTC+2, Pawani Agarwal a écrit : > >> Hello Vincent, >> >> I have sent you my proposal directly though I am not sure if you have >> received it. Please do let me know if it will be possible for you to >> provide a feedback and also if I need to send my proposal here. >> >> On Friday, March 28, 2025 at 6:11:24 PM UTC+5:30 Vincent Neiger wrote: >> >>> Dear Pawani Agarwal, >>> Thank you for your interest in this project. Thank you also for your >>> first contributions to Sagemath. Recall the short description gives ideas >>> for the project and you, the potential contributor, are expected to turn >>> the ideas into a detailed proposal. >>> Best regards, >>> Vincent Neiger >>> >>> Le lundi 17 mars 2025 à 22:33:09 UTC+1, Pawani Agarwal a écrit : >>> >>>> Hello, >>>> >>>> I am Pawani, a 4th year student at BITS Goa pursuing a dual degree in >>>> MSc Mathematics and BE Computer Science. >>>> I have been contributing to SageMath for sometime now and I have also >>>> created PRs (#39528 and #39472), though they haven't been reviewed. This >>>> has given me a bit of familiarity with the codebase and I am also >>>> exploring >>>> deeper into it. >>>> >>>> For this project I have already started reading up on the fundamental >>>> concepts, including minimal polynomials, Krylov subspaces, and their >>>> applications in kernel and co-kernel computations over K[x] modules. >>>> >>>> I am very excited about this project and would love to contribute >>>> actively. Please let me know if there are any other specific directions or >>>> initial tasks I should focus on. Looking forward to your guidance! >>>> >>>> Best regards, >>>> Pawani Agarwal >>>> >>>> The information contained in this electronic communication is intended >>>> solely for the individual(s) or entity to which it is addressed. It may >>>> contain proprietary, confidential and/or legally privileged information. >>>> Any review, retransmission, dissemination, printing, copying or other use >>>> of, or taking any action in reliance on the contents of this information >>>> by >>>> person(s) or entities other than the intended recipient is strictly >>>> prohibited and may be unlawful. If you have received this communication in >>>> error, please notify us by responding to this email or telephone and >>>> immediately and permanently delete all copies of this message and any >>>> attachments from your system(s). The contents of this message do not >>>> necessarily represent the views or policies of BITS Pilani. >>>> >>> >> The information contained in this electronic communication is intended >> solely for the individual(s) or entity to which it is addressed. It may >> contain proprietary, confidential and/or legally privileged information. >> Any review, retransmission, dissemination, printing, copying or other use >> of, or taking any action in reliance on the contents of this information by >> person(s) or entities other than the intended recipient is strictly >> prohibited and may be unlawful. If you have received this communication in >> error, please notify us by responding to this email or telephone and >> immediately and permanently delete all copies of this message and any >> attachments from your system(s). 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