# Tag: LaTeX

In the early days of math-blogging, one was happy to get LaTeXRender working. Some years later, the majority of math-blogs were using the, more user-friendly, wp-latex plugin to turn LaTeX-code into png-images. Today, everyone uses MathJax which works with modern CSS and web fonts instead of equation images, so equations scale with surrounding text at all zoom levels.

However, MathJax has one downside : it doesn’t parse in ePub-readers. Peter Krautzberger wrote a post Epub and mathematics in which he suggested two methods to turn MathJax into ePub, but after dozens of experiments I still fail to reproduce these.

No doubt, someone will soon come up with a working alternative, but for the impatient here’s a quick but dirty method to turn your MathJax powered wordpress post into ePub :

## the tools

• download and install the ePub export plugin. It automatically creates an ePub file when a post or page is published or updated. The ePubs are stored in the uploads directory (to be found in the wp-contents directory).
• download and install the wp-latex plugin. MathJax uses the normal \$tex-delimeters whereas wp-latex requires \$latex, so this plugin doesn’t interfere with the default use of MathJax.
• download the wp2latex python script. It converts a standard LaTeX file into a format that is ready to be copied into WordPress.

## the routine

• Edit the post you want to convert to ePub. Copy the contents of the post box to a file say post1.tex and save this in the same directory containing the latex2wp.py script.
• In Terminal go to that directory and type the command ‘python latex2wp.py post1.tex’. It will produce a new file post1 in the same directory.
• Copy the contents of post1 into the post box of your WordPress-post and press the update button. This time the TeX-commands in your post will be rendered using wp-latex and the ePub export-plugin will have created an ePub-version of it.
• Locate this newly created ePub file in the relevant wp-contents/uploads/ folder (file has a number.epub name) and, if wanted, change its name into something easier to recognize and copy it somewhere outside the uploads directory. This will be your desired ePub-version of the post.
• Replace the contents of the post box of your WordPress-post with the contents of the post1.tex file and hit the ‘Update’ button, to restore your original post (powered by MathJax).
• Email your ePub-file to your iPad and open it with iBooks. Not quite as nice as MathJax-parsed TeX but a lot better than reading unparsed TeX-commands.

Perhaps, the tips and tricks I did receive to turn a selection of wordpress-posts into a proper ePub-file may be of use to others, so I will describe the procedure here in some detail.

It makes a difference whether or not some of the posts contain TeX. This time, I’ll sketch the process for non-LaTeX posts and hence we will turn the Bourbaki-code posts into ePub-format to read on your iPad, rather than merely into a pdf-file as last time. Next time, I’ll add some tricks to repeat this when some of your posts do contain LaTeX.

1. Install the ePub export plugin

Get the epub export wordpress plugin, install and activate it in the usual way. ePub Export automatically creates an ePub file when a post or page is published or updated. The ePubs are stored in the uploads directory. For later use, remember that your uploads directories are located under BLOGHOME/wp-content/uploads.

2. Update the posts you want to include

Decide which posts you want to include in your eBook, edit them (or not) and press for each one of them the update-button. This will populate today’s uploads-directory with a number of epub-files. Transfer them all, for example using Transmit, to a directory on your home-computer, named say MyFirstEBook.

3. Unpack the epub-files

The crucial fact to remember about epub-files is that they are really zipped archives containing xhtml-, css- and other files and directories. As we want to edit some of those, we first have to unpack the directories. So, change the .epub extensions to .zip and double-click on them to create the directories.

The crucial files in each directory are preface.xhtml (containing title author and blog-name), text.html (containing the blog-post) and the images-directory (containing copies of all the images used in the post).

4. Rename the directories user-friendly

As all the posts will be chapters in our eBook in some specific order, we will rename the numbers of the directories to something more user-friendly such as shortened blog-titles. To do this, double-click in each of the directories on the preface.xhtml file. This will open Safari and will show the title of the blog-post. Use it to rename that directory. For convenience let us call the directory corresponding to the first chapter in our book MasterDirectory

5. Move all images to the master directory

For each of the other chapter-directories, drag all the files contained in the images-subdirectory to MasterDirectory/images.

6. Edit the MasterDirectory/text.xhtml file

Because we will have to open and copy-paste all the text.xhtml files of the different directories, it is perhaps best to rename momentarily the MasterDirectory/text.xhtml file to something like master.xhtml.

Now, open this file with a text-processor such as TextWrangler. Edit it to remove unwanted html-code (such as links to other posts at the start if you are using the series-plugin, or previous/next post links at the end). Also add the title of the blog-post between h1-tags (and if you want to include a table of contents later, give it an anchor-name).

Go to the directory of your second chapter, open that text.xhtml file and copy/paste only the post-content over to the master-xhtml file at the appropriate place. As before, add title/anchor before the copied post-content.

Repeat this procedure, in order, for all the chapters of your eBook.

Once finished, doubleclick the master.xhtml file and correct remaining errors (as it is an xhtml-file, it is rather picky about opening and closing tags) and see whether all your images are included. If you’re satisfied with it, rename the master.xhtml to text.xhtml (don’t forget this!).

7. Edit the MasterDirectory/preface.xhtml file

Open the preface.xhtml file and change the first blogpost-title to the title of your booklet, alter your name (by default it uses your wp-nick) and add a frontipiece-picture if you so desire.

8. Re-package the directory into an epub-file

This is the (only) tricky part. E-book readers require that the mimetype file is the first one in the zip document. What’s more, to be fully compliant, this file should start at a very specific point – a 30-byte offset from the beginning of the zip file (so that the mimetype text itself starts at byte 38).

Here’s how to do this on a Mac (Linux-users being the geeks they are will have given up on reading this post a while ago and as to Windows-users, yeah well …). Open Terminal.app and cd to your MasterDirectory. Now type:

zip -X MyFirstEBook.epub mimetype

Next, type:

zip -rg MyFirstEBook.epub * -x *.DS_Store

(of course you’ll have to change your book-title to whatever you want). If you want to know more about these 2 magical commands, read this post.

Get Calibre and add the MyFirstEBook.epub to Calibre by clicking on the ‘Add Books’ button.

You can preview your eBook by clicking on the ‘View’-button. Next, click the ‘Edit metadata’-button and alter the title and author entries (and whatever else you want to include) and click the OK button. Then click ‘Save to disk’.

Finally, we want to see how it looks on the iPad. Mail MyFirstEBook.epub to yourself as attachement, open it with iBooks and enjoy!

There were some great comments by Peter before this post was taken offline. So, here they are, once again.

In preparing for next year’s ‘seminar noncommutative geometry’ I’ve converted about 30 posts to LaTeX, centering loosely around the topics students have asked me to cover : noncommutative geometry, the absolute point (aka the field with one element), and their relation to the Riemann hypothesis.

The idea being to edit these posts thoroughly, add much more detail (and proofs) and also add some extra sections on Borger’s work and Witt rings (and possibly other stuff).

For those of you who prefer to (re)read these posts on paper or on a tablet rather than perusing this blog, you can now download the very first version (minimally edited) of the eBook ‘geometry and the absolute point’. All comments and suggestions are, of course, very welcome. I hope to post a more definite version by mid-september.

I’ve used the thesis-documentclass to keep the same look-and-feel of my other course-notes, but I would appreciate advice about turning LaTeX-files into ‘proper’ eBooks. I am aware of the fact that the memoir-class has an ebook option, and that one can use the geometry-package to control paper-sizes and margins.

Soon, I will be releasing a LaTeX-ed ‘eBook’ containing the Bourbaki-related posts. Later I might also try it on the games- and groups-related posts…

Penrose tilings are aperiodic tilings of the plane, made from 2 sort of tiles : kites and darts. It is well known (see for example the standard textbook tilings and patterns section 10.5) that one can describe a Penrose tiling around a given point in the plane as an infinite sequence of 0’s and 1’s, subject to the condition that no two consecutive 1’s appear in the sequence. Conversely, any such sequence is the sequence of a Penrose tiling together with a point. Moreover, if two such sequences are eventually the same (that is, they only differ in the first so many terms) then these sequences belong to two points in the same tiling,

Another remarkable feature of Penrose tilings is their local isomorphism : fix a finite region around a point in one tiling, then in any other Penrose tiling one can find a point having an isomorphic region around it. For this reason, the space of all Penrose tilings has horrible topological properties (all points lie in each others closure) and is therefore a prime test-example for the techniques of noncommutative geometry.

In his old testament, Noncommutative Geometry, Alain Connes associates to this space a $C^*$-algebra $Fib$ (because it is constructed from the Fibonacci series $F_0,F_1,F_2,…$) which is the direct limit of sums of two full matrix-algebras $S_n$, with connecting morphisms

$S_n = M_{F_n}(\mathbb{C}) \oplus M_{F_{n-1}}(\mathbb{C}) \rightarrow S_{n+1} = M_{F_{n+1}}(\mathbb{C}) \oplus M_{F_n}(\mathbb{C}) \qquad (a,b) \mapsto ( \begin{matrix} a & 0 \\ 0 & b \end{matrix}, a)$

As such $Fib$ is an AF-algebra (for approximately finite) and hence formally smooth. That is, $Fib$ would be the coordinate ring of a smooth variety in the noncommutative sense, if only $Fib$ were finitely generated. However, $Fib$ is far from finitely generated and has other undesirable properties (at least for a noncommutative algebraic geometer) such as being simple and hence in particular $Fib$ has no finite dimensional representations…

A couple of weeks ago, Paul Smith discovered a surprising connection between the noncommutative space of Penrose tilings and an affine algebra in the paper The space of Penrose tilings and the non-commutative curve with homogeneous coordinate ring $\mathbb{C} \langle x,y \rangle/(y^2)$.

Giving $x$ and $y$ degree 1, the algebra $P = \mathbb{C} \langle x,y \rangle/(y^2)$ is obviously graded and noncommutative projective algebraic geometers like to associate to such algebras their ‘proj’ which is the quotient category of the category of all graded modules in which two objects become isomorphisc iff their ‘tails’ (that is forgetting the first few homogeneous components) are isomorphic.

The first type of objects NAGers try to describe are the point modules, which correspond to graded modules in which every homogeneous component is 1-dimensional, that is, they are of the form

$\mathbb{C} e_0 \oplus \mathbb{C} e_1 \oplus \mathbb{C} e_2 \oplus \cdots \oplus \mathbb{C} e_n \oplus \mathbb{C} e_{n+1} \oplus \cdots$

with $e_i$ an element of degree $i$. The reason for this is that point-modules correspond to the points of the (usual, commutative) projective variety when the affine graded algebra is commutative.

Now, assume that a Penrose tiling has been given by a sequence of 0’s and 1’s, say $(z_0,z_1,z_2,\cdots)$, then it is easy to associate to it a graded vectorspace with action given by

$x.e_i = e_{i+1}$ and $y.e_i = z_i e_{i+1}$

Because the sequence has no two consecutive ones, it is clear that this defines a graded module for the algebra $P$ and determines a point module in $\pmb{proj}(P)$. By the equivalence relation on Penrose sequences and the tails-equivalence on graded modules it follows that two sequences define the same Penrose tiling if and only if they determine the same point module in $\pmb{proj}(P)$. Phrased differently, the noncommutative space of Penrose tilings embeds in $\pmb{proj}(P)$ as a subset of the point-modules for $P$.

The only such point-module invariant under the shift-functor is the one corresponding to the 0-sequence, that is, corresponds to the cartwheel tiling

Another nice consequence is that we can now explain the local isomorphism property of Penrose tilings geometrically as a consequence of the fact that the $Ext^1$ between any two such point-modules is non-zero, that is, these noncommutative points lie ‘infinitely close’ to each other.

This is the easy part of Paul’s paper.

The truly, truly amazing part is that he is able to recover Connes’ AF-algebra $Fib$ from $\pmb{proj}(P)$ as the algebra of global sections! More precisely, he proves that there is an equivalence of categories between $\pmb{proj}(P)$ and the category of all $Fib$-modules $\pmb{mod}(Fib)$!

In other words, the noncommutative projective scheme $\pmb{proj}(P)$ is actually isomorphic to an affine scheme and as its coordinate ring is formally smooth $\pmb{proj}(P)$ is a noncommutative smooth variety. It would be interesting to construct more such examples of interesting AF-algebras appearing as local rings of sections of proj-es of affine graded algebras.