Programmation en Python pour les mathématiques Nous [1] venons de publier un ouvrage consacré à l’utilisation du langage Python en cours de mathématiques, du collège jusqu’aux premières années universitaires. Le langage universel n’existe pas et l’utilisation de Python pourra être mise en parallèle avec d’autres langages, notamment fonctionnels, qui éclairent d’autres pans des mathématiques que nous aimons enseigner. Ces dernières pourront être travaillées avec profit grâce à Python qui reste, tout en étant à la fois simple et clair, robuste et professionnel. Ce langage est largement répandu et illustre naturellement de nombreux concepts de notre matière. Pour poursuivre la réflexion sur les rapports entre le langage mathématique et les langages de programmation, on pourra lire cet article de Gilles Dowek Au moins deux pistes s’offrent à nous : illustrer de manière efficace et justifiée une notion mathématique à l’aide de l’outil informatique ou inversement, faire des mathématiques en explorant une notion informatique. #! #! Listes Python
Learn Algorithms A Modeling Language for Mathematical Programming A comprehensive guide to building optimization models, for beginning or experienced users Written by the creators of AMPL, this book is a complete guide for modelers at all levels of experience. It begins with a tutorial on widely used linear programming models and presents all of AMPL's features for linear programming with extensive examples. Additional chapters cover network, nonlinear, piecewise-linear, and integer programming; database and spreadsheet interactions; and command scripts. Most chapters include exercises. Download free "student editions" of AMPL with MINOS, CPLEX, and other solvers for experiment, evaluation, and education. AMPL for Courses provides size-unrestricted, time-limited copies of AMPL and popular solvers for teaching optimization in courses of many kinds.
Python Course: Tutorial, Reference and Advanced Topics How Game Theory Solved a Religious Mystery The Bankruptcy Problem A man owes debts of 100, 200, and 300, but dies with insufficient funds to pay everyone. How should his estate be divided? As we all know, there might not be one correct answer. A parent promises gifts to his children, but has to back off when a bonus is smaller than expectedA publicly traded company issues stock and bonds, but soon goes bankrupt in an accounting scandalPartygoers order items at a restaurant, with promises to pay, and then end up arguing over the best way to split the bill There isn’t a single right way to approach any of these problems. Some people prefer proportional division that depends on debt size. Others prefer splitting things up equally. What gets accepted depends on social custom. One of the earliest discussions of fair division comes from the Babylonian Talmud, a record of discussions about Jewish laws and customs. The Talmud answer How should an estate be divided among three creditors claiming sums of 100, 200, and 300? Why stop there?
Python Course: Introduction into the Sys Module Information on the Python Interpreter Like all the other modules, the sys module has to be imported with the import statement, i.e. import sys If there are questions about the import statement, we recommend the introductory chapter of our basic course concerning this topic Modular Programming and Modules The sys module provides information about constants, functions and methods of the Python interpreter. dir(system) gives a summary of the available constants, functions and methods. Another possibility is the help() function. The module sys informs e.g. about the maximal recursion depth (sys.getrecursionlimit() ) and provides the possibility to change ist (sys.setrecursionlimit()) The current version number of Python can be accessed as well: >>> import sys >>> sys.version '2.6.5 (r265:79063, Apr 16 2010, 13:57:41) \n[GCC 4.4.3]' >>> sys.version_info (2, 6, 5, 'final', 0) >>> Command-line arguments #! We save this script as arguments.py. Standard data streams $ python streams.py < numbers.txt
Video Lectures | Introduction to Algorithms (SMA 5503) | Electrical Engineering and Computer Science Liste des algorithmes La liste complète de tous les principaux algorithmes (300), dans tous les domaines. Avec pour but de fournir un programme prêt à tourner pour chacun, ou une description de l'algorithme. Les langages de programmation incluent Java, JavaScript, et PHP, C ou C++ soit sous forme directe, soit générés à partir d'un source en Scriptol. Automate Powerset construction. Bioinformatique et chémoinformatique Needleman-Wunsch. Compression Compression sans perte Burrows-Wheeler transform. Codage par entropie Principe d'encodage qui assigne des codes aux symboles de sorte que la longueur des codes corresponde à la probabilité des symboles. Huffman coding. Compression avec perte d'information Linear predictive coding. Cryptographie Cryptage à clé secrète (symétrique) Utilise une clé secrète (ou une paire de clés directement liées), à la fois pour l'encryptage et le décryptage. Cryptage à clé publique (asymétrique) Utilise une paire de clés, dites clé publique et clé privée. Générateur de code de contrôle Voir.
Hungarian algorithm Combinatorial optimization algorithm that solves the assignment problem in polynomial time James Munkres reviewed the algorithm in 1957 and observed that it is (strongly) polynomial.[3] Since then the algorithm has been known also as the Kuhn–Munkres algorithm or Munkres assignment algorithm. The time complexity of the original algorithm was , however Edmonds and Karp, and independently Tomizawa noticed that it can be modified to achieve an running time.[4][5][how?] One of the most popular[citation needed] variants is the Jonker–Volgenant algorithm.[6] Ford and Fulkerson extended the method to general maximum flow problems in form of the Ford–Fulkerson algorithm. The problem[edit] Example[edit] The Hungarian method, when applied to the above table, would give the minimum cost: this is $6, achieved by having Paul clean the bathroom, Dave sweep the floors, and Chris wash the windows. Matrix formulation[edit] where L and R are permutation matrices. Bipartite graph formulation[edit] . a potential if
Calque The Stony Brook Algorithm Repository This WWW page is intended to serve as a comprehensive collection of algorithm implementations for over seventy of the most fundamental problems in combinatorial algorithms. The problem taxonomy, implementations, and supporting material are all drawn from my book The Algorithm Design Manual. Since the practical person is more often looking for a program than an algorithm, we provide pointers to solid implementations of useful algorithms, when they are available. Because of the volatility of the WWW, we provide local copies for many of the implementations. Many of these codes have been made available for research or educational use, although commercial use requires a licensing arrangement with the author. Use at your own risk.