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.

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-coq package to be installed.

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.

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. Homepage: http://www.geomview.org.

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

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.

GNU libmatheval is library comprising several procedures that makes possible to create in-memory tree representation of mathematical functions over single or multiple variables and later use this representation to evaluate function for specified variable values, to create corresponding tree for function derivative over specified variable or to print textual representation of in-memory tree to 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 libraries.

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 calculus transformations,
• do standard, complex number, and polynomial arithmetic,
• generate optimized C, Java, and Python language code from simplified equations,
• 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.

This package is an empty 'virtual' package whose sole purpose is to install the current Octave version from the 2.1 branch (the recommended testing branch) .

Once you have the octave2.1 package installed, you can remove this package.

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 uses some of the best and most respected numerical libraries as balgen, dassl, eispack, fftpack, lapack, linpack, minpack, odepack, ranlib, slatec-fn and villad. 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 package contains extra data files for PARI/GP:

 the Galois resolvants for the polgalois function.
 the elliptic curves database for the ellsearch function.

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.

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.

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.

Regina is a suite of mathematical software for 3-manifold topologists. It focuses upon the study of 3-manifold triangulations and includes support for normal surfaces and angle structures.

Highlights of Regina include triangulation analysis and simplification, census creation and normal surface enumeration. It offers embedded Python scripting giving full access to the calculation engine.

This package includes the KDE user interface and the command-line Python interface, as well as the users' handbook. For the Python reference (i.e., the API documentation for the Regina calculation engine), see the package regina-normal-doc.

Components of Regina that are designed to run on clusters are no longer shipped in this package. They can now be found in the separate package regina-normal-mpi.

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.

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, ...

Current features

• 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.

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

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.

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.

nauty (no automorphisms, yes?) is a set of procedures for determining the automor- phism 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.

Bliss is a backtracking algorithm based on individualization and refinement for labeling a graph. Data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are provided. This package provides the command line tool bliss; a C++ and C API is also available.

There is also a libbliss-dev which changes the last line of the long description. At the moment I propose not to create a shared library package since upstream doesn't make one, and in the short term there won't be any rdepends in debian. I could be convinced otherwise of course.

GeoGebra is a dynamic geometry system. 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.

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.