Installing and using Sage just got even easier.

+Sage Mathematical Software System just moved to git!

This is awesome news for a variety of reasons. First of all it's great for development (you can take a look at the github repo here: https://github.com/sagemath/sage. There's a good talk about the git workflow for development by +Volker Braun here: http://www.youtube.com/watch?v=0tejiKN5ctY.

The other great reason why this is awesome is that it just got really easy to use and install Sage.

Here's a short video demonstrating everything I've done below:

If you're familiar with git then you know this but if you're not then you can simply open up a terminal on anything *nix (linux/Mac OS) and type the following:

$ cd ~
$ git clone git://github.com/sagemath/sage.git 

This basically goes to the git repository on github and clones it to a folder called sage in your home directory (if you don't have git installed you'll have to do that first).

Once you've done that you need to 'make' sage:

$ cd ~/sage
$ make

This will take a little while (it goes and gets most of what you need so it's hard to say how long as it depends on your machine) but after that you'll have Sage on your machine. If you're still in the ~/sage directory you can simply type ./sage to start sage.

You'll want to add sage to your path so that you can use it from any directory. In this video I did this by using a bit of a trick but here's I'll do something simpler: create a symbolic link to the sage file in ~/sage directory and place that symbolic link in your path (in /usr/bin/local). To do that type this:

$ ln -s ~/sage/sage /usr/local/bin/sage

Now you can type sage anywhere and you'll get sage up and running.

What's really great about all this is that if and when updates/development happens you can just git pull to get all up to date changes. Based on the +Sage Mathematical Software System post on G+: here: it looks like you can already play around with the develop branch...

Awesome.

Of course if you want the easiest way to use Sage then simply grab an account on +The Sagemath Cloud. I gave a talk last week at the Cardiff Django/Python user group about it and  +William Stein was kind enough to drop in and take some questions: http://www.youtube.com/watch?v=OYVLoTL4xt8 (sound quality isn't always great because I move around a fair bit...)

Setting up bup as my backup system, making it act like a timemachine.

This is one of those: 'writing this post to make sure I remember how I've done this'.

+William Stein posted about bup which he is using to backup +The Sagemath Cloud (if you haven't seen that before make sure you go check it out, here's a video in which I describe it: http://goo.gl/5DtYQq).

bup is a piece of backup software based on git. Here's a talk by +Zoran Zaric explaining it:

The documentation isn't too great for bup, this is the blog post I found the most helpful on it: http://kacper.blog.redpill-linpro.com/archives/tag/bup

the ubuntu man pages are also pretty helpful.

Anyway, here's how I setup bup to work like apple's time machine.

Once bup is installed (super easy following readme instruction on Mac OSX and ubuntu). I run:

$ bup -d pathtochosenharddrive init

By default bup uses the ~/.bup directory for everthing. Using the -d flag tells bup to run whatever command (in the above instance: init)  in a chosen hard drive. If you're happy to backup to your ~ then ignore all instances of -d pathtochosenharddrive in the following. (Note you can also change $BUP_DIR to take care of this, and you'll also need to know the path to your given hard drive).

This initialises a git repository (you only need to do this once really).

I put the following in a script (backup.sh):

bup -d pathtochosenharddrive index -ux /directorytobackup
bup -d pathtochosenharddrive save -n backupname /directorytobackup

The first line indexes the files (the -ux flags are something to do with recursively going through the files: type man bup index to read more). The second line checks the index and then saves all files as required (giving them a name).

To setup this backup script to run every hour I write the following to a txt file (crontab.txt):

0 */1 * * * globalpathtobackupscript/backup.sh

To add this to the cron jobs:

$ crontab crontab.txt

If you type:

$ crontab -l

You should see the the contents of the crontab.txt file now added to the scheduled jobs. The first 0 implies that it'll run at the 0th minute, the */1 means every one hour (so you can easily change this), the other * mean 'every', day, month and day of the week.

The first time you run this it should take a fair while (especially if you're backing up your whole ~) but afterwards it shouldn't take too long at all.

To check what bup has done, run:

$ bup -d pathtochosenharddrive ls

That should return:

backupname/

and/or any other names of backups. If you want to see the actual backup snapshots:

$ bup -d pathtochosenharddrive ls backupname

which will return a list of timestamped snapshots.

This has been working pretty seamlessly for a week for me now and I'm probably going to set it up on my work Mac instead of timemachine.

Explaining floats in LaTeX

A PhD students recently had a hard time placing floats (figures and table environments) where they wanted in their LaTeX document. I also have just finished teaching LaTeX to all our first years here at +Cardiff University so I thought I'd brush up on my own understanding of these things to make sure that I was explaining things correctly.

I stumbled on the following stackoverflow TeX.Stackexchange (thanks to +Torbjørn Taskjelle for pointing out this and other mistakes) answer: http://goo.gl/A9iJnP

Here's a +writeLaTeX document working through some examples showing the various options that allow you to control floats within the default restrictions: https://www.writelatex.com/read/qkjpvqptqrwd (at the moment that's a read only link but I've suggested it as a template to the writeLaTeX team in case it's useful to anyone). EDIT: Here's the link to the template: http://goo.gl/UmLFr3

I think that reading through the code (which explains how I understand these things to work) could prove helpful when trying to explain how the various options work. Once that's done I'd suggest playing with the following options on the rabbit figure:

- [t]
- [!t]
- [p]
- [!h]
- [!htbp]

and others to see the effects.

If anything I've written in that document (https://www.writelatex.com/read/qkjpvqptqrwd) isn't quite right I'd appreciate being told :)

How to handle float error for plots near discontinuities in Sage

Last week I read this blog post by +Patrick Honner. In the post +Patrick Honner plots a graph of a function with a removable discontinuity on Desmos and when zooming in enough he got some errors.

I was waiting around to start this (ridiculously fun) Hangout on Air with a bunch of mathematicians hosted by +Amy Robinson of +Science on Google+:

While waiting I rushed to write this blog post claiming that if you did the same thing with +Sage Mathematical Software System you did not get any errors. It was quickly pointed out to me on twitter and in the comments that I just had not zoomed in enough.

I edited the blog post to first of all change the title (it was originally 'When Sage doesn't fail' but now reads 'When Sage also fails') and also to include some code that shows that the exact same error appears.

On G+, +Robert Jacobson (who's the owner of the Mathematics community which you should check out if you haven't already) pointed out that you could surely use Sage's exact number fields to avoid this error.

He put together some code and shared it with me on +The Sagemath Cloud that does exactly this. Here's a slight tweak of the code Robert wrote (hopefully you haven't changed your mind and still don't mind if I blog this Robert!):

f(x) = (x + 2) / (x ^ 2 + 3 * x + 2) # Define the function
discontinuity = -1  # The above function has two discontinuities, this one I don't want to plot
hole = -2  # The hole described by Patrick Honner

def make_list_for_plot(f, use_floats=False, zoom_level=10^7, points=1001):
    count = 0  # Adding this to count how many tries fail
    z = zoom_level
    xmin = hole - 10/z # Setting lower bound for plot
    xmax = min(hole + 10/z, discontinuity - 1/10) # Setting upper bound for plot only up until the second (messy) discontinuity
    x_vals = srange(start=xmin, end=xmax, step=(xmax-xmin)/(points-1), universe=QQ, check=True, include_endpoint=True)

    # If we are using floating point arithmetic, cast all QQ numbers to floating point numbers using the n() function.
    if use_floats:
        x_vals = map(n, x_vals)

    lst = []
    for x in x_vals:
        if x != hole and x != discontinuity:  # Robert originally had a try/except statement here to pick up ANY discontinuities. This is not as good but I thought was a bit fairer...
            y = f(x)
            lst.append((x, y))

    return lst

The code above makes sure we stay away from the discontinuity but also allows us to swap over to floating point arithmetic to see the effect. The following plots the functions using exact arithmetic:

exact_arithmetic = make_list_for_plot(f)

p = list_plot(exact_arithmetic, plotjoined=True)  # Plot f
p += point([hole, -1], color='red', size=30)  # Add a point
show(p)

We see the plot here (with no errors):

To call the plots with floating point arithmetic:

float_arithmetic = make_list_for_plot(f, use_floats=True)

p = list_plot(float_arithmetic, plotjoined=True)  # Plot f
p += point([hole, -1], color='red', size=30)  # Add a point
show(p)

We see that we now get the numerical error:

Just to confirm here is the same two plots with an even higher zoom:

To change the zoom, try out the code in the sage cell linked here: simply change the zoom_level which was set to $10^12$ for the last two plots.

(Going any higher than $10^14$ seems to bring in another error that does not get picked up by my if statement in my function definition: Robert originally had a try except method but I thought that in a way this was a 'fairer' way of doing things. Ultimately though it's very possible and easy to get an error-less plot.)