Debian Science Mathematics packages

Axiom is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.

Axiom has been in development since 1973 and was sold as a commercial product. It has been released as free software.

Efforts are underway to extend this software to (a) develop a better user interface (b) make it useful as a teaching tool (c) develop an algebra server protocol (d) integrate additional mathematics (e) rebuild the algebra in a literate programming style (f) integrate logic programming (g) develop an Axiom Journal with refereed submissions.

This package contains the main program binary and all precompiled algebra and autoloadable modules.

Bliss is a backtracking algorithm for computing automorphism groups and canonical forms of graphs, based on individualization and refinement. Its data structures, subroutines, and pruning heuristics are specially designed for fast handling of large and sparse graphs.

This package provides the command line tool bliss.

Coq is a proof assistant for higher-order logic, which allows the development of computer programs consistent with their formal specification. It is developed using Objective Caml and Camlp5.

This package provides coqtop, a command line interface to Coq.

A graphical interface for Coq is provided in the coqide package. Coq can also be used with ProofGeneral, which allows proofs to be edited using emacs and xemacs. This requires the proofgeneral package to be installed.

DOLFIN is the C++/Python interface of FEniCS, providing a consistent PSE (Problem Solving Environment) for ordinary and partial differential equations.

This package contains executable scripts for DOLFIN.

The vision of FEniCS is to set a new standard in Computational Mathematical Modeling (CMM), which is the Automation of CMM (ACMM), towards the goals of generality, efficiency and simplicity, concerning mathematical methodology, implementation and application. FEniCS is organized as a collection of sub projects/components, including DOLFIN, FErari, FFC, FIAT, Instant, SyFi UFC, UFL, and Viper.

FreeFEM is a language adapted to Partial Differential equation. The underlying method used is the Finite Element Method. This tool has been successfully used as a teaching tool and even as a research tool.

FreeMat is a 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. FreeMat is available under the GPL license.

GAP is a system for computational discrete algebra with particular emphasis on computational group theory, but which has already proved useful also in other areas. In the example text, gap is used to analyse Rubik's Cube using group theory. A kernel implements a Pascal-like language.

This is a dummy package that depends on the standard GAP components.

GeoGebra is a dynamic geometry program. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly.

Support for many geometric constructions is provided, as well as support for many calculus-based tools (derivatives, osculating circle, ...).

GeoGebra files can be exported in many different formats, or as interactive applets for web pages.

Geomview is interactive geometry software which is particularly appropriate for mathematics research and education. In particular, geomview can display things in hyperbolic and spherical space as well as Euclidean space.

Geomview allows multiple independently controllable objects and cameras. It provides interactive control for motion, appearances (including lighting, shading, and materials), picking on an object, edge or vertex level, snapshots in SGI image file or Renderman RIB format, and adding or deleting objects is provided through direct mouse manipulation, control panels, and keyboard shortcuts. External programs can drive desired aspects of the viewer (such as continually loading changing geometry or controlling the motion of certain objects) while allowing interactive control of everything else.

Gerris is a system for the solution of the partial differential equations describing fluid flow.

A brief summary of its main (current) features:

• Solves the time-dependent incompressible variable-density Euler, Stokes or Navier-Stokes equations
• Adaptive mesh refinement: the resolution is adapted dynamically to the features of the flow
• Entirely automatic mesh generation in complex geometries
• Second-order in space and time
• Unlimited number of advected/diffused passive tracers
• Flexible specification of additional source terms
• Portable parallel support using the MPI library
• Volume of Fluid advection scheme for interfacial flows

For multi-cpu MPI support, install gerris-mpi instead.

GiNaC (which stands for "GiNaC is Not a CAS (Computer Algebra System)") is a library for doing symbolic (i.e. non-numeric) computation directly in the C++ programming language.

This package provides some additional tools, like the popular ginsh (GiNaC interactive shell) and viewgar (for inspecting GiNaC archive files).

Gmsh is an automatic 3D finite element mesh generator (primarily Delaunay) with build-in CAD and post-processing facilities. Its design goal is to provide a simple meshing tool for academic test cases with parametric input and up to date visualization capabilities.

Gmsh is built around four modules: geometry, mesh, solver and post-processing. The specification of any input to these modules is done either interactively using the graphical user interface or in ASCII text files using Gmsh's own scripting language.

See Gmsh's reference manual for a more thorough overview of Gmsh's capabilities.

KSEG allows you to interactively create a geometrical construction, similar to what you can do with a straight edge and compass. Points may be inserted on the page with right mouse-button clicks, and then used to form segments, lines, circles, or other geometrical objects. At any time you can drag existing points around, and watch how the constructed objects respond.

GNU libmatheval is a library comprising of several procedures that make it possible to create an in-memory tree representation of mathematical functions over single or multiple variables and later use this representation to evaluate functions for specified variable values, to create corresponding trees for function derivatives over specified variables or to print textual representations of in-memory trees to a specified string. The library supports arbitrary variable names in expressions, decimal constants, basic unary and binary operators and elementary mathematical functions.

This package contains the runtime shared library.

This package provides some applications codes(source and executables) such as laplacian with cG and dG methods, stokes, heat transfer, solid mechanics(static and dynamic).

Life is a versatile finite element library to solve partial differential equations

Support 1D, 2D, 3D

Support the following basic entities: simplices (segment, triangle, tetrahedron) and product of simplices (quadrangle, hexahedron)

Support various point sets on these basic entities: equispaced points, quadrature points, interpolation points (Gauss-Lobatto, Fekete, WarpBlend?)

Support continuous and discontinuous Galerkin methods

Support various polynomial sets:

• Lagrange(continuous,discontinuous,all dimensions,all interpolation point sets)

• Dubiner(discontinuous), boundary adapted(continuous)

• Legendre(discontinuous), boundary adapted(continuous)

Provide mathematical concept for higher order abstraction (Function spaces and associated elements, forms and operators)

Provide a language embedded in C++ for variational formulations, projection and numerical integration

The linear programming (LP) problem can be formulated as: Solve A.x >= V1, with V2.x maximal. A is a matrix, x is a vector of (nonnegative) variables, V1 is a vector called the right hand side, and V2 is a vector specifying the objective function.

An integer linear programming (ILP) problem is an LP with the constraint that all the variables are integers. In a mixed integer linear programming (MILP) problem, some of the variables are integer and others are real.

The program lp_solve solves LP, ILP, and MILP problems. It is slightly more general than suggested above, in that every row of A (specifying one constraint) can have its own (in)equality, <=, >= or =. The result specifies values for all variables.

lp_solve uses the 'Simplex' algorithm and sparse matrix methods for pure LP problems. If one or more of the variables is declared integer, the Simplex algorithm is iterated with a branch and bound algorithm, until the desired optimal solution is found. lp_solve can read MPS format input files.

Homepage http://www.geocities.com/lpsolve/

A convex polyhedron is the set of points satisfying a finite family of linear inequalities. The study of the vertices and extreme rays of such systems is important and useful in e.g. mathematics and optimization. In a dual interpretation, finding the vertices of a (bounded) polyhedron is equivalent to finding the convex hull (bounding inequalities) of an (arbitrary dimensional) set of points. Lrs (lexicographic reverse search) has two important features that can be very important for certain applications: it works in exact arithmetic, and it consumes memory proportional to the input, no matter how large the output is.

The MAGNUS computational group theory package is an innovative symbolic algebra package providing facilities for doing calculations in and about infinite groups. Almost all symbolic algebra systems are oriented toward finite computations that are guaranteed to produce answers, given enough time and resources. By contrast, MAGNUS is concerned with experiments and computations on infinite groups which in some cases are known to terminate, while in others are known to be generally recursively unsolvable.

MAGNUS features an intuitive graphical user interface, facilities for running different algorithms on the same problem in parallel, generation of approximations for working on otherwise infeasible problems, genetic algorithms and a plug-in package manager.

Mathomatic implements most of the rules of algebra for the mathematical operators +, -, *, /, % (modulus), and power (including roots).

Mathomatic can symbolically:

• combine and solve equations,
• completely simplify and compare expressions and equations,
• do simple calculus transformations and series,
• do standard, complex number, modular, and polynomial arithmetic,
• generate optimized C, Java, and Python language code from simplified equations,
• plot expressions with gnuplot in two or three dimensions,
• do quick calculations, colorize expressions, etc.

MUMPS implements a direct solver for large sparse linear systems, with a particular focus on symmetric positive definite matrices. It can operate on distributed matrices e.g. over a cluster. It has Fortran and C interfaces, and can interface with ordering tools such as Scotch.

NETGEN is an automatic 3d tetrahedral mesh generator. It accepts input from constructive solid geometry (CSG) or boundary representation (BRep) from STL file format. NETGEN contains modules for mesh optimization and hierarchical mesh refinement.

Octave is a (mostly Matlab (R) compatible) high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving linear and nonlinear problems numerically.

Octave can be dynamically extended with user-supplied C++ files.

Octaviz is a visualization system for Octave. It is a wrapper that makes all VTK classes accessible from within Octave using the same object-oriented syntax as in C++ or Python. Octaviz also provides high-level functions for 2D and 3D visualization. Using those functions, most common visualization tasks (3D surface plots, contour plots etc) can be accomplished without any knowledge about VTK.

PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers, etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.

Originally developed by Henri Cohen and his co-workers (University Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors.

This is a dummy package which depends on

 pari-galdata: the Galois resolvants for the polgalois function.
 pari-elldata: the elliptic curves database for the ellsearch function.
 pari-seadata: the modular polynomials for the ellap function.
It can be safely removed after the upgrade.

PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.

Originally developed by Henri Cohen and his co-workers (University Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors.

This package contains the GP calculator.

Polylib is a free C library for doing computations on polyhedra. The library is operating on objects like vectors, matrices, lattices, polyhedra, Z-polyhedra, unions of polyhedra and other intermediary structures. It provides functions for all important operations on these structures.

This package contains various utilities to perform polyhedral operations.

Proof General is a major mode to turn Emacs into an interactive proof assistant to write formal mathematical proofs using a variety of theorem provers.

This package provides the Proof General support for Coq, PhoX and LEGO.

Proof General is a major mode to turn Emacs into an interactive proof assistant to write formal mathematical proofs using a variety of theorem provers. It works with either XEmacs or GNU Emacs.

This package provides the Proof General support for the Coq theorem prover which is available as another package. The package is however not required to just edit Coq files.

The FEniCS Form Compiler FFC provides state-of-the-art automatic and efficient evaluation of general multilinear forms (variational formulations) for FEniCS. FFC functions as the form evaluation system for DOLFIN but can also be used to compile forms for other systems.

FFC works as a compiler for multilinear forms by generating code (C or C++) for the evaluation of a multilinear form given in mathematical notation. This new approach to form evaluation makes it possible to combine generality with efficiency; the form can be given in mathematical notation and the generated code is as efficient as hand-optimized code.

OpenTURNS is a powerful and generic tool to treat and quantify uncertainties in numerical simulations in design, optimization and control. It allows both sensitivity and reliability analysis studies:

• defining the outputs of interest and decision criterion;
• quantify and model the source of uncertainties;
• propagate uncertainties and/or analyse sensitivity and
• rank the sources of uncertainty

OpenTURNS is a large project with more than 300 C++ classes which uses well known and supported software such as R for the statistical methods and BLAS/LAPACK for the linear algebra.

This package provides a textual user interface that gives access to all the functionalities provided by the OpenTURNS library.

Besides offering an attractive front-end to GNU Octave, an environment for numerical computation highly compatible with MATLAB, QtOctave currently also features matrix data entry and display and some GUI shortcuts to frequently used Octave functions. It also offers access in place to Octave's documentation with octave-htmldoc or octave-info.

Regina is a suite of mathematical software for 3-manifold topologists. It focuses on the study of 3-manifold triangulations and normal surfaces.

Other highlights of Regina include angle structures, census enumeration, combinatorial recognition of triangulations, and high-level tasks such as 3-sphere recognition and connected sum decomposition. Regina comes with a full graphical user interface, and also offers Python bindings and a low-level C++ programming interface.

This package includes the graphical user interface and the command-line Python interface. The users' handbook and the API documentation are in the separate package regina-normal-doc, and the MPI-enabled utilities for high-performance clusters are in the separate package regina-normal-mpi.

Rheolef is a computer environment that serves as a convenient laboratory for computations in applied mathematics involving finite element-like methods. It provides a set of commands and C++ algorithms and containers.

Most basically, containers cover the classic graph data structure for sparse matrix formats and finite element meshes. At a higher level of abstraction, they can handle approximate finite element spaces, discrete fields, and bilinear forms.

Current applications include:

• massively distributed memory finite element environment, based on MPI;
• Poisson problems in d=1,2 and 3 dimension with high order Lagrange elements, up to fifth order;
• linear elasticity, including incompressible and nearly incompressible elasticity;
• Stokes problems in d=2 or 3 dimension, with P2-P1 or P1 bubble-P1 elements;
• characteristic method for convection-diffusion, time-dependent problems and Navier-Stokes equations;
• nonlinear problems with either fixed-point algorithms or a provided generic damped Newton solver;
• auto-adaptive mesh approaches;
• axisymmetric problems;
• multi-regions and variable coefficient problems.

This package provides the rheolef commands. These support input and output in various file formats for mesh-generators and numerical data visualization systems such as MayaVi, Paraview, and gnuplot.

This metapackage is part of the Debian Pure Blend "Debian Science" and installs packages related to statistics. This task is a general task which might be useful for any scientific work. It depends from a lot of R packages as well as from other tools which are useful to do statistics. Moreover the Science Mathematics task is suggested to optionally install all mathematics related software.

Scilab is a matrix-based scientific software package. Scilab contains hundreds of built-in mathematical functions, rich data structures (including polynomials, rationals, linear systems, lists, etc...) and comes with a number of specific toolboxes for control, signal processing, ...

This package also provides Xcos, a graphical editor to design hybrid dynamical systems models. Models can be designed, loaded, saved, compiled and simulated. Stable and efficient solution for industrial and academics needs, Xcos provides functionalities for modeling of mechanical systems (automotive, aeronautics...), hydraulic circuits (dam, pipe modeling...), control systems, etc. Modelica capabilities are also provided.

Scilab is one of the most credible alternatives to Matlab and Simulink.

For a minimum version of scilab, install package "scilab-cli".

This module implements artificial neural networks capabilities into the Scilab language. Current features are:

• Only layered feedforward networks are supported directly at the moment (for others use the "hooks" provided)
• Unlimited number of layers
• Unlimited number of neurons per each layer separately
• User defined activation function (defaults to logistic)
• User defined error function (defaults to SSE)
• Algorithms implemented so far:
• standard (vanilla) with or without bias, on-line or batch
• momentum with or without bias, on-line or batch
• SuperSAB with or without bias, on-line or batch
• Conjugate gradients
• Jacobian computation
• Computation of result of multiplication between "vector" and Hessian
• Some helper functions provided

This toolbox is providing plotting capabilities in the Scilab language. Plotlib functions matches the one from Matlab and therefor is dedicated to users switching from Matlab to Scilab.

This toolbox is providing symbolic capabilities with the Scilab languages.

It is based on Maxima which is a fully symbolic computation program. It is full featured doing symbolic manipulation of polynomials, matrices, rational functions, integration, Todd-coxeter methods for finite group analysis, graphing, multiple precision floating point computation.

SIVP intends to do image and video processing tasks. SIVP is meant to be a useful, efficient, and free image and video processing toolbox for Scilab. Its goals include tasks such as filtering, blurring, edge detection, thresholding, histogram manipulation, segmentation, mathematical morphology, and color image processing.

This package also provides some functions on video processing.

Wavelet is a powerful signal processing tool developed and developing in the last two decades. Scilab Wavelet Toolbox is a free software package to enable you using wavelet analysis tools freely in Scilab on most OSes including GNU/Linux, BSD and Windows. Scilab Wavelet Toolbox is designed to work with any Scilab Image Processing Toolbox like SIP or SIVP for displaying 2-D results.

What Scilab Wavelet Toolbox supposed to do:

• Discrete Fast Wavelet Transform, daubechies wavelets
• 1-D single level signal decomposition and reconstruction
• 1-D multi-level signal decomposition and reconstruction
• 2-D single level image decomposition and reconstruction
• 2-D multi-level image decomposition and reconstruction

Its purpose is to apply graph theory, with a divide and conquer approach, to scientific computing problems such as graph and mesh partitioning, static mapping, and sparse matrix ordering, in application domains ranging from structural mechanics to operating systems or bio-chemistry.

The SCOTCH distribution is a set of programs and libraries which implement the static mapping and sparse matrix reordering algorithms developed within the SCOTCH project.

SCOTCH has many interesting features:

• Its capabilities can be used through a set of stand-alone programs as well as through the libSCOTCH library, which offers both C and Fortran interfaces.

• It provides algorithms to partition graph structures, as well as mesh structures defined as node-element bipartite graphs and which can also represent hypergraphs.

• It can map any weighted source graph onto any weighted target graph. The source and target graphs may have any topology, and their vertices and edges may be weighted. Moreover, both source and target graphs may be disconnected. This feature allows for the mapping of programs onto disconnected subparts of a parallel architecture made up of heterogeneous processors and communication links.

• It computes amalgamated block orderings of sparse matrices, for efficient solving using BLAS routines.

• Its running time is linear in the number of edges of the source graph, and logarithmic in the number of vertices of the target graph for mapping computations.

• It can handle indifferently graph and mesh data structures created within C or Fortran programs, with array indices starting from 0 or 1.

• It offers extended support for adaptive graphs and meshes through the handling of disjoint edge arrays.

• It is dynamically parametrizable thanks to strategy strings that are interpreted at run-time.

• It uses system memory efficiently, to process large graphs and meshes without incurring out-of-memory faults;

• It is highly modular and documented. Since it has been released under the CeCILL-C free/libre software license, it can be used as a testbed for the easy and quick development and testing of new partitioning and ordering methods.

• It can be easily interfaced to other programs. The programs comprising the SCOTCH project have been designed to run in command-line mode without any interactive prompting, so that they can be called easily from other programs by means of system() or popen() calls, or piped together on a single command line. Moreover, vertex labeling capabilities allow for easy renumbering of vertices.

• It provides many tools to build, check, and display graphs, meshes and matrix patterns.

• It is written in C and uses the POSIX interface, which makes it highly portable. PT-SCOTCH uses the MPI interface, and optionally the POSIX threads.

SINGULAR is a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.

Main computational objects: ideals/modules over very general polynomial rings over various ground fields.

SnapPea is Jeff Weeks' computational tool for mathematicians working in low-dimensional topology. It is used for creating and studying hyperbolic 3-manifolds, and is accessible via Python scripts as well as through a traditional graphical user interface.

wxMaxima is a graphical user interface for the computer algebra system Maxima. It eases the use of Maxima by making most of its commands available through a menu system and by providing input dialogs for commands that require more than one argument. It also implements its own display engine that outputs mathematical symbols directly instead of depicting them with ASCII characters.

wxMaxima also features 2D and 3D inline plots, simple animations, mixing of text and mathematical calculations to create documents, exporting of input and output to TeX, and a browser for Maxima's manual including command index and full text searching.

Maxima is a fully symbolic computation program. It is full featured doing symbolic manipulation of polynomials, matrices, rational functions, integration, Todd-coxeter methods for finite group analysis, graphing, multiple precision floating point computation. It has a symbolic source level debugger for maxima code. Maxima is based on the original Macsyma developed at MIT in the 1970s. It is quite reliable, and has good garbage collection, and no memory leaks. It comes with hundreds of self tests.

This package contains an X Windows interface using the tcl/tk libraries.

XMDS is a code generator that integrates equations, from Ordinary Differential Equations (ODEs) up to stochastic Partial Differential Equations (PDEs). You write them down in human readable form in an XML file, and it goes away and writes and compiles a C++ program that integrates those equations as fast as it can possibly be done in your architecture.

NETGEN is an automatic 3d tetrahedral mesh generator. It accepts input from constructive solid geometry (CSG) or boundary representation (BRep) from STL file format. NETGEN contains modules for mesh optimization and hierarchical mesh refinement.

This package contains the user manual (in PDF format) and example files.

Extends simulation, distribution, quantile and density functions to univariate and multivariate parametric extreme value distributions, and provides fitting functions which calculate maximum likelihood estimates for univariate and bivariate maxima models, and for univariate and bivariate threshold models.

nauty (no automorphisms, yes?) is a set of procedures for determining the automorphism group of a vertex-coloured graph. It provides this information in the form of a set of generators, the size of the group, and the orbits of the group. It is also able to produce a canonically-labelled isomorph of the graph, to assist in isomorphism testing. This package provides the main command line tool dreadnaut, and some utilities ('gtools'). A C API is also available.

E is a fully automatic theorem prover for full first-order logic with equality. It accepts a mathematical specification and, optionally, a hypothesis, and tries to prove the hypothesis and/or find a saturation representing a (counter-)model for the specification.

E is based on a purely equational problem representation and implements a variant of the superposition calculus. Proof search can be guided with a multitude of options or a powerful automatic configuration mode. The system can process input in a number of different formats, including the standard TPTP-2 and TPTP-3 formats. It can generate proof objects in PCL2 or TPTP-3/TSTP format.

E is considered one of the most powerful and friendly automated theorem provers for first-order logic. It has consistently been among the top system in the major categories of the CASC system competition, and usually been the strongest free software system.

Sage is a mathematical software package with support for a wide range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.

Sage integrates several dozen mathematical software packages, making it possible to combine the best algorithms from several different packages together in a single Sage program.

Much of the Sage core and the Sage interfaces are implemented in Cython, helping Sage avoid the usual performance problems associated with Python.

Sage has a friendly command-line interface based on iPython and a web-based notebook interface which can run locally or connect to a remote Sage server over the network.

Features a choice of several ready-to-use logics (Higher Order Logic, Higher Order Logic augmented with Scott's Logic for Computable Functions, First Order Logic, Zermello-Frankel, an extensional version of Martin-Lof Type Theory, Barendregt's Lambda Cube, a few sequent calculi (including modal and linear logics), ...) or defining your own logic / deductive system, a procedural and a declarative proof style, rich automation for classical reasoning, equational logic and algebra, LaTeX and X-Symbols notational support.

Isabelle can also be used as a generic framework for rapid prototyping of deductive systems.