• GAP

  • Referenced in 3067 articles [sw00320]
  • discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language ... used in research and teaching for studying groups and their representations, rings, vector spaces, algebras ... extend it for your special use. Computer algebra system...
  • Magma

  • Referenced in 3136 articles [sw00540]
  • supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics ... defining and working with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs ... number of databases designed to aid computational research in those areas of mathematics which...
  • LiE

  • Referenced in 160 articles [sw01075]
  • perform computations of a Lie group theoretic nature. It focuses on the representation theory ... their Weyl groups and root systems. LiE does not compute directly with elements...
  • TopSpin

  • Referenced in 13 articles [sw00972]
  • detailed in the user manual), uses computational group theory to automatically determine a group...
  • LOOPS

  • Referenced in 43 articles [sw07728]
  • computational tool that integrates standard notions of loop theory with libraries of loops and group...
  • Canon

  • Referenced in 5 articles [sw00102]
  • dummy (summed over) indices. Solution method: Computational Group Theory algorithms have been used, specially algorithms...
  • Mincer

  • Referenced in 68 articles [sw09009]
  • field theory for the Schoonschip system. We present a SCHOONSCHIP program for analytical computation ... sufficient to perform four-loop renormalization group calculations within the minimal subtraction scheme in four...
  • BioGAP

  • Referenced in 4 articles [sw08793]
  • Bacterial Genomics and Computational Group Theory. Bacterial genomes can be modelled as permutations of conserved ... trees) can be tackled by use of group-theoretical tools such as the word distance ... finding geodesic words, etc. Most of the groups involved in this research are well-studied ... this talk we describe how the computational tools are used in these biological projects...
  • Coxeter

  • Referenced in 23 articles [sw07827]
  • computer program for the study of combinatorial aspects of Coxeter group theory, particularly those related ... following : Reduced expression and normal form computations; Bruhat ordering; Ordinary Kazhdan-Lusztig polynomials; Kazhdan-Lusztig...
  • CCalc

  • Referenced in 78 articles [sw09899]
  • logic described in the paper ”Nonmonotonic causal theories” by Enrico Giunchiglia, Joohyung Lee, Vladimir Lifschitz ... system is being maintained by Texas Action Group at Austin. The semantics of the language ... related to default logic and logic programming. Computationally, CCalc uses ideas of satisfiability planning...
  • ETPS

  • Referenced in 158 articles [sw06302]
  • various mathematical activities, promoting development of formal theories in a wide variety of disciplines, deductive ... facility for saving formulas, definitions, and modes (groups of flag settings). The interactive facilities ... inference in specified ways, and the computer handles the details of writing the appropriate lines ... Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, Second Edition, Kluwer Academic...
  • Francy

  • Referenced in 2 articles [sw25788]
  • discrete algebra with an emphasis on computational group theory. The existing XGAP package...
  • LieART

  • Referenced in 57 articles [sw08573]
  • frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra ... classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems ... output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast...
  • BraidedJunctions

  • Referenced in 1 article [sw23622]
  • paper. The main focus is on computing group theory related information for string junction vectors...
  • Atlas of Lie Groups

  • Referenced in 13 articles [sw09356]
  • computational methods. We are also planning to make information about Lie groups and representation theory...
  • XSSR

  • Referenced in 3 articles [sw02306]
  • special purpose computer algebra system for combinatorial group and semigroup theory. It is intended...
  • MAGNUS

  • Referenced in 7 articles [sw04278]
  • computing with infinite groups. We describe an experimental approach to studying infinite groups using ... Group Theory Cooperative. This approach emphasises infinite groups and partial and experimental computation. These computations...
  • Quantum Espresso

  • Referenced in 47 articles [sw06129]
  • computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane ... some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main...
  • SaddleDrop

  • Referenced in 14 articles [sw00824]
  • mathematics behind the computer program SaddleDrop. Based upon ideas of a group at Cornell University ... explained as we contrast the well-developed theory of one variable complex dynamics with...
  • BIGEBRA

  • Referenced in 19 articles [sw00078]
  • groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology ... well as more geometric topics of invariant theory, e.g., the Graßmann-Cayley bracket algebra ... through direct calculations using symbolic manipulation and computer algebra system (CAS). We discuss problems which...