Math softwares

Reading through Digg, I came across this real good article which talked about the various math tools available free online. It starts of with three free softwares and the readers have added many new and good ones in the comments. So thought of collecting them into a single post.
Courtesy: 3 awesome free math programs by antonio
Well Known Softwares, like the

• Mathematica - a complete package for mathematics from a small calculator to a system simulator
• Matlab - personally the only software I have used and benefited from. Similar, but is more on the engineering side rather than math
• Maple - I used this for fun. To try and visualize various plots and formulas. Can be used as we do math on a notebook.
  

Know is the fact that these are not free and for research and educational purposes they are pretty costly. So there are a list of alternatives which are free (Long Live The Open Source)

• Maxima - It is a Computer Algebra System (CAS) similar to Maple. A CAS is a system which is able to perform symbolic manipulation for the resolution of common problems.
  
• Axiom
• Sage
• Yacas
• SciLab - The free replacement for Matlab. It is a good plotting and visualization tool
  
• Octave - from the linux group
• Euler - uses yacas
• R - Yes thats it. That is the name of the software. When there is 'C' why can't there be a 'R'. Anyway, For statistical computing and analysis in the Open Source world nothing can get better than R. It is similar to the commercial S-plus
  

The above were the ones discussed by the author and the following would be the once I picked from the comments. Where there is a community there is a solution ;)

• Scipy - Scientific Programming using Python. Provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization.
• newt - this is read as (Eta Epsilon Omega Tau). This says to be a demo version used for plotting funcitons
• Geogebra - GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus.
• FreeMat - free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB from Mathworks, and IDL from Research Systems, but is Open Source
• GAP - does not seem impressive. A user comment "for real mathematics, there’s GAP, which allows you to manipulate groups, permutations, graphs, rewriting systems, Lie algebras, etc, using a Python-like language. Lots of standard algorithms for computational algebra are implemented in the standard library."
• Math Code Snippets - Codes that can be re-used. User comment "For several–specific–numerical mathematical routines. The routines posted off this page are based on good-quality code, mostly from the NETLIB repository of algorithms. Very handy (quick, easy-to-use, and free!) for when numbers are required, but a user might not want to install and start up a whole software package."
• Grace - Plotting tool. Stands for "GRaphing, Advanced Computation and Exploration of data."
• ChartAll - The name says it all. A web utility to chat and plot information
• TEECHART OFFICE - Another charting tool.

Hope these are useful.