Rodeo!

Octave is a computer program for performing numerical computations which is mostly compatible with MATLAB. It is part of the GNU Project. It is free software under the terms of the GNU General Public License.

Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing.

IPython is an interactive shell for the Python programming language that offers enhanced introspection, additional shell syntax, syntax highlighting, tab completion and rich history. It is a component of the SciPy package.

RStudio™ is a new integrated development environment (IDE) for R. RStudio combines an intuitive user interface with powerful coding tools to help you get the most out of R.

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation.

Spyder (previously known as Pydee) is a free open-source Python development environment providing MATLAB-like features in a simple and light-weighted software, available for Windows XP/Vista/7, GNU/Linux and Mac OS X.

Code smarter and faster with Komodo IDE, the cross-platform professional development environment for dynamic languages and open technologies. Komodo's award-winning feature set includes standard editor functionality like code formatting, commenting, auto-indent and syntax coloring, plus intelligent tools for debugging, regular expressions, team development and customization.

Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software and includes hundreds of mathematical functions with the possibility to add interactively programs from various languages (C, C++, Fortran…).It has sophisticated data structures (including lists, polynomials, rational functions, linear systems...), an interpreter and a high level programming language.

Notepad more focused on developing than just scribble down notes.

wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations. wxMaxima is distributed under the GPL license.

Maple is a general-purpose commercial computer algebra system. Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and visualization. Examples of symbolic computations are given below.Maple incorporates a dynamically typed imperative-style programming language which resembles Pascal. The language permits variables of lexical scope. There are also interfaces to other languages (C, C#, Fortran, Java, MATLAB, and Visual Basic). There is also an interface with Excel.Maple supports MathML 2.0, a W3C format for representing and interpreting mathematical expressions, including their display in Web pages. »

PyScripter is a free and open-source Python Integrated Development Environment (IDE) created with the ambition to become competitive in functionality with commercial Windows-based IDEs available for other languages. Being built in a compiled language is rather snappier than some of the other Python IDEs and provides an extensive blend of features that make it a productive Python development environment.