Sagetex: Implicit disconnected plots with pgfplots

ImplicitPlotDisconnectedIn an earlier post I put together some code to illustrate how sagetex could be used to create an implicit plot, provided the plot was connected. If the graph is disconnected, such as a hyperbola, then the code would only plot 1 of the pieces. I've modified the code to handle disconnected implicit plots, such as the screenshot above. The template is posted on the Plotting with Sagetex page.

LaTeX emphasis: soul package

SoulPackageIf you took the time to explore the website in point 3 of the last post, you might have come across the soul package. The soul package gives you even more ways to emphasize text. You can:

  1. increase the spacing between the letters
  2. small/large capitals
  3. highlight text
  4. strike through text
  5. underline text

The capabilities are illustrated in the screen shot above. I've added this information to the page on emphasizing text, along with a template/example to illustrate the basics.

Odds and Ends: April 5, 2014

1. I've added explanations on the probability of 4 of a kind and a full house. You can download the files from the Handouts page.

2. April is Math Awareness Month. Head on over to the Math Aware website and check out the Activity Calendar. With each day that passes a video and activity is revealed. As the website says, "Each page also includes activities for engaging with the underlying mathematical ideas at a variety of levels, with challenge questions, written explanations, and references.".

3. This website shows off the Aurial handwriting font. It looks great and, if you take the time to look around you'll notice some nice \LaTeX templates here.

Updates: April 1, 2014

There's a new website, PGFPlots.net, that showcases the some elegant pgfplots examples. If you're a fan of TeXample.net (and who isn't?!?) then you'll like love this site, too. Both sides are run by Stefan Kottwitz and PGFPlots.net already has a good selection of plots. The only drawback is that a bunch of the examples don't work when you open them online because you need something else (e.g. gnuplot/luatex to get them to work. The Mandelbrot Set example was something I wanted to see running but if you click on "Open in WriteLaTeX" it won't run because LuaTeX is needed. Too bad sage isn't used for computations via Sagemath Cloud.

I've added a link to PGFPlots.net on the sidebar. And while I was Tikz/pgfplots was on my mind, I added to the LaTeX page. There are now links to TikZ/pgfplots documentation, pgfplots manual, and a Minimal Introduction to TikZ. All three additions are long overdue as I migrated to Tikz/pgfplots some time back thanks to Stefan Kottwitz, Alain Matthes (Altermundus website), and the ability to combine sage with tikz and pgfplots.

Rematch!

With one round to go, Viswanathan Anand has won the right to challenge Magnus Carlsen for the next world chess championship in November! Anand, with 8 points, is 1.5 points ahead of Karjakin, Kramnik, Mamedyarov, Andreikin and Aronian. Anand vaults up more than 15 points on the Live Chess Ratings to claim 3rd place behind Carlsen and Aronian.

Needless to say, this wasn't supposed to happen. After a lackluster performance for the last 2+ years and a poor showing in the last world chess championship, it was clear Vishy Anand's play had declined. And is that really surprising? Anand has had a remarkably long career. Age catches up to everyone, even to one of the greatest natural chess talents in the history of the game.

Fresh off his stinging defeat by Carlsen at the world chess championship (0 wins, 3 losses), it seemed all but certain there would be a new challenger for the title. Aronian and Kramnik were logical favorites but they cracked under the rigors of competitive play. In fact, it seemed as if only Anand played well while the rest of the field played poorly/erratically. I consider this the most telling statistic of the tournament: After 13 round of play, only Anand has a plus score. Karjakin, Kramnik, Mamedyarov, Andreikin and Aronian had even scores and Mamedyarov, Svidler, and Topolov had minus scores. If you followed the games, there were enough blunders to go around: Kramnik blundered on move 7 in round 9 followed by a blunder in round 10 that eliminated him completely from contention.

Carlsen, with an enormous rating advantage, the title, and the jitters from playing in his first world championship out of the way has to be the comfortable favorite for the upcoming match, but as we've seen from this Candidates tournament, anything is possible.

Sagetex: implicit plots with pgfplots

ImplicitPlot2The utility of the sagetex package for plotting is on display with another proof of concept: implicit plots. I've added two templates to the Plotting with Sagetex page. Getting the list of points is more complicated with graphs which aren't functions and the code for the graph above works because the graph is in one piece. To make the graph look better, it's important to plot small points (around 0.17pt) because otherwise you'll see the points as "beads" connected by line segments. You can download the templates here.

Sagetex: Combinatorics between sets

CombProb4I've added another problem type to the (slowly) growing collection of randomized test problems with solutions. It consists of two problems of the form "how many functions are there from an m element set to an n element set?" and "how many of [those] functions are one-to-one?". It's problem type 4 on Sagetex: Combinatorics and Probability page; you can download the question and answer and insert into your randomized test with answer key.