MixedMath - explorations in math and programing

Another year, another TeXLive reinstallation

David Lowry-Duda — Mon, 15 Apr 2024 03:14:15 +0000

Every year, TeX Live updates in a breaking way. This year it was on 13 March 2024.

I don't notice until I need to do something somewhat uncommon with my TeX distribution, such as compiling a new template or style file. Today, I'm writing a funding proposal and was (re)compiling a similar proposal I wrote a couple of years ago. It happens to use the extdash package, which I don't have installed. But trying to install it now (via tlmgr) throws an error saying that my distribution is 2023, and now it's 2024, so it's time to upgrade.

LaTeX distributions come in two forms: the main binaries and packages. Packages are updated continually and can be updated throughout the year. The main binaries are updated once each year. But once a binary is updated, the package manager (associated to a previous binary) will no longer allow package updates.

The effect is that a new texlive installation is required each year. There are some update scripts, but these are unsupported and still essentially require downloading as much material as a full install.

I haven't heard a compelling reason why this behavior is tolerated (let alone desirable). Further, following instructions typically leads with several side-by-side installations of tex (although each installation is HUGE and this is also unacceptable).

The only benefit of this is that keeping older versions allows snapshot recompilation of older documents, or snapshot recompilation using packages with backwards incompatible updates (such as moderncv, which breaks all the time). But I don't like having that bloat, so I end up completely removing old versions and installing a fresh texlive each year.

I sometimes want bleeding-edge latex things and don't use my linux distribution's package manager for this. Instead, I do it myself through the texlive package manager tlmgr. These are my notes on updating texlive from year to year.

(In particular, these are the steps that I went through just now so that I can compile what I really wanted to compile).

Remove the previous installation

I keep the texlive source in $HOME/src/texlive.¹ ¹You can probably guess where I keep source files for other things that I build and manage myself). Looking now, I see that I have 598832 bytes of stuff there, meaning that the complete size of my texlive distribution for all latex that I've compiled in the last year is approximately 585MB. This is about 1/10th the size of the standard TeXLive Full installation on Ubuntu, which is one of the reasons why I prefer to manage the installation myself.² ²I began to use tlmgr to manage texlive when I was using a chromebook as my main driver, and I needed to be able to fit texlive on my tiny harddrive. I learned a lot about resource constraints then.

I note for interest that 261MB of my texlive is dedicated to documentation for installed packages. Another 96MB is for fonts.

Regardless, I remove the entirety of my $HOME/src/texlive at once.

Acquire and run the new installer

Go to tug.org and download the texlive internet installer. This year, this is a 5.5MB file install-tl-unx.tar.gz .

Move it to a freshly created $HOME/src/texlive and unpack it.

cd into the new directory and run the installer (which is a little perl script).

I now customize many of the options. For people who read this that aren't me, I emphasize that my usecase might not be the same as your usecase. Now is an obvious time to deviate from my procedure.

Verify that it detects the correct platform, GNU/Linux on x86_64 for me.
Change the installation scheme from scheme-full (which takes 8.253GB this year) to custom .
Go into the Collections submenu. I default to having too little and then install things later with tlmgr as necessary later. Thus I first deselect all, and then I install exactly three collections: Essential programs and files, LaTeX fundamental packages, and XeTeX and packages.
Set the installation directories. I use $HOME/src/texlive and I do not separate by year. I also set TEXMFHOME to ~/.texmf (i.e. I change it to be a hidden file instead of polluting my home directory visibly).
I set tex to use letter size instead of A4 by default, because I live in the US. I note that I keep the "install font/macro doc tree" option, which downloads documentation and which ultimately doubles the size of my installation. I actually read the documentation sometimes. I think this is unusual.
Set the installation to proceed.

This year, this apparently uses 557MB of disk space.

This led to texlive installing 181 packages (and their commented source and documentation) and took less than 10 minutes.

Afterwards, the installer will display a very important message about setting MANPATH, INFOPATH, and PATH. In principle I would alter these in my .bashrc, but in practice my previous .bashrc points to these new spots since I'm overwriting where my texlive installation directory.

Remove texlive installer

TeXLive is now installed, so I can remove $HOME/src/texlive/. The exact name is different, depending on the date.

Install utility packages

I use various utilities frequently. I install these with

which tlmgr  # to make sure that new tlmgr is detected
tlmgr install latexmk lacheck chktex latexdiff pdfcrop \
              pdfjam texdiff texdoc

These are utility packages that are less common. I use lacheck and chktex for latex linting. I use texdoc to see documentation for packages. I use latexmk to handle recompilation. I use the others for various scripts I've written. All of these are tiny.

Installation took 31 seconds.

Install specific packages I use

I have four fundamental types of papers that I often compile.

A generic research paper that I might post to the arxiv.
Personal notes
Public notes
Beamer presentations

I have different templates and packages that I use for each of these. I know that I'll make all four again this year and I know exactly which packages they need. I install those now.

tlmgr install setspace mathtools booktabs wrapfig changebar \
              xcolor lipsum tocloft fancyvrb enumitem threeparttable \
              beamer beamertheme-metropolis adjustbox pgfopts \
              xkeyval collectbox times minted ragged2e multirow

I made this list a couple of years ago by checking what was necessary to compile a couple specific documents.

I install any other package as necessary throughout the year. Right now, my installation uses 706MB.³ ³Wow, that's 150 MB more than my entire distribution last year, including various packages installed throughout the year for ad hoc reasons! I wonder what changed so much. I see that 334MB, which is 73MB more than before.

FLT3 at LftCM2024

David Lowry-Duda — Sat, 30 Mar 2024 03:14:15 +0000

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Quanta on Murmurations

David Lowry-Duda — Tue, 05 Mar 2024 03:14:15 +0000

Quanta wrote an article Elliptic Curve 'Murmurations' Found With AI Take Flight (link to article).

The article describes some of the story behind the recent murmurations in number theory phenomena that I've been giving talks about. I think it's a pretty well-written article that gives a reasonable overview. Check it out!

It touches on my recent work with Bober, Booker, and Lee.If they'd waited a couple of weeks, then they might have been able to include forthcoming work with Booker, Lee, Seymour-Howell, and Zubrilina! But we're a couple of weeks away for that, I think.

And as far as I see, Quanta is the only outlet (in English) that covers recent research developments in math for a non-specialist audience (pop-math). It's certainly the case that mathematicians aren't doing a particularly job covering our own work in an accessible way.

Not quite 3 and a half years

David Lowry-Duda — Wed, 21 Feb 2024 03:14:15 +0000

Publishing Record

I submitted a paper on 2 September 2020. It was accepted this week, on 17 February 2024.

I'm continuing to include more of the tiny evaluations I do all the time with my computing environments. These may be easy manual calculations — but I've been known to make simple mistakes.

from datetime import date
from dateutil.relativedelta import relativedelta

submitted = date(2020, 9, 2)
accepted = date(2024, 2, 17)

print(accepted - submitted)
# >> datetime.timedelta(days=1263)

print(relativedelta(accepted, submitted))
# >> relativedelta(years=+3, months=+5, days=+15)

That was 1263 days, or 3 years, 5 months, and 15 days. It wasn't quite long enough to include a leapday — it missed by two weeks.

This beats my previous record (of 2 years and 3 months). I too am guilty: during the same time, I took a year to review a paper.

This is an annoying aspect of academia and publishing.¹ ¹At least this isn't one of those stoires where years pass and then the paper is rejected. I haven't had that happen, and I haven't done this as a reviewer. But it does happen too.

I don't think I kept enough records to track my average time from submission to publication. Perhaps I should keep better track and report this on my Research page too.

Examining Excess in the Schmidt Bound

David Lowry-Duda — Tue, 13 Feb 2024 03:14:15 +0000

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Bounds on partial sums from functional equations

David Lowry-Duda — Tue, 16 Jan 2024 03:14:15 +0000

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Paper: Towards a Classification of Isolated $j$-invariants

David Lowry-Duda — Wed, 15 Nov 2023 03:14:15 +0000

I'm happy to announce that a new paper, "Towards a classification of isolated $j$-invariants", now appears on the arxiv. This was done with my collaborators Abbey Bourdon, Sachi Hashimoto, Timo Keller, Zev Klagsbrun, Travis Morrison, Filip Najman, and Himanshu Shukla.

There are many collaborators because this was borne out of a workshop at CIRM from earlier this year, and we all attacked this problem together. This is the first time I have collaborated with any of these collaborators (though several of us are now involved in another project that will eventually appear).

The modular curve $X_1(N)$ is moduli space and an algebraic curve (defined over $\mathbb{Q}$ for us) whose points parametrize elliptic curves with a point of order $N$. We study isolated points, which are morally points on $X_1(N)$ that don't come from infinite families.

Perhaps the simplest form of infinite families comes come from a rational map $f: X_1(N) \longrightarrow \mathbb{P}^1$ of degree $d$. By Hilbert's irreducibility theorem, $f^{-1}(\mathbb{P}^1(\mathbb{Q}))$ contains infinitely many closed points of degree $d$.

Similarly, to any closed point $x$ of degree $d$ one can associate the rational divisor $P_1 + \cdots + P_d$, where $P_j$ are the points in the Galois orbit associated to $x$. This gives a natural map $\Phi_d: X_1(N)^{(d)} \longrightarrow \mathrm{Jac}(X_1(N))$. If $\Phi_d(x) = \Phi_d(y)$ for some point $y$, one can show that there exists a nonconstant function $f : X_1(N) \longrightarrow \mathbb{P}^1$ of degree $d$ again. Thus positive rank abelian subvarieties of the Jacobian also give infinite families of points.

Roughly, we say that a closed point $x$ is isolated if it doesn't come from either of the two constructions ($\mathbb{P}^1$, which we call $\mathbb{P}^1$ isolated — and abelian subvariety, which we call AV-isolated) above. Further, a closed point $x$ of degree $d$ is called sporadic if there are only finitely many closed points of degree at most $d$.

If $x \in X_1(N)$ is an isolated point, we say $j(x) \in X_1(1) \cong \mathbb{P}^1$ is an isolated $j$-invariant. In this paper, we seek to answer a question of Bourdon, Ejder, Liu, Odumodo, and Viray.

Question: Can one explicitly identify the (likely finite) set of isolated $j$-invariants in $\mathbb{Q}$?

Our main result is decision algorithm. Given a $j$-invariant, our algorithm produces a finite list of potential (level, degree) pairs such that one only needs to verify that degree $\mathrm{degree}$ points on $X_1(\mathrm{level})$ are not isolated.

Stated differently, our algorithm has one-sided error. It either reports that an element is not isolated, or it reports that it might be isolated and gives a list of places containing the data where isolated points must come from.

In principle, this sounds like it might be insufficient. But we ran our algorithm on every elliptic curve in the LMFDB and the outputs of our algorithm are always the empty set — except for $4$ exceptions where we know the $j$-invariants are isolated.

Concretely, we know that for any non-CM elliptic curve over $\mathbb{Q}$ with an isolated $j(E) \in \mathbb{Q}$ and with

conductor up to $500000$,
or with conductor that is $7$-smooth,
or of prime conductor $p < 3 \cdot 10^8$,

then $j(E) \in \{ -140625/8, -9317, 351/4, -162677523113838677 \}$. These latter correspond to $\mathbb{P}^1$ isolated points on $X_1(21), X_1(37), X_1(28)$, and $X_1(37)$ (respectively).¹ ¹An appendix to our paper by Derickx and Mark van Hoeij shows that the last $j$-invariant is actually isolated, not merely sporadic.

More generally, we are led to conjecture that these (and the CM $j$-invariants) are all of the isolated points on $X_1(N)$.

Broadly, our algorithm works by first considering the Galois image of elliptic curves (thanks to the code of David Zywina and the efforts of David Roe and others for making this broadly accessible). An earlier result of Bourdon and her collaborators² ²Abbey proposed this problem at the workshop based on the observation that her result might make things tenable. She was right!

allows one to radically narrow the focus of the Galois image to a minimal set of points of interest. We do this narrowing. We also show that no elliptic curve with adelic image of genus $0$ gives an isolated point, which allows us to ignore many potential leafs of computation.

The details are interesting and we try to be as explicit as possible. The code for this project is also available, and can be found on my github at github.com/davidlowryduda/isolated_points.

Paper: Congruent number triangles with the same hypotenuse

David Lowry-Duda — Tue, 14 Nov 2023 03:14:15 +0000

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Bringing back the blogroll

David Lowry-Duda — Mon, 13 Nov 2023 03:14:15 +0000

It used to be very common for sites to have a page that said "blogroll" at the top and it linked to a bunch of blogs and sites that the author liked. People used to find other sites like this, and these sorts of links powered early search engines.

I stopped having a blogroll after I switched away from Wordpress and didn't think too much about it.

But things changed. RSS worked¹ ¹RIP Google Reader, 2013. It died so that Google+ could... also die a quiet death. and google search/Twitter were semi-reliable ways to find new things.

Now Twitter is dead, email newsletters are awful² ²though almost all of them were almost always awful. The medium is inferior to RSS in almost every way except a very important one: it's easier to monetize. , and Google search has lost its utility to the combination of earnest actors paying top dollar to appear at the top and SEO optimzer spam flooding the web.³ ³And Goodhart's Law strikes again!

The web is full of walled gardens, hiding the beautiful things within behind large, bland, stone walls.

The fundamental problem of internet content discovery is hard again! It's now rather hard to find places with consistently good content. I love longform media. It requires thought and intention. And it requires time.

So I'm bringing back my blogroll (and more generally, a list of sites, links, resources, and books that I find interesting). It is at the top of every page. Check it out!

If you have a site, bring out your blogroll. Help the small web flourish.

MixedMath - explorations in math and programing

Another year, another TeXLive reinstallation

Remove the previous installation

Acquire and run the new installer

Remove texlive installer

Install utility packages

Install specific packages I use

FLT3 at LftCM2024

Quanta on Murmurations

Not quite 3 and a half years

Publishing Record

Examining Excess in the Schmidt Bound

Bounds on partial sums from functional equations

Paper: Towards a Classification of Isolated $j$-invariants

Paper: Congruent number triangles with the same hypotenuse

Bringing back the blogroll

Blogroll (and interesting links)