Computer Algebra Links

• SymbolicNet (Symbolic Mathematical Computation Information Center)
• Mathematica (Wolfram Research).
  • MathGroup (discussion group)
  • Internal`DistributedTermsList is a good alternative for MonomialList, which is no longer present in Mathematica 4. Read a short description of this great tool for work with polynomials in several variables.
  • The Mathematica GuideBooks, a four-volume set by Michael Trott at Springer:
    • The Mathematica Guidebook for Programming
    • The Mathematica Guidebook for Graphics
    • The Mathematica Guidebook for Numerics
    • The Mathematica Guidebook for Symbolics
  • Introductory Mathematica course (in Dutch) by André Heck.
• Maple (Waterloo Maple)
  • Maple on the Web by Alejandro S. Jakubi
• Reduce (an interactive program designed for general algebraic computations of interest to mathematicians, scientists and engineers)
• Matlab (integrates mathematical computing, visualization, and a powerful language to provide a flexible environment for technical computing)
• Octave (GNU Octave is a high-level language, primarily intended for numerical computations. It is mostly compatible with Matlab.)
• Sage (a free open-source mathematics software system)
• Mathemagix (a free computer algebra system under development)
• GAP
  • Can also be downloaded from Alexander Hulpke's site
• Magma
• Macaulay
• SINGULAR (for polynomial computations)
• ACE (Algebraic Combinatorics Environment)
• LiE (Lie theory computations)
• Home Page for SF (Symmetric Functions), posets, and coxeter/weyl (John Stembridge's Maple packages)
• Felix (for computation in commutative and non-commutative rings and modules)
• Combinatorial Software and Databases (Séminaire Lotharingien de Combinatoire)
• computer algebra and special functions
• Schubert, a Maple package for intersection theory and enumerative geometry (Sheldon Katz, Stein Arild Strømme, Jan-Magnus Økland)
• FeynCalc, Tools and Tables for Quantum Field Theory Calculations (in Mathematica).
• AXIOM
• NCAlgebra (non-commutative algebra package in Mathematica)
• CLIFFORD (a Maple package for Clifford algebra computations)
• PAFF : Package for Algebraic Function Fields in one variable (by Gaétan Haché)
• FORM (program for large scale symbolic manipulation) by Jos Vermaseren.
• RATE - A Mathematica guessing machine (by Christian Krattenthaler: to guess a closed form expression for a sequence of numbers or rational functions
• Algolib: combinatorics package for Maple by Bruno Salvy and coworkers (INRIA, France)
• Haskell (a purely functional programming language)
• GrInvIn, an interactive software application for studying graphs and their invariants
• pages on fast algorithms by Ekatherina Karatsuba:
  • Fast Algorithms and the FEE Method
  • The Karatsuba method "Divide and Conquer"
  • Answers to frequently asked questions
• Documentation on the Grobner Package for Gap 4 by A.M. Cohen and D.A.H. Gijsbers (TU Eindhoven)
• Perfectly Scientific, Inc. (PSI), an algorithm company.
  They offer PrimeKit: Mathematica implementations for the algorithms in the book R. Crandall and C. Pomerance, Prime numbers.
• Schoonschip, Version 91 was instrumental in the research leading to the Nobel Prize in Physics 1999. See the short manual Schoonschip '91, by M. Veltman and David M. Williams, pdf format. It also occurs in the poem by Michael Wester.