[sage-devel] Consultation for adding functions related to elliptic genera
Hi everyone, I am a newcomer to SageMath and have written some functions that I would like to contribute to Sage. Specifically, I have developed functions to: 1. Compute the bases of Weak Jacobi forms for both integral weights and half-integral indices. 2. Compute the coefficients of elliptic genera represented by Chern numbers. 3. Compute integrations of cohomology classes of homogeneous spaces and their complete intersections. I have a few questions regarding these functions: Question 1: Would it be appropriate to push these functions as a ‘Geometry and Topology’ library in Sage? Question 2: I cannot find any SageMath polynomial library that supports polynomials of rational degrees. However, elliptic genera are Laurent polynomial series of rational degrees. What is the most appropriate representation for this? Question 3: In my code, I have redefined the zeta function only for negative integers due to computation time. Is it acceptable to use such ad-hoc coding, or should I use the zeta function of the SageMath library in the code to be published? Here are some additional details about my codes: 1. Compute the bases of Weak Jacobi forms for both integral weights and half-integral indices. * For each pair of integers n and half-integer k, the function outputs a list of bases of the space of weak Jacobi forms of weight n and index k. * For any weak Jacobi form of weight n and index k, the function outputs the coefficients when we express the form by the basis which is output by the above function. 2. Compute the coefficients of elliptic genera represented by Chern numbers * For each dimension d, the function outputs the elliptic genera of varieties of dimension d whose coefficients are written by Chern numbers. 3. Compute integrations of cohomology classes of homogeneous spaces and their complete intersections. * We define abstract classes of varieties and vector bundles with abstract functions 'Chern classes', 'Chern characters', and 'Todd classes'. * We also define classes of homogeneous spaces, equivariant vector bundles on them, and their complete intersections, which implements the above abstract classes and computes the integrations of any cohomology classes on them. * By combining these, we can compute the Chern numbers of these spaces. Thank you for your time and consideration. Kenta Kobayashi, Ph.D student at Tokyo University -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/f9a55abd-28f4-47b0-b808-24733ca6c527n%40googlegroups.com.
[sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
Google's chatbot Bard is at https://bard.google.com/ Bard isn't available in my country. I heard that the main difference between ChatGPT and Bard is that ChatGPT is offline during the chat. Asking Bard about the genus of a curve would be an interesting comparison. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD__9APP5iTQwxYdNpCSOuJ%2B66EH_X4xghSQVxLoUxeK7A%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
On Sun, 26 Mar 2023 at 17:26, Georgi Guninski wrote: > Google's chatbot Bard is at https://bard.google.com/ > > Bard isn't available in my country. You can always spoof where you are with the Tor Onion browser -- Dr. David Kirkby, Kirkby Microwave Ltd, drkir...@kirkbymicrowave.co.uk https://www.kirkbymicrowave.co.uk/ Telephone 01621-680100./ +44 1621 680100 Registered in England & Wales, company number 08914892. Registered office: Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United Kingdom -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CANX10hCCZE9z26v7qOteGGADK9_MAi8OySdeW7HiWxYxMSbXuA%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
On Sun, Mar 26, 2023 at 5:32 PM Dr. David Kirkby wrote: > > > On Sun, 26 Mar 2023 at 17:26, Georgi Guninski wrote: >> >> Google's chatbot Bard is at https://bard.google.com/ >> >> Bard isn't available in my country. > > > You can always spoof where you are with the Tor Onion browser I just tried, and got > You’ve been added to the waitlist! > Thanks for your interest in Bard. We’ll email you when it’s your turn. > > > -- > Dr. David Kirkby, > Kirkby Microwave Ltd, > drkir...@kirkbymicrowave.co.uk > https://www.kirkbymicrowave.co.uk/ > Telephone 01621-680100./ +44 1621 680100 > > Registered in England & Wales, company number 08914892. > Registered office: > Stokes Hall Lodge, Burnham Rd, Althorne, Chelmsford, Essex, CM3 6DT, United > Kingdom > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/CANX10hCCZE9z26v7qOteGGADK9_MAi8OySdeW7HiWxYxMSbXuA%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq0rmHepMQE8bGCKUrcjSVJjBUGtBbG-Gf2MmuN_DFTscw%40mail.gmail.com.
[sage-devel] Re: Consultation for adding functions related to elliptic genera
On Sunday, 26 March 2023 at 05:54:09 UTC-7 kenta kobayashi wrote: Question 1: Would it be appropriate to push these functions as a ‘Geometry and Topology’ library in Sage? Nowadays, for brand new code that isn't obviously extending or improving already existing capabilities in sage, it's probably a good idea to start with packaging the code into a stand-alone repository. It's your choice how nicely packaged you want to make it: you can just make it a directory that people can download and then link into sage (at their barest, python modules really just consist of a directory with python files), or you can wrap it up in a pip-installable package on github and/or publish it on pypi. (see for instance https://github.com/nbruin/RiemannTheta for an "intermediately polished" example) It has the advantage that the code is available immediately and that for the first while you can respond very quickly to bugs and issues that arise (so SageMath development cycle or review to contend with!). It also allows for a period to gauge how people actually use the code, which can be quite different from what you envisaged. Once the usage has stabilized a bit, it's worth pushing for inclusion into the sagemath library itself, so that your code is kept up-to-date with other changes in the library (over longer time spans this becomes important). At that point you can archive the original repo with a pointer to the relevant code in sagemath. This process also has the advantage that there is a specific place for you to point at to show what you've accomplished (for job and grant applications). Question 2: I cannot find any SageMath polynomial library that supports polynomials of rational degrees. However, elliptic genera are Laurent polynomial series of rational degrees. What is the most appropriate representation for this? LaurentPolynomialRing (for finite series) and LaurentSeriesRing Question 3: In my code, I have redefined the zeta function only for negative integers due to computation time. Is it acceptable to use such ad-hoc coding, or should I use the zeta function of the SageMath library in the code to be published? You could look if this redefinition is already available somewhere in sage and then you can import it from there. In general, you should probably use whatever feature is already available that significantly fills your need, to avoid duplication of effort and also because your (first) version would probably not handle edge cases and variations of inputs as gracefully as more mature code does. Your redefinition obviously needs to stay confined to your own modules and then for maintainability it should probably be named "modified_zeta" to match (so that other people reading your code understand it's not the usual zeta function). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/3f0b0133-77ab-4c26-bf4c-556d273d6035n%40googlegroups.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
I have 2 questions for the AIs: 1: In sagemath how do I check if `2^(2^50)` is integer? > RuntimeError: Aborted 2: Is `pi^(pi^(pi^(pi^(pi^42` integer? > I believe rigorous proof doesn't exist yet -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAGUWgD9H7GAFp%3D-JPfm0zaP45RUaMibYCZuneP6KeF-pGJA%2BNA%40mail.gmail.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
On Sun, 26 Mar 2023 at 19:07, William Stein wrote: > > Ok, that "proof" from GPT-4 is pretty absurd nonsense to put it mildly. I > wonder if there will be a new surge in crank math papers this year. Apparently the way that the chat GPT models are trained is that the source data comes from having humans use them and then rate the quality of the answers they get given. Then they train a model to predict how humans would rate the answers and then they use that to train new iterations of GPT. After some iterations of that they go back to the humans again and so on. What that means is that ultimately the target of the chat models is to try to satisfy the humans who are using them in testing. They have used any old humans though rather than say "experts" so the goal is not to be "correct" but just to try to satisfy the human users. One implication of this training goal is that the models are optimised towards giving superficially plausible answers. A clever sounding but incorrect answer has a chance to satisfy a human who does not read carefully. A negative result like "Sorry I can't answer" is likely to receive a poor rating from most humans even if it is the most correct answer. Also these models will actually try to judge what sort of human you are. If your question suggests that you do know what you are talking about then the bot will try to give an answer that would please someone who knows what they are talking about. Naturally the converse applies as well. This means that the wording of your question can alter the answers that you receive in more ways than you might immediately expect. These models are called language models for good reason because they are really just trained to be good at language. Their ability to answer questions that seem to involve some reasoning is no different from a human BS-monger who can google for a bit and knows how to string some sentences together in a way that momentarily resembles the language of someone who knows what they are talking about. The limits of their actual reasoning are quite clear in the final part of this proof where we go from a theorem like algebraic^algebraic -> transcendental in one step to transcendental^transcendental -> transcendental. Quite apart from the bogus algebra this is a failure in pretty elementary logic. However I think that Chat GPT on some level *knows* that the logic is bogus. It has just scored that bogusness and decided that it is better than the alternatives it could generate for the problem at hand (and the user at hand!). If you castigate the bot and point out its fallacies or even just tell it lies then it will rework its answer to be some new BS it thinks you will be more likely to be satisfied by. -- Oscar -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAHVvXxRw-b1KPe9DwwgPgK1-H9K36FBXYzT7L1PNBr11qerf%3Dw%40mail.gmail.com.
[sage-devel] Re: Consultation for adding functions related to elliptic genera
Thank you very much Mr.Bruin for your helpful advice. I will follow your suggestion and try to start with a stand-alone repository. Thank you once again. Kenta Kobayashi 2023年3月27日月曜日 1:53:58 UTC+9 Nils Bruin: > On Sunday, 26 March 2023 at 05:54:09 UTC-7 kenta kobayashi wrote: > > Question 1: > Would it be appropriate to push these functions as a ‘Geometry and > Topology’ library in Sage? > > > Nowadays, for brand new code that isn't obviously extending or improving > already existing capabilities in sage, it's probably a good idea to start > with packaging the code into a stand-alone repository. It's your choice how > nicely packaged you want to make it: you can just make it a directory that > people can download and then link into sage (at their barest, python > modules really just consist of a directory with python files), or you can > wrap it up in a pip-installable package on github and/or publish it on pypi. > (see for instance https://github.com/nbruin/RiemannTheta for an > "intermediately polished" example) > > It has the advantage that the code is available immediately and that for > the first while you can respond very quickly to bugs and issues that arise > (so SageMath development cycle or review to contend with!). It also allows > for a period to gauge how people actually use the code, which can be quite > different from what you envisaged. > > Once the usage has stabilized a bit, it's worth pushing for inclusion into > the sagemath library itself, so that your code is kept up-to-date with > other changes in the library (over longer time spans this becomes > important). At that point you can archive the original repo with a pointer > to the relevant code in sagemath. > > This process also has the advantage that there is a specific place for you > to point at to show what you've accomplished (for job and grant > applications). > > > Question 2: > I cannot find any SageMath polynomial library that supports polynomials > of rational degrees. > However, elliptic genera are Laurent polynomial series of rational > degrees. > What is the most appropriate representation for this? > > > LaurentPolynomialRing (for finite series) and LaurentSeriesRing > > > Question 3: > In my code, I have redefined the zeta function only for negative integers > due to computation time. > Is it acceptable to use such ad-hoc coding, or should I use the zeta > function of the SageMath library in the code to be published? > > > You could look if this redefinition is already available somewhere in sage > and then you can import it from there. In general, you should probably use > whatever feature is already available that significantly fills your need, > to avoid duplication of effort and also because your (first) version would > probably not handle edge cases and variations of inputs as gracefully as > more mature code does. > > Your redefinition obviously needs to stay confined to your own modules and > then for maintainability it should probably be named "modified_zeta" to > match (so that other people reading your code understand it's not the usual > zeta function). > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/f7fb620d-c0f6-4dda-9c13-ce1d3a1e1674n%40googlegroups.com.
Re: [sage-devel] OT: google's chatbot Bard is at https://bard.google.com/
... the goal is not to be "correct" but just to try to satisfy the human users. A nice insight into what ChatGPT does. AI is human in that respect. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/4bec12c5-a199-4fcf-8bcf-a161372dc816n%40googlegroups.com.
