DoCon is a program for symbolic computation in mathematics - package of modules DoCon joins the categorial approach to the mathematical computation expressed via the Haskell type classes, and explicit processing of the domain description terms. It implements recently a good piece of commutative algebra: linear algebra, polynomial gcd, factorization, Groebner bases, and other functions. They are programmed under the very generic assumptions , like "over any Euclidean ring", over any GCD-ring, any field, and so on. DoCon also supports the constructions on domains: Fraction, Polynomial, Residue ring, and others. That is certain set of operations on a constructed domain is built automatically.
Sage is a free, open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common, Python-based interface. The project goal is to create a viable free, open source alternative to Magma, Maple, Mathematica and Matlab.
Storm is a distributed and fault-tolerant realtime computation system. Similar to how Hadoop provides a set of general primitives for doing batch processing, Storm provides a set of general primitives for doing realtime computation. Storm is simple, can be used with any programming language, and is a lot of fun to use!
John Baez Algebraic Topological Methods in Computer Science 2008, University of Paris Diderot (Paris 7) July 7, 2008 Computation and the Periodic Table By now there is an extensive network of interlocking analogies between physics, topology, logic and computer science, which can be seen most easily by comparing the roles that symmetric monoidal closed categories play in each subject. However, symmetric monoidal categories are just the n = 1, k = 3 entry of a hypothesized "periodic table" of k-tuply monoidal n-categories. This raises the question of how these analogies extend. We present some thoughts on this question, focusing on how symmetric monoidal closed 2-categories might let us understand the lambda calculus more deeply. This is based on work in progress with Mike Stay. Click on this to see the transparencies of the talk:
An introduction to 2-categories is given by illustrating how the structure of typed lambda calculus may naturally be viewed as a 2-category. In this vein. the structure of computations or conversions gives rise to notions of lax 2':"adjointness.
The Collected Algorithms (CALGO) is part of a family of publications produced by the ACM. Software associated with papers published in the Transactions on Mathematical Software, as well as other ACM journals are incorporated in CALGO.
‘A Byte of Python’ is a free book on programming using the Python language. It serves as a tutorial or guide to the Python language for a beginner audience.
Established in 1969 the CPC Program Library now contains more than 2200 programs in computational physics and chemistry. Papers describing the programs are published in the Computer Physics Communications Journal and are available online via Science Direct.
REDUCE is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot above) but also provides a full programming language, with a syntax similar to other modern programming languages.
This book contains guidelines and advices on how to write efficient software using the C++ language. Software correctness and maintainability are taken into account, but are not the primary concerns of the guidelines.
What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape: P, NP, etc.
Interpreting types as abstract values [The Abstract of the lecture notes] We expound a view of type checking as evaluation with `abstract values'. Whereas dynamic semantics, evaluation, deals with (dynamic) values like 0, 1, etc., static semantics, type checking, deals with approximations like int. A type system is sound if it correctly approximates the dynamic behavior and predicts its outcome: if the static semantics predicts that a term has the type int, the dynamic evaluation of the term, if it terminates, will yield an integer. As object language, we use simply-typed and let-polymorphic lambda calculi with integers and integer operations as constants. We use Haskell as a metalanguage in which to write evaluators, type checkers, type reconstructors and inferencers for the object language.
Gnuplot is a portable command-line driven graphing utility for Linux, OS/2, MS Windows, OSX, VMS, and many other platforms. The source code is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally created to allow scientists and students to visualize mathematical functions and data interactively, but has grown to support many non-interactive uses such as web scripting. It is also used as a plotting engine by third-party applications like Octave. Gnuplot has been supported and under active development since 1986.
E. Elmroth, F. Hernandez, und J. Tordsson. FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF GRID COMPUTING-THEORY METHODS AND APPLICATIONS, 26 (2):
245-256(Februar 2010)
A. Bhagat, B. Sayankar, und P. Agrawal. International Journal on Recent and Innovation Trends in Computing and Communication, 3 (2):
545--548(Februar 2015)