Debian Science Mathematics packages

Agda is a dependently typed functional programming language: It has inductive families, which are like Haskell's GADTs, but they can be indexed by values and not just types. It also has parameterised modules, mixfix operators, Unicode characters, and an interactive Emacs interface (the type checker can assist in the development of your code).

Agda is also a proof assistant: It is an interactive system for writing and checking proofs. Agda is based on intuitionistic type theory, a foundational system for constructive mathematics developed by the Swedish logician Per Martin-Löf. It has many similarities with other proof assistants based on dependent types, such as Coq, Epigram and NuPRL.

This is a meta package which provides Agda's emacs mode, executable, standard library and its documentation.

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 は個別化と精緻化をもとに自己同形群や図の標準形を計算するための バックトラック機構です。そのデータ構造やサブルーチン、ヒューリスティックス の間引きは巨大でまばらな図を高速に処理するよう、特別に設計されています。

このパッケージはコマンドラインツール bliss を提供します。

Coq は高階述語論理の証明アシスタントで、コンピュータプログラムを形式的な仕 様との整合性を保ちながら開発できます。Objective Caml と Camlp5 を用いて開発 されています。

本パッケージは Coq へのコマンドラインインターフェース coqtop を提供します。

Coq のグラフィカルインターフェースは coqide パッケージが提供します。 Coq は ProofGeneral とも併用でき、証明を emacs や xemacs で編集できるように なります。これには proofgeneral パッケージのインストールが必要です。

DOLFIN is the Python and C++ interface of the FEniCS project for the automated solution of differential equations, providing a consistent PSE (Problem Solving Environment) for solving ordinary and partial differential equations. Key features include a simple, consistent and intuitive object-oriented API; automatic and efficient evaluation of variational forms; automatic and efficient assembly of linear systems; and support for general families of finite elements.

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 は偏微分方程式に適した言語です。根本にある手法は有限要素法です。 このツールは教材としてだけではなく、研究道具としてもうまく使えます。

FreeFem++ is an implementation of a language dedicated to the finite element method. It enables you to solve Partial Differential Equations (PDE) easily.

Problems involving PDE from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFem++ includes a fast quadtree-based interpolation algorithm and a language for the manipulation of these data on multiple meshes. It contains also a powerful mesh generation and adaption tool integrated seamlessly in FreeFem++ called bamg.

FreeFem++ is written in C++ and the FreeFem++ language is a C++ idiom allowing for a smooth learning curve.

This package contains the executables of FreeFem++.

FreeFEM3D (aka ff3d) is a 3D solver of partial differential equations (PDE). It is a member of the familly of the freefem programs (see http://www.freefem.org).

ff3d, as well as its cousins, is a PDE solver driven by a user-friendly language. It solves many kind of problems such as elasticity, fluids (Stokes and Navier-Stokes) and a lot more. The user has to enter the equation associated with the problem, giving either the PDE in strong formulation or weak (variational) formulation.

ff3d can use either the Finite Elements method (the mesh of the geometry being provided by the user) or a Fictitious Domain like approach where the geometry is described using Constructive Solid Geometry (CSG). This description is done using the POV-Ray language but others such as VRML could be added.

The processing of the results is left to the user. One can use various graphic tools: output in the MEdit mesh format or VTK are supported. The implementation of a VTK base visualization module is underway.

The goal of ff3d is to provide a good teaching tool and a research toolbox (the code is written in C++ and its design is such that new methods can be easily implemented).

FreeMat は高速な設計や科学プロトタイピングそしてデータ処理のための フリーな環境です。Mathworks 製 MATLAB や、Research Systems 製 IDL のような商用システムに似ていますが、オープンソースです。 FreeMat は GPL ライセンスのもとで利用できます。

GAP は、特定の計算群理論を重視した計算離散代数のシステムで、他の領域 にも有用であることが既に証明されています。例題では、群理論を使用した Rubik's Cube の解析に GAP が使われています。中心は pascal に似た言語 で実装されています。

本パッケージは、標準の GAP コンポーネントに依存しているダミーパッケー ジです。

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 は対話的な幾何的図形ソフトウェアで、数学の研究および教育に特に適し ています。特に、geomview は双曲空間、球面空間やユークリッド空間にある物体を 表示できます。

Geomview では複数の対象物やカメラを各々独立に操作できます。動きや外観 (照明 や陰、素材感を含む)、オブジェクトや端・頂点の選択、SGI 画像ファイルまたは Renderman RIB 形式のスナップショットを対話的に制御できます。オブジェクトの 追加や削除は、マウスでの直接の操作、コントロールパネル、キーボードショート カットで行えます。(位置の変化を連続的にロードしたり、特定のオブジェクトの動 きを制御したり、といった) ビューアの望ましい機能を外部プログラムから制御し 実現できると同時に、その他あらゆる点について対話的に制御することが可能です。

Gerris は、流体を表す偏微分方程式を解くためのシステムです。

(現在の) 主要機能の概要は次の通りです:

• 時間依存の非圧縮性可変密度オイラー、ストークスまたはナビエ・ストークス 方程式を解きます
• 適合細分化格子 (AMR) 法: 分解能は流体の特徴に動的に適応します
• 複雑な形状の完全自動格子生成
• 空間と時間で二次オーダー
• 個数無制限の移流・拡散パッシブトレーサ
• 追加のソース項を柔軟に指定できます
• MPI ライブラリを使用した移植性の高い並列サポート
• 界面流体の Volume of Fluid (VOF) 法による移流スキーム

複数 cpu 向けの MPI サポートを利用するには、本パッケージではなく gerris-mpi を インストールしてください。

GetDP is a general 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.

See GetDP's reference manual for a more thorough overview of GetDP's capabilities: http://www.geuz.org/getdp

GiNaC ("GiNaC is Not a CAS (Computer Algebra System)" の略称) は記号的 (す なわち、数値的ではない) 計算用ライブラリであり、直接 C++ プログラミング言語 で書かれています。

本パッケージは 有名な ginsh (GiNaC 対話的シェル) や viewgar (GiNaC アーカイ ブファイルを調べるツール) のような追加ツールをいくつか提供します。

Gmsh は三次元の有限要素網 (主にドロネー) を自動的に生成するプログラムで、内 蔵 CAD および後処理機能が付属しています。この設計目標は、パラメータで入力で き、最新の視覚化機能を備えた、学術的なテストケース用のシンプルな網生成ツー ルを提供することです。

Gmsh は、4 個のモジュールで構成されます: ジオメトリ、メッシュ、ソルバ、後処 理。これらのモジュールに対するあらゆる入力の定義は、グラフィカルユーザイン ターフェースを使って対話式に行うか、Gmsh 専用のスクリプト言語を使って ASCII テキストファイルの形で行います。

Gmsh の機能のより詳しい全体像は、Gmsh のリファレンスマニュアルを参照してく ださい。

HOL Light is an interactive theorem prover for Higher-Order Logic with a very simple logical core running in an OCaml toplevel. HOL Light is famous for the verification of floating-point arithmetic as well as for the Flyspeck project, which aims at the formalization of Tom Hales' proof of the Kepler conjecture.

Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, mostly written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, FFTs, and string processing. Julia programs are organized around defining functions, and overloading them for different combinations of argument types (which can also be user-defined).

This package provides a complete Julia installation (JIT compiler, standard library, text-based user interface).

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.

Givaro is a C++ library for arithmetic and algebraic computations. Its main features are implementations of the basic arithmetic of many mathematical entities: Primes fields, Extensions Fields, Finite Fields, Finite Rings, Polynomials, Algebraic numbers, and Arbitrary precision integers and rationals (C++ wrappers over gmp).

Givaro also provides data-structures and templated classes for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, structured), univariate polynomials (and therefore recursive multivariate).

It contains different program modules and is fully compatible with the LinBox linear algebra library and the Athapascan environment, which permits parallel programming.

This package contains runtime files for Givaro.

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

線形計画法 (LP) は、次のように定式化されます: A.x >= V1 を V2.x を最小にして解く。A は行列、x は (正の値を持つ) ベクトル、 V1 は右辺値と呼ばれるベクトル、そして V2 は目標関数を指定するベクトルである。

整数線形計画法 (ILP) は全ての変数が整数であるという制限を持つ LP 問題である。 混合整数線形計画法 (MILP) では、変数のいくつかは整数、他の変数が実数である。

プログラム lp_solve は LP、ILP、そして MILP 問題を解きます。 上記で推奨されているよりもより汎用的であり、A の全ての列 (一つの拘束条件を 定義) は独自の等価性、すなわち <=、>= 又は = を持ち得ます。 結果は全ての変数に対する値を指定します。

lp_solve は 'Sumplex' アルゴリズムおよび純粋な LP 問題に対して疎行列法を利用 します。一つ又は複数の変数を整数として宣言すると、Simplex アルゴリズムは 望んだ最適解が見つかるまで branch and bound アルゴリズムを繰り返します。 lp_solve は MPS フォーマットの入力ファイルを受け付けます。

ホームページ: 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.

Matita は (余) 帰納構成的論理に基づくグラフィカルで対話的な自動証明系です。

The MCL package is an implementation of the MCL algorithm, and offers utilities for manipulating sparse matrices (the essential data structure in the MCL algorithm) and conducting cluster experiments.

MCL is currently being used in sciences like biology (protein family detection, genomics), computer science (node clustering in Peer-to-Peer networks), and linguistics (text analysis).

Despite the NP completeness of the satisfiability problem of Boolean formulas (SAT), SAT solvers are often able to decide this problem in a reasonable time frame. As all other NP complete problems are reducible to SAT, the solvers have become a general purpose tool for this class of problems.

MiniSat is a minimalistic, open-source SAT solver, developed to help researchers and developers alike to get started on SAT. Winning all the industrial categories of the SAT 2005 competition, MiniSat is a good starting point both for future research in SAT, and for applications using SAT.

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 は、自動三次元四面体メッシュジェネレータです。Constructive Solid Geometry (CSG) 又は STL ファイルフォーマットが由来の境界表現 (BRep) から 入力を受け取ります。NETGEN には、メッシュの最適化と階層的メッシュ改善用 モジュールが含まれます。

Octave は、(Matlab (R) とほぼ互換な) 高レベル言語であり、数値計算を第一の 目的にしています。線形問題および非線形問題を数値的に解くための便利な コマンドラインインターフェースを提供します。

Octave はユーザ指定の C++ ファイルで動的に拡張できます。

This package contains various tools to work with lattice polytopes:

• mori.x computes star triangulations of a polytope
• cws.x creates weight systems and combined weight systems
• class.x classifies reflexive polytopes
• poly.x computes data of a polytope
• nef.x computes Hodge numbers of nef-partitions

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 は、幅広く利用されている計算機代数システムであり、数論の高速計算 (因数分解、代数的数理論、楕円曲線など) のために設計さえています。 しかし、行列、多項式、級数、代数などの数学的要素の計算といった他の有用な 機能や、超越関数も多数含まれています。

もともとは、Henri Cohen と彼の同僚 (フランスのボルドー第一大学) により開発 されていましたが、PARI は、現在 GPL のもとで公開されており、多数のボランティア 開発者の助けを借りながら Karim Belabas により維持されています。

本パッケージには、GP 計算機が含まれます。

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 Proof General support for Coq. (There is no other proof assistant that one could sensibly support.)

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.

This package provides the Prover9 resolution/paramodulation theorem prover and the Mace4 countermodel generator.

Prover9 is an automated theorem prover for first-order and equational logic. It is a successor of the Otter prover. Prover9 uses the inference techniques of ordered resolution and paramodulation with literal selection.

The program Mace4 searches for finite structures satisfying first-order and equational statements, the same kind of statement that Prover9 accepts. If the statement is the denial of some conjecture, any structures found by Mace4 are counterexamples to the conjecture.

Mace4 can be a valuable complement to Prover9, looking for counterexamples before (or at the same time as) using Prover9 to search for a proof. It can also be used to help debug input clauses and formulas for Prover9.

DEAP is intended to be an easy to use distributed evolutionary algorithm library in the Python language. Its two main components are modular and can be used separately. The first module is a Distributed Task Manager (DTM), which is intended to run on cluster of computers. The second part is the Evolutionary Algorithms in Python (EAP) framework.

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. Flexible and powerful expressions are used to specify 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.

このメタパッケージは Debian Pure Blend "Debian Science" の一部で、統計学に 関連したパッケージをインストールします。このタスクはどんな科学的研究にも使 える一般的なタスクです。たくさんの R パッケージに加え、統計処理を行うのに便 利な他のツールに依存します。さらに、オプションで数学関連の全ソフトウェアを インストールできる Science Mathematics タスクを提案します。

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.

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 は計算機代数システム Maxima のグラフィカルなユーザインターフェース です。メニューシステムを通じてコマンドのほとんどを利用でき、複数の引数が必 要なコマンドに対しては入力ダイアログを提供するので、簡単に Maxima を利用で きます。また、ASCII 文字で表現するのではなく直接数式記号を出力する独自の表 示エンジンを実装しています。

wxMaxima は 2D や 3D でのインラインプロットや、単純なアニメーション、テキス トと数値計算の混成による文書作成、TeX での入出力、コマンド索引や全文検索を 含む Maxima マニュアル用ブラウザ、といった機能もあります。

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 は、自動三次元四面体メッシュ生成ツールです。STL ファイル形式の constructive solid geometry (CSG) または境界表現 (BRep) を入力に受け取りま す。NETGEN には、メッシュの最適化と階層的メッシュ精密化用モジュールが含まれ ます。

このパッケージには、ユーザマニュアル (PDF 形式) とサンプルファイルが含まれ ています。

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.

This package does not provide MATLAB. Instead, it configures an existing MATLAB installation to integrate more comfortably in a Debian installation.

Currently it provides /usr/bin/matlab through the alternatives system, offers to work around incompatibilities between the libraries bundled with MATLAB and system libraries, and provides a helper utility meant to be used by other packages to compile MEX extensions.

Install this if you would like your MATLAB installation to behave more like an ordinary Debian package. Other packages may depend on this one if they install MATLAB code, for example in order to compile MEX extensions.

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.

The core of PolyBoRi is a C++ library, which provides high-level data types for Boolean polynomials and monomials, exponent vectors, as well as for the underlying polynomial rings and subsets of the powerset of the Boolean variables. As a unique approach, binary decision diagrams are used as internal storage type for polynomial structures. On top of this C++-library we provide a Python interface. This allows parsing of complex polynomial systems, as well as sophisticated and extendable strategies for Groebner base computation. PolyBoRi features a powerful reference implementation for Groebner basis computation.

This package contains the PolyBoRi's shell ipbori.

The core of PolyBoRi is a C++ library, which provides high-level data types for Boolean polynomials and monomials, exponent vectors, as well as for the underlying polynomial rings and subsets of the powerset of the Boolean variables. As a unique approach, binary decision diagrams are used as internal storage type for polynomial structures. On top of this C++-library we provide a Python interface. This allows parsing of complex polynomial systems, as well as sophisticated and extendable strategies for Groebner base computation. PolyBoRi features a powerful reference implementation for Groebner basis computation.

This package contains the PolyBoRi's PolyGUI.

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.

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-Löf 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.

This package contains the isabelle toolchain.

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.

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.