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Post AfggaFyP23tj6CmVLk by [email protected] |
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More posts by [email protected] |
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Post #AfgNntxzkbXLlvNqEK by [email protected] |
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This curve is not an elliptic curve - because even though you can write it in a… |
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Post #AfgQ55SoSS4GGE7XzE by [email protected] |
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First let's count the solutions of y² = x³ - x² in the field with 2 elem… |
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Post #AfgRq83kiyI1sNOV5U by [email protected] |
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Now let's count the solutions of y² = x³ - x² in some fields with 3ⁿ e… |
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Post #AfgSnz0XVXjNB3QpnM by [email protected] |
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@johncarlosbaez Sage(Math) is freeware - do you mean to say you use a free onli… |
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Post #AfgTPDtz5tSG5N7heC by [email protected] |
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@dimpase - yes, that wasn't very clearly written! I use this:https://coca… |
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Post #AfgTqZWun2jcyxNE9Y by [email protected] |
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@johncarlosbaez you need WSL (WSL2) in Windows running. This is a virtual machi… |
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Post #AfgU01TIH01sFQBbrk by [email protected] |
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@dimpase - okay, I'll never do this! Installing a virtual machine, etc. et… |
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Post #AfgU6RKt1TmyCbJW1A by [email protected] |
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@johncarlosbaez You might want to edit the values for 3^n at the beginning ... … |
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Post #AfgU6RP8lfBwPnIueG by [email protected] |
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@glc - thanks! I did! |
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Post #AfgUY7k3SzXRXaHqUK by [email protected] |
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@johncarlosbaez it's really not hard, to install a WSLhttps://learn.microso… |
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Post #AfgVESVce2is6yisvw by [email protected] |
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I wonder if @williamstein has a budget for sponsoring users like you. I couldn&… |
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Post #Afgc6ANkr7HZFq2I4m by [email protected] |
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@johncarlosbaez @dimpase I feel you there completely! Especially the constant d… |
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Post #Afgc8f9xOfLNHvlxaa by [email protected] |
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@RefurioAnachro @williamstein @dimpase - Thanks for the offer, Refurio. I can a… |
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Post #AfggaFyP23tj6CmVLk by [email protected] |
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@johncarlosbaez The fact that you sometimes get p^n + 1 points seems weird to m… |
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Post #AfgpzqXB8UQVJlKAsK by [email protected] |
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@macbro wrote: "The fact that you sometimes get p^n + 1 points seems weird… |
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Post #AfgqUgv2vzayTTCEWu by [email protected] |
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@pschwahn @johncarlosbaez I don't think that Sage running in a WSL2 is noti… |
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Post #AfgqUh00dXZ6irWCGW by [email protected] |
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@dimpase wrote: "the trick is to only use native Linux (virtual) disk, and… |
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Post #AfgrCqAFvD2TtEMWjA by [email protected] |
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@macbro @johncarlosbaez the projective line over F_q has q+1 points. The nodal … |
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Post #AfgrCqEre4j27WWCuW by [email protected] |
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@macbro @johncarlosbaez maybe a better way to see it: the node "blows up&q… |
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Post #AfgrCqIPQtYqIWB2R6 by [email protected] |
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@Elliptickiwi @johncarlosbaez Maybe I'm not understanding right, but this s… |
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Post #AfgrCqMJCOgEUc09Vw by [email protected] |
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@macbro @Elliptickiwi - we see it can have one more, since the equationy² = x�… |
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Post #Afgs4L5ffbH79YjCb2 by [email protected] |
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@johncarlosbaez @Elliptickiwi Oh, I wonder if char(k) = 3 is what's causing… |
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Post #AfgvRprFk8Zv6Esawq by [email protected] |
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@johncarlosbaez @macbro @Elliptickiwi You can make the change of variables y = … |
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Post #Afh1G5FdHk975h3wK8 by [email protected] |
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@johncarlosbaez it was really a remark for Paul, I should have trimmed the list… |
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Post #Afh1LJSFu6l4afSayu by [email protected] |
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@macbro @johncarlosbaez here's another singular cubic case to try: y^2 = x^… |
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Post #Afh1LJW9fbsSmlHi3k by [email protected] |
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@Elliptickiwi @macbro - yes, y² = x³ has a cusp rather than a node, so the co… |
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Post #Afh1jQIi6OQSlzUaA4 by [email protected] |
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@dimpase - I had to learn to use Word to write grant proposals with coauthors w… |
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Post #Afh4QkNhWET1Pbc3DE by [email protected] |
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@johncarlosbaez @macbro a really cool fact is that the usual elliptic curve gro… |
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Post #Afh4QkRxGPrzcnbRqK by [email protected] |
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@Elliptickiwi - oh cool! I hadn't really absorbed the meaning of "add… |
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Post #AfhoFfhLBchTaqSKGm by [email protected] |
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> point at infinityHow do we write this? Like PF³ has {-1,0,1,oo} as elemen… |
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Post #Afhorm2G4YtKFiPNnk by [email protected] |
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That in particular seems like it would be easy to check? But the hilarious part… |
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Post #AfiT87GCvGSQseHRvE by [email protected] |
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@RefurioAnachro - I can't tell if you're using F³ to mean the 3-elemen… |
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Post #AfiYiJe6qn6tUOXc80 by [email protected] |
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Argh. Of course I knew projective spaces, and how homogeneous coordinates work,… |
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Post #AfiZOD0vtjSV5EC0ky by [email protected] |
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All the stuff in your new post is fine, @RefurioAnachro. I was a bit worried … |
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Post #AfiaXNvWnGGLUObVVg by [email protected] |
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I do Python for bread, so I find the following easy enough to read:for n in ran… |
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Post #AfiagX7VyxkiblZaPg by [email protected] |
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Thanks, @johncarlosbaez !@macbro |
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Post #AfidgCtjT4xNkhf8CG by [email protected] |
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@johncarlosbaez @RefurioAnachro I think the notation P^n(k) is somewhat common … |
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Post #Afin42PD1r53kSp7wm by [email protected] |
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@macbro @RefurioAnachro - good point: Pⁿ is a scheme which can be seen as a f… |
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Post #Afine7KyAdsLT72pPc by [email protected] |
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@RefurioAnachro - I try to avoid looking at programs too closely. I find the s… |
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Post #Afipz3OuCYLdFVzr7I by [email protected] |
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I have given up on really knowing any single programming language completely my… |
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Post #AfiqJqPVh5jV2fC2W8 by [email protected] |
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> P^n is a schemeI like functors.Those other notations, however, are slightl… |
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Post #AfkL4QozqHZV4ZCkqW by [email protected] |
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@Elliptickiwi @macbro - thanks! I'm coming out with a blog article on this… |
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Post #AfkOpe22qMIHW7Vq64 by [email protected] |
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@RefurioAnachro - projectivizing a Hilbert space is also a functor, so you shou… |
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Post #AfkUR1ami1zV4cPBpY by [email protected] |
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@johncarlosbaez @RefurioAnachro I thought that projectivizing wasn't a func… |
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Post #AfkYPFZY9znFfZElMG by [email protected] |
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@OscarCunningham @RefurioAnachro - projectivization is a functor from the categ… |
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Post #AjUc3EyJBtqz2izUmG by [email protected] |
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@johncarlosbaez @dimpase Another option that is sometimes preferable is just to… |
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Post #AjUer7EKRpxJQ7OVO4 by [email protected] |
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@johncarlosbaez @RefurioAnachro @macbro A minor point about notation (from alge… |
