Equation editor for iPad - MathBot

Updated note:  The problem on launch with MathBot has now been fixed and the app is working again.  Among other changes, the new version allows landscape mode and an auto complete feature (last updated Feb. 23, 2012)

Pages is a nice word processor and page layout program, but one major omission is an equation editor. On the Mac scientists and mathematicians usually use either MathType, or write the entire document in LaTeX using TeXShop. Unfortunately MathType is not available for the iPad.

In this column I will show you how to place high quality mathematical equations into Pages (or Keynote) on the iPad using the MathBot app. While MathBot is free, you will need to purchase the $4.99 in-app upgrade to remove the watermark and to activate all necessary export options.

So what exactly is MathBot? It takes expressions in LaTeX, renders them into beautifully typeset equations, and then allows export as high quality scaleable PNG images into Pages, Keynote or indeed any other app that accepts images. This works best on the iPad, although MathBot will work on any iPad, iPhone or iPod Touch running iOS 4.0 or higher. I have only tried it on an iPad 2 for this review.  This figure shows a MathBot generated equation pasted into a Pages document on an iPad.

LaTeX is a math typesetting markup language developed by Lesley Lampert in the 1980's. It grew out of the TeX typesetting markup system developed by Donald E. Knuth in 1977.  LaTeX is the preferred way to create high quality math rich materials and many journals in the sciences require authors to provide LaTeX copies of papers.  A lengthy introduction to LaTeX is available here.  MathBot is not a full LaTeX typesetting system but only handles equations.

LaTeX is a markup language. For example "x^2" is how we write superscripts. Greek letters and special symbols are written with the special lead character \ followed by the name e.g. "\alpha". Curly brackets are nonprinting characters used to keep expressions together e.g. "{x+3}\over{2\pi}". Those used to WYSIWYG equation editors will at first find LaTeX slow and awkward, but it does become more natural with use, and it produces elegant output. There are various online introductions to LaTeX and listings of commands.



MathBot makes the writing of LaTeX somewhat easier through extra keyboard symbols for the most often used characters and expressions, grouped in logical ways. I show below a screen capture for MathBot. The top portion is the rendered equation (rendering is done automatically and it will update as you add to the equation markup expression).The middle portion is the corresponding LaTeX markup code. You can directly enter code from the normal iPad keyboard, but it is much easier to use the special extra line of characters which are the top line in the bottom panel. Just below that line is a series of buttons for different categories. For example one has all the Greek symbols.

You can edit the markup contents of the middle panel in all the normal ways such as copy and paste. If you hold down over a letter it will bring up the magnified view to allow precise positioning. MathBot comes with several example equations. Those learning LaTeX will find it helpful to use these as starting points.

To enter a new equation you first press the bookmark symbol at the top left, and then select Add New Equation at the bottom. You can attach name labels to each equation, and frequently used equations can be stored.

When your equation is ready for export to Pages (or other applications) you select the output button near the top right, and then Export Equation. It will present several options, including email and placing an image in your photo collection, but I prefer to use the pasteboard copy and paste process. Once you have pasted it in Pages (or other applications) you can then scale the equation (by default it will come out large and then you scale it down). I have found that the quality is excellent even after reasonable scaling. One slight irritation in the copy and paste process is that MathBot only works in portrait mode, so if your other application prefers landscape, you are constantly turning your iPad around.

Both Pages and Keynote support applying styles to the pasted equations, and this can be used to in one click provide nice features like boxes of various types around the inserted equations, or as shown below background shading.

MathBot is created by a small software company wiApps, based in Germany.  They have a Mac app as well as several iOS apps.  For those who want a complete LaTeX environment (for writing LaTeX entire documents and not just equations), they should consider TeX Touch. TeX Touch uses a unique approach of editing on the iPad, sending the code through Dropbox to your Mac where it is compiled and the pdf sent back to your Mac via Dropbox.  The limitation on executable code on iOS devices require such an approach. I may review TeX Touch in some future posting.

I hope that at some point Pages will include a built-in equation editor.  Until then, your best option is MathBot.  Those who already know LaTeX will find it an easy transition, and will appreciate that they can paste in, or copy out, LaTeX code for equations. I found that the scaling of equations in Pages maintained high quality equations after appropriate scaling.  There will be a learning curve for those who have not used LaTeX before, and I recommend starting with one of the many internet guides on LaTeX. The line of LaTeX symbols on the extended keyboard will ease the learning curve somewhat. I wish that the app supported landscape mode, as I like to work on Pages exclusively in landscape using the stand on my iPad case, and it is awkward having to turn the iPad as you go between modes as you develop and paste equations. My overall rating of MathBot is a 7 (out of 10).

Wolfram Alpha

The Wolfram Alpha iPhone/iPad app is a convenient way to access mathematical and scientific resources from Wolfram on your your iPad, iPhone or iPod Touch. While similar resources can be accessed directly from the Wolfram Alpha website, the app offers an easier interface, and now it is very reasonably priced at just $1.99.  Note that although it works on both iPad and iPhone, there are two different apps so make sure you purchase the right one (for this review I have only tried it on an iPad).  They also have a copy for Android based tablets.

The Wolfram Alpha resource, called a knowledge engine, is somewhat unconventional, and I found the coverage of areas of science uneven, but this is a real gem for any students or professionals in mathematics and science.  It is nice in that you simply can type what you want in a way that is similar to everyday life - e.g. typing "integrate cos x dx from x=0 to pi" will then produce the symbolic form for the integral, the answer (0 in this case) and a graph with the integral area shaded.

Even if you use only the mathematical features, it is well worth the investment.  For example, if you want to perform symbolic algebraic derivatives or integrals, it is simply a matter of entering the input function.  There are also tools for numerically computing functions and definite integrals.  It comes with samples, and most of the time you can go to one of these, and then change the function to meet your needs.  A particularly nice feature is there is a link to show the intermediate steps in a solution that can be turned on or off.   Functions are plotted automatically as part of the solution, and alternative forms are often displayed.  The matrix operations are nice - provide the entries for a matrix, and it will show you the determinant, trace, eigenvectors and eigenvalues, for example.

The Statistics and Data Analysis has a number of very useful features, including the possibility of doing regression analysis with linear, cubic and exponential fits. It also does various distributions including norma and Poisson.  Those with a more elementary interest in the topic of probability and statistics may want to play with entering different numbers of coin tosses, and check out the probability of various answers (e.g. there is apparently a 14% chance of exactly equal numbers of heads and tails if you do 32 coin flips).

I explored the engineering functions a little bit.  One topic that I am interested in is the design of digital filters, and it allows you to design Chebyshev type 2 filters, for example.  It comes up with a canned example, but if you click on change input values it allows you to specify the gain, cut-ff attenuation, stopband attenuation, and frequency range, and it will both compute the filter and show a pole-zero plot as well as the response function.  Very nice!

Units and measures will be helpful to most users.  The open format allows you to type in something like "25 acres in hectares" and it gives the result, as well as additional conversions.  It also will display comparisons (e.g. in this case it told me that 25 acres is about 1.8 times the area of the base of the Great Pyramid in Gaza).

To see how much more there is beyond the categories given, I tried a topic from general relativity, typing in gravitational time dilation.  What it came up with was the closest match of time dilation, which was simply the special relativity time dilation.  Therefore those not familiar with an area have to be careful that it is giving you what you want.  I think the tool is best used as a way to rapidly perform computations, or to independently check a computation.  It is useful, for the topics covered, in an instructional mode using the show steps feature.

Now at $1.99 (initially it was many times this cost) it is hard to argue that any scientist or engineer should not purchase this app! I think many others, including those with an armchair interest in science, will find it a fascinating way to explore topics from a wide range of topics.  In that connection the sections Interesting Modern Results and Famous Paradoxes are good starting places.  For example, Famous Paradoxes in physics include the twin paradox in special relativity, the Boltzmann paradox and the EPR paradox in quantum mechanics.

It will also be useful beyond science of course.  I typed the name of my small town (Sackville) and it gave the current population, a map, distances to nearby towns and cities, as well as the current weather, coordinates, etc. The Word Properties section allows you to do everything from finding words that rhyme with another word, to finding synonyms of words (and a lot more).  It even allows you to type Scrabble xylophone, for example, and it confirms that it is a word, and will give you the scrabble score for the word.

I give it a rating of 9.0 (out of 10). It is excellent value for the money, is amazing particularly for mathematical computations, and is a broad and useful resource.  It is the somewhat uneven coverage that keeps me from giving it a perfect 10.