Free equation software for linux

Equation Grapher is a 2D implicit equation grapher.

Equation Grapher allows you to plot equations of the form f(x,y) = g(x,y), with all of the standard operators (log, exp, sqrt, ...) as well as differentiation.

Example equations:

y = sin(x)
x = sin(y)
(xy)^2 = sin(cos(x^2 + y^2))
y = deriv(exp(-x^2/2),x)

Modest Ordinary Differential Equation Library is a C++ library to model rate equations.
MODEL is a numeric simulation library written during my PhD to simulate systems of rate equations describing Vertical Cavity Surface Emitting Lasers (VCSELs). I decided to write one myself after looking at existing libraries and deciding that they were either too complicated to use (having a target user base of mathematicians) or too opaque (i like to know what the code is doing, exactly).
Since most of my programming before has been done in C/C++, what you see here is a C++ library composed of various interacting classes which have the following main functionalities:
deterministic integration of any system of well-behaved differential equations.
- stochastic integration of these systems, with the possibility of specifying the correlations present in the noise
- nonlinear rootfinder, to find stationary solutions
- eigenvalue determination, for stability analysis
- easy time modulation of input parameters
- diverse data collecting classes for data analysis
- Small signal analysis (first order)
The following will be added RSN:
- Fourier transforms, for spectral analysis (although this can be done in an external program)
- Periodic solution finder
It furthermore provides a numerical vector class, vectorfunction classes, LU solver and random generators.
As I developed it using publicly available resources, GNU/Linux and other GPLed software, I decided that it should be GPL as well. However (Oh no, a "however" ! Lets hope it does not invalidate the copyleft), I would very much appreciate it if you let me know if you have used MODEL in any of your applications/simulations/research and provide a reference (this way, I can refer to your work, too).
At the moment, MODEL has the rather arbitrary version number 1.0. Meaning it is useful. Period. Some interfaces (especially the stochastics) might still change, and I would like to add some ieee floating point exception trapping to avoid silly numerical errors.
Enhancements:
- Add features/limitations/changes here

Q-Audio is a digital audio interface for Q. Q-Audio project contains three modules which together provide the basic functionality needed to write digital audio applications.
The audio module implements a (nearly) real-time audio interface on top of the PortAudio library. The sndfile module allows you to access sound files in various formats using libsndfile.
The wave module provides basic operations for creating and manipulating wave data, including operations to convert sample rates, to calculate Fourier transforms, and to display wave data in a GGI visual.
About Q language:
Q is a functional programming language based on term rewriting. Thus, a Q program or "script" is simply a collection of equations which are used to evaluate expressions in a symbolic fashion. The equations establish algebraic identities and are interpreted as rewriting rules in order to reduce expressions to "normal forms". For instance, here is how you define a function sqr which squares its argument by multiplying it with itself:
sqr X = X*X;
Note that, as in Prolog, capitalized identifiers are used to indicate the variables in an equation, which are bound to the actual values when an equation is applied. Equations may also include a condition part, as in the following definition of the factorial function:
fact N = N*fact (N-1) if N>0;
= 1 otherwise;
Functions on structured arguments are defined by "pattern matching". E.g., the product of a list (denoted in Prolog-like syntax) can be computed with these two equations:
prod [] = 1;
prod [X|Xs] = X*prod Xs;
With this definition, the factorial can now also be defined as follows (the notation [1..N], as in Haskell, denotes an arithmetic sequence):
fact N = prod [1..N];
As you can see, the definitions are really just like mathematical equations. The syntax is superficially similar to other modern functional languages like Miranda and Haskell, except that Q is "free-format", i.e., it does not use layout to indicate syntactical structure (thus the semicolon is used to terminate an equation).
Due to its term rewriting heritage, Q goes well beyond most other functional languages in that it also allows you to perform computations with symbolic expressions. For instance, with the definition of the sqr function from above, you will find that sqr (X+1) evaluates to (X+1)*(X+1). This might first look like an arcane feature, but it is actually quite useful, because you can try your definitions with symbolic inputs, too.
Enhancements:
- src/wave.c: minor fixes for compatibility with latest gcc versions

Qalculate! is a multi-purpose desktop calculator for GNU/Linux. Qalculate! project is small and simple to use but with much power and versatility underneath.
Features include customizable functions, units, arbitrary precision, plotting, and a user-friendly interface (KDE or GTK+).
Main features:
- Redesigned GUI with history view in the main window
- Display of as-you-type expression parsing and function hints
- Enhanced completion
- Scaling of result display to vertically fit the window
- Nicer history listing
- Enhanced result display with much nicer parentheses
- Meta modes
- 67 new units: bel (B) and neper (Np), information units such as bit and byte, many convenience units (km/h, deciliter, etc), and more.
- Binary prefixes
- Some new variables and functions
- Fixed help display in new yelp
- Fixed compile with cln-1.1.10
- Fixed regressions in simplification
- Fixed f(x) return type analysis (ex. log(x) represents a real number if x represents a positive). This was by accident unused.
- ...and many more bug fixes and enhancements...
Enhancements:
- Use Lambert W to solve more equations and avoid infinite loop when solving some equations
- More data on elements
- Fix simplification of (1-1/x)^3 and similar
- Fix clumsy mistakes in with prefixes leading to crashes
- Fix parsing of unit expressions (when converting) such as W/(m K)
- Add more exact values for sin() and cos() and avoid floating point underflow by, in approximate mode, checking against the value of pi
- Always input decimal separator sign on keypad separator press
- New units: typographic units, pouce, pied du roi, grams of TNT and tons of TNT
- New functions: lambertW(), addDays(), addMonths(), addYear(), addTime(), isNumber(), isReal(), isRational(), isInteger(), representsNumber(), representsReal(), representsRational(), representsInteger()
- New variable: omega constant
- Other minor fixes and enhancements

MathStudio project is an interactive equation editor and step-by-step solver.
MathStudio is a project aimed at making math-typing, plotting, and symbolic math easier.
Its user can easily input, plot, and save/load math data in various formats (e.g., MathML). Step-by-step resolution makes this a powerful learning tool.
Main features:
- Open Source
- Cross-platform
- Compiler support
- Easy to use
- Simple, extensible
- Intermediate steps

Mantissa is a collection of various mathematical tools aimed towards for simulation.
Mantissa contains a collection of algorithms, among which:
a small set of linear algebra classes
a least squares estimator
some curve fitting classes
several ordinary differentials equations integrators, either with fixed steps or adaptive stepsize control (see below)
vectors and rotations in a three dimensional space
algebra-related classes like rational and double polynomials
various orthogonal polynomials:
Chebyshev
Hermite
Laguerre
Legendre
some random numbers and vectors generation classes:
Robert M. Ziff four tap shift register (contributed by Bill Maier)
Makoto Matsumoto and Takuji Nishimura Mersenne twister
generators for vectors with correlated components
some basic (min, max, mean, standard deviation) statistical analysis classes
some optimization algorithms using direct search methods:
the Nelder-Mead simplex method
Virginia Torczons multi-directional method
Enhancements:
- For many basic objects provided by Mantissa like Vector3D, Rotation, and the various Polynomial classes, instances are now guaranteed to be immutable.
- This greatly simplifies safe sharing of instances without forcing users to either put severe restrictions on their use of Mantissa classes or make numerous copies just to make sure everything is safe.
- Since the change is a semantic change on the contract of the classes, this version introduces some incompatibilities with respect to previous ones.
- Upgrading to this version is not difficult, though.