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solveLinEqs calculates the exact solution, if it exists, to a set of linear equations belonging to the Rationals. It does this by doing the calculation with the type num/den, where num and den are unlimited length integers. There is no limit to the number of linear equations which are to be solved. If the coefficient matrix has zero determinant, then that matrix is augmented with the right hand side vector or matrix and its reduced row echelon form is output. This can be used to determine if the equations are self-consistent.
Gnuplot is a portable command-line driven graphing utility for Linux, OS/2, MS Windows, OSX, VMS, and many other platforms. It was originally created to allow scientists and students to visualize mathematical functions and data interactively, but has grown to support many non-interactive uses such as web scripting. It is also used as a plotting engine by third-party applications like Octave.
PSPP is a program for statistical analysis of sampled data. It is a free replacement for the proprietary program SPSS. PSPP has both text-based and graphical user interfaces. PSPP can perform descriptive statistics, T-tests, anova, linear and logistic regression, cluster analysis, factor analysis, non-parametric tests and more. Its backend is designed to perform its analyses as fast as possible, regardless of the size of the input data.
Freemat is an interpreted, matrix-oriented development environment for engineering and scientific applications, similar to the commercial package MATLAB. Freemat provides visualization, image manipulation, and plotting as well as parallel programming.
OverSAT is unique among SAT solvers in that it uses a grammar to detect conflicts, can tell you when it cannot solve a problem, and, it does not need a heuristic. It also uses skip lists! OverSAT works by parsing a CNF file into a grammar of conflicts and implications. As OverSAT makes a guess, it attempts to reduce a string using the grammar until it reaches a conflicted state. At that point, OverSAT makes another guess.
The Large Time/Frequency Analysis Toolbox (LTFAT) is a Matlab/Octave/C toolbox for working with time-frequency analysis and synthesis. It is intended both as an educational and a computational tool. The toolbox provides a large number of linear transforms including Gabor and wavelet transforms along with routines for constructing windows (filter prototypes) and routines for manipulating coefficients.
Yacas (Yet Another Computer Algebra System) is a small and highly flexible general-purpose Computer Algebra System (CAS). The syntax uses an infix-operator grammar parser. The distribution contains a small library of mathematical functions, but its real strength is in the language in which you can easily write your own symbolic manipulation algorithms. The core engine supports arbitrary precision arithmetic and is able to execute symbolic manipulations on various mathematical objects by following user-defined rules.
SASfit has been written for analyzing and plotting small angle scattering data. It can calculate integral structural parameters like radius of gyration, scattering invariant, Porod constant. Furthermore it can fit size distributions together with several form factors including different structure factors. Additionally an algorithm has been implemented, which allows to simultaneously fit several scattering curves with a common set of (global) parameters. This last option is especially important in contrast variation experiments or measurements with polarized neutrons. The global fit helps to determine fit parameters unambiguously which by analyzing a single curve would be otherwise strongly correlated.
This Explorer allows to perform various statistical analyses and data mining operations in a very easy and intuitive way. As the name implies, this software aims at exploring data and getting quick insight of the order of magnitude of the observed objects. That's why it does focus on graphical representation and mouse driven operations, unlike the traditional statistical tools cluttered with numerous dialog boxes and lists with five decimal figures. You can, however, have the detailed numbers once your analysis is completed.
Runge is an Interactive Solver for Systems of Ordinary Differential Equations. It solves initial value problem (aka Cauchy problem). It utilizes BLAS and LAPACK libraries optimized for modern multi-core processors. It allows you to start a solution by mouse click on a plane. It uses Runge Rule to adjust step length to satisfy required precision on each step. When it needs to compute derivatives (Jacobian matrix, for example) it does that analytically, i.e. without using numerical methods. It allows to export results to MS Excel and MATLAB.
Elmer is a finite element software for numerical solution of partial differential equations and multiphysical problems. It includes models of structural mechanics, fluid dynamics, heat transfer, electromagnetics etc. Features: multiphysical finite element software; modern user interface based on Qt; parallelization with MPI; active user community; extensive support of different element types.
GetDP is a free finite element solver using mixed elements to discretize de Rham-type complexes in one, two and three dimensions. The main feature of GetDP is the closeness between the input data defining discrete problems (written by the user in ASCII data files) and the symbolic mathematical expressions of these problems.
Dr Fit enables to automatically fit a curve to your experimental dose-response data. The data, which should be saved in .xls files, is uploaded through the software which then automatically models it. The resulting curve can be saved in a high resolution figure or as a matlab figure. Responses/Effects can also be interpolated/extrapolated at various doses.
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MathMod is a mathematical modeling software that visualize and animate implicit and parametric surfaces. Features: Isosurfaces and parametric surfaces support; 3D and 4D hypersurfaces support; Rotation, scale and morph effect support; Load scripts in Json file format / export the result as OBJ; Extensive set of examples; Export K3DSurf (.k3ds) scripts to MathMod (.js) scripts; Memory usage and the maximum value of the Grid for Iso/Parametric surfaces are set via the configuration file; Integrated small editor; Solid texturing support.
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors. Maxima yields high precision numerical results by using exact fractions, arbitrary-precision integers and variable-precision floating-point numbers. Maxima can plot functions and data in two and three dimensions.
Finite Elements Software
An open source finite elements software framework intended to unleash free and robust finite element simulation in a standalone executable. Relying on a wxWidgets GUI including VTK visualiser, engineers and scientists will be able to deal with pre-processing, assembly-and-solve and post-processing phases in a rather simple finite elements code. A clearly depicted code structure may unleash the power of finite element simulation for a variety of physical problems.
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Dislin is a high-level plotting library for displaying data as curves, polar plots, bar graphs, pie charts, 3D-color plots, surfaces, contours and maps. Dislin is intended to be a powerful and easy to use software package for scientists and programmers. There are only a few graphics routines with a short parameter list needed to display the desired graphical output. A large variety of parameter setting routines can then be called to create individually customized graphics.
REDUCE is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations but also provides a full programming language, with a syntax similar to other modern programming languages.
APBS is a software package for the numerical solution of the Poisson-Boltzmann equation, a popular continuum model for describing electrostatic interactions between molecular solutes over a wide range of length scales. Features: molecular modeling; electrostatics; implicit solvent models; finite difference solver; finite element solver.
Monte Carlo eXtreme (MCX) is a fast photon transport simulation software for 3D heterogeneous turbid media. By taking advantage of the massively parallel threads and extremely low memory latency in a modern graphics processing unit (GPU), this program is able to perform Monte Carlo (MC) simulations at a blazing speed, typically hundreds to a thousand times faster than a fully optimized CPU-based MC implementation.
gretl is a cross-platform software package for econometric analysis, written in the C programming language.
- Easy intuitive interface (18 languages besides English)
- A wide variety of estimators: least squares, maximum likelihood, GMM; single-equation and system methods
- Time series methods: ARIMA, GARCH, VARs and VECMs, unit-root and cointegration tests, Kalman filter, etc.
- Limited dependent variables: logit, probit, tobit, heckit, interval regression, models for count and duration data, etc.
- Output models as LaTeX files, in tabular or equation format
- Integrated powerful scripting language...
VV Free Stat
Statistical program, somewhat like shareware DataFit. You may provide a custom template (or exchange the template library with your friends or Internet) and test your tabled data. Calculates F-ratio.
Note: The main project language is Russian. Howewer, it contains fully functional English translation.
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Nonlinear Schrödinger equation (NSE) is a fundamental equation in nonlinear optics that describes the propagation of a pulse through a dispersive and nonlinear medium. Nonlinear Pulse Propagation Solver (NPP) is a program, written in C/C++, that solves NSE in an arbitrary waveguide. It has a user friendly interface, which allows a user to enter the pulse and waveguide parameters and execute simulations. The program can be invoked within MATLAB and any other scripting language. It can export the results in different formats including ASCII text '.txt' and MATLAB '.mat' format. The program can also utilize the power of GPU via CUDA.
Sequalator stands for Simultaneous Equations Calculator. It is a software for solving Linear Simultaneous Equations. The solver is based on the Gauss Jordan elimination method for solving Linear Simultaneous Equations. The resulting solution can also be analyzed using the built-in capabilities of the utility, which provide you with information about any errors in your equations.
R is a language and environment for statistical computing and graphics. R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, …) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity.
ESTA is an Eclipse-like GUI to support model based statistical testing.
- usage model creation, editing, and analysis
- test case generation
- test results recording and analysis.
Ascend is a system for solving systems of equations, aimed at engineers and scientists. It allows you to build up complex models as as systems constructed from simpler sub-models. Using Ascend it is simple to play around with your model, examine its behaviour, and work out how it can best be solved. You can easily change which variables are fixed and which are to be solved, and you can examine the way in which the model is being solved.
SimplexNumerica is an object-oriented numerical data analyzer, plotting and visualization program. SimplexNumerica is proving to be extremely popular among scientists. It has Ergonomic programming using the newest Windows programming guidelines with toolbars, context dialogs and interactive diagrams providing easy handling with difficult numeric mathematics. SimplexNumerica is best suited for publication type graphics, analysis of arbitrary data, analysis of measuring data, etc.
Euler Math Toolbox
Euler Math Toolbox (EMT) is a well stylized application that offers you a complete and comprehensive environment where you can perform both simple and complex mathematical calculations.
With EMT, you can
- experience numerical as well as symbolic mathematics with ease and beauty,
- present results with nice graphics, which can be exported to files or to web pages, or can be pasted into presentations,
- do quick and reliable numerical computations using real or complex numbers, intervals, vectors or matrices, ...
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This program calculates pi and other mathematical constants to arbitrary precision, only limited by processing power and memory. Its main feature is not speed, but multiplatform capability and a nice GUI.
Scilab is an interactive platform for numerical computation providing a powerful computing environment for engineering and scientific applications.
Gathering both industrial needs and scientific advances, Scilab covers a wide spectrum of areas: aerospace, automotive, energy, defense, finance, chemistry, biology, medicine...
Scilab includes hundreds of mathematical functions. It has a high level programming language allowing access to advanced data structures, 2-D and 3-D graphical functions.
Are you tired of stupid, heavy and messy plotters? Turbo Plot is here to help you draw nice shapes and functions for your dissertation!
What are the unique Turbo Plot features that make it so powerful?
- As any drawing application, Turbo Plot can save images. But it can also save Vector Image Files. A Vector image file is an image based on vectors (and not pixels), and thus it can be rendered, printed, drawn or saved into a PDF without aliasing and at any scale rate!
- Turbo Plot can save TPLXML files, text files that contain what you have created in text commands so you can load them easily or edit them manually.
- Turbo Plot can save SWF files (Adobe Flash), which are Animated Vector Files. These allow you to create high quality unaliased graphics with animation!
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Prime95 is a program designed to be used to find Mersenne Prime numbers.
An integer greater than one is called a prime number if its only divisors are one and itself. The first prime numbers are 2, 3, 5, 7, 11, 13, 17, etc.
A Mersenne prime is a prime of the form 2P-1. The first Mersenne primes are 3, 7, 31, 127, etc.
There are two ways to use this program. The automatic way uses a central server, which we call the PrimeNet server, to get work to do and report your results. The second method is the manual method (recommended for computers with no Internet access).
MS Mathematics provides a set of mathematical tools that help students get school work done quickly and easily. With MS Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus.
MS Mathematics includes a full-featured graphing calculator that’s designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equations.
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