The Pari Package On Linux
The pari package (named after the French capital Paris, where the idea for this package originated) is a computer algebra system designed to work under several Unix derivatives, and of course Linux is one of them. It is well-known to a small group of mathematicians, and most probably useful for anyone who wants to perform symbolic or numerical computations or who just likes to have a powerful calculator. Its features include arbitrary-precision numerical computation, symbolic calculations, matrix/vector operations, plotting facilities (text mode or X11), and tons of number theoretic functions. Pari provides an interactive interface (the GP calculator) as well as its own programming facilities and a library for using the kernel within its own C/C++ programs. An emacs lisp file (pari.el) for using the GP calculator within an emacs buffer is included in the package. Pari is not so extensive as the commercial packages Maple, Mathematica, or Axiom are, but its major advantage is its speed. Pari claims to be 5 to 100 times faster than the commercial counterparts. I personally like its very economical use of memory. It performs really well on my “low end” 386/40 with 8 meg RAM.
Pari is available by anonymous ftp from megrez.math.u-bordeaux.fr as pari-1.39a.tar.gz, together with examples, benchmarks, and a manual (160 pgs.) which includes a function reference and a tutorial. The authors are C. Batut, D. Bernardi, H. Cohen, and M. Olivier, who are well-known number-theorists. You can contact them at firstname.lastname@example.org.
On megrez.math.u-bordeaux.fr, you will find precompiled Linux binaries (gplinux.tar.gz) as well as the source package pari-1.39a.tar.gz. Because it contains the documentation and the examples, I recommend getting the source package even if you get the binaries. pari-1.39a.tar.gz unpacks into three subdirectories: doc, examples, and src. If you have gcc installed, recompiling is quite straightforward. After running configure i386 and performing a minor hack in the Makefile (read the src/INSTALL file), you are prepared to run make. You can optionally compile the gp calculator with readline support, meaning you have a command history, programmable keystrokes, and other features as within GNU bash. The source to bash also contains the necessary readline library.
It's easy to install the pari library and the gp calculator by issuing make install as root. Installing emacs support is a little bit tricky and requires you to edit some pathnames and constants defined in pari.el to match your configuration. Once pari.el is installed, you can start gp by issuing M-x gp and get an overview via M-x describe-mode, like most emacs modes.
After compiling and installing it successfully, let's start gp and try a few expressions at the “?” prompt:
? 2*3 %1 = 6 ? 4/3*5/14 %2 = 10/21 ? 4.0/3*5/14 %3 = 0.4761904761904761904761904761
As you can see, pari tries to use exact integer and rational numbers as long as possible. As soon as you introduce one real (floating point) number, the result will be real. You may request (almost) arbitrary precision:
? \precision=50 precision = 50 significant digits ? pi %4 = 3.1415926535897932384626433832795028841971693993751
You may enter expressions with indeterminates
? (x+2)*(x^2+1) %5 = x^3 + 2*x^2 + x + 2
? x=2 %6 = 2
and evaluate, e.g., our (x+2)*(x2+1)
? eval(%5) %7 = 20
or compute some factorial
? 1000! %8 = 4023872600770937735437024339230039857193748642107146 3254379991042993851239862902059204420848696940480047 998861019719605863166687299480855890132382966994459...
Of pari's basic types, until now you have seen integer, rational, and real numbers and rational expressions with indeterminates (polynomials/rational functions). Integers can store values with up to 315,623 decimal digits. The precision of reals is controlled by the
\precision=n setting, where n is restricted to be not greater than 315623. Further, you can work with complex numbers, power series, row or column vectors, matrices, and more. You can combine these types (i.e. vectors of matrices); pari handles these using a recursive technique.
|Making Linux and Android Get Along (It's Not as Hard as It Sounds)||May 16, 2013|
|Drupal Is a Framework: Why Everyone Needs to Understand This||May 15, 2013|
|Home, My Backup Data Center||May 13, 2013|
|Non-Linux FOSS: Seashore||May 10, 2013|
|Trying to Tame the Tablet||May 08, 2013|
|Dart: a New Web Programming Experience||May 07, 2013|
- RSS Feeds
- Making Linux and Android Get Along (It's Not as Hard as It Sounds)
- New Products
- Drupal Is a Framework: Why Everyone Needs to Understand This
- A Topic for Discussion - Open Source Feature-Richness?
- Home, My Backup Data Center
- Validate an E-Mail Address with PHP, the Right Way
- New Products
- Trying to Tame the Tablet
- Developer Poll
2 min 39 sec ago
- not living upto the mobile revolution
2 hours 53 min ago
- Deceptive Advertising and
3 hours 29 min ago
- Let\'s declare that you have
3 hours 30 min ago
- Alterations in Contest Due
3 hours 31 min ago
- At a numbers mindset, your
3 hours 32 min ago
- Do not get Just Almost any
3 hours 36 min ago
- A fantastic rule-of-thumb to
3 hours 37 min ago
- Keren mastah..
4 hours 35 min ago
- mini tablet compare
5 hours 54 min ago
Enter to Win an Adafruit Prototyping Pi Plate Kit for Raspberry Pi
It's Raspberry Pi month at Linux Journal. Each week in May, Adafruit will be giving away a Pi-related prize to a lucky, randomly drawn LJ reader. Winners will be announced weekly.
Fill out the fields below to enter to win this week's prize-- a Prototyping Pi Plate Kit for Raspberry Pi.
Congratulations to our winners so far:
- 5-8-13, Pi Starter Pack: Jack Davis
- 5-15-13, Pi Model B 512MB RAM: Patrick Dunn
- Next winner announced on 5-21-13!
Free Webinar: Linux Backup and Recovery
Most companies incorporate backup procedures for critical data, which can be restored quickly if a loss occurs. However, fewer companies are prepared for catastrophic system failures, in which they lose all data, the entire operating system, applications, settings, patches and more, reducing their system(s) to “bare metal.” After all, before data can be restored to a system, there must be a system to restore it to.
In this one hour webinar, learn how to enhance your existing backup strategies for better disaster recovery preparedness using Storix System Backup Administrator (SBAdmin), a highly flexible bare-metal recovery solution for UNIX and Linux systems.