• Macaulay2

  • Referenced in 1658 articles [sw00537]
  • supporting research in algebraic geometry and commutative algebra, whose creation has been funded ... since 1992. Macaulay2 includes core algorithms for computing Gröbner bases and graded or multi-graded ... installation of methods for computing specifically with them. Macaulay2 can compute Betti numbers, Ext, cohomology ... integral closure of rings, and more. Computer algebra system...
  • DLMF

  • Referenced in 2225 articles [sw04968]
  • covered include mathematical formulas, graphs, references, methods of computation, and links to software. Special features ... example, or for input to computer algebra systems. These and other problems, and some partially...
  • FEniCS

  • Referenced in 553 articles [sw04314]
  • computing, with a particular focus on automated solution of differential equations by finite element methods ... library of finite elements, high performance linear algebra and many more...
  • Chebfun

  • Referenced in 327 articles [sw05897]
  • MATLAB that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise ... also implements continuous analogues of linear algebra notions like the QR decomposition...
  • BLAD

  • Referenced in 19 articles [sw08612]
  • This paper describes applications of a computer algebra method, differential elimination, to applied mathematics problems ... which is embedded in the MAPLE computer algebra software, and the BLAD libraries which...
  • REDLOG

  • Referenced in 160 articles [sw04250]
  • that extends the computer algebra system REDUCE to a computer logic system, i.e., a system ... theorem provers, the methods applied know about the underlying algebraic theory and make...
  • BoomerAMG

  • Referenced in 158 articles [sw00086]
  • been a recent resurgence of interest in algebraic multigrid (AMG). AMG is attractive in that ... development of massively parallel computers, and has sparked much research into developing algorithms for them ... task, however. While much of the AMG method parallelizes readily, the process of coarse-grid ... Jones, Coarse grid selection for parallel algebraic multigrid, in: A. Ferriera, J. Rollin, H. Simon...
  • ApaTools

  • Referenced in 17 articles [sw01344]
  • software toolbox ApaTools for approximate polynomial algebra. This package includes Maple and Matlab functions implementing ... developing other numerical and symbolic methods in computational algebra...
  • redbKIT

  • Referenced in 162 articles [sw12977]
  • presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses ... implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors ... decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both ... posteriori error analysis. Reduced basis methods for partial differential equations. An introduction. The whole mathematical...
  • STRINGVACUA

  • Referenced in 41 articles [sw00920]
  • powerful algebro-geometric methods, as implemented in the free computer algebra system Singular, but requires...
  • CRACK

  • Referenced in 57 articles [sw07754]
  • computer program. A method to reduce the length of the equations for large bilinear algebraic ... equations are studied. An overview of the computer algebra program CRACK used in this paper...
  • xTras

  • Referenced in 27 articles [sw16622]
  • present the tensor computer algebra package xTras, which provides functions and methods frequently needed when ... classical) field theory. Amongst others, it can compute contractions, make Ansätze, and solve tensorial equations ... built upon the tensor computer algebra system xAct, a collection of packages for Mathematica...
  • SLICOT

  • Referenced in 80 articles [sw01095]
  • algorithms for computations in systems and control theory. Based on numerical linear algebra routines from ... BLAS and LAPACK libraries, SLICOT provides methods for the design and analysis of control systems...
  • SOCS

  • Referenced in 124 articles [sw07737]
  • algebra technology to solve very large optimization problems orders of magnitude faster than traditional methods ... solved efficiently on desktop computers. The Sparse Nonlinear Programming software is available as an integral...
  • Mgfun

  • Referenced in 8 articles [sw06227]
  • which makes the class amenable to computer algebra methods and enjoy numerous algorithmic closure properties...
  • ODEtools

  • Referenced in 11 articles [sw09257]
  • order ODEs using symmetry methods. A Maple V R.3/4 computer algebra package, ODEtools ... differential equations (ODEs) using Lie group symmetry methods is presented. The set of commands includes...
  • Homology

  • Referenced in 30 articles [sw04871]
  • Computing simplicial homology based on efficient Smith normal form algorithms Geometric properties of topological spaces ... algebraic invariants of the space. This paper focuses on methods for the computer calculation ... example with calculations of Lie algebra homology...
  • ADAM

  • Referenced in 8 articles [sw21957]
  • discrete models of biological systems using computer algebra. BACKGROUND: Many biological systems are modeled qualitatively ... Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM ... dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors ... equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete...
  • Algorithm 731

  • Referenced in 37 articles [sw12847]
  • CWRESU and CWRESX, which compute the residuals of the differential algebraic equations (DAE) system obtained ... must be applied, for example, a BDF method such as implemented in the DAE solvers...
  • CWRESU

  • Referenced in 37 articles [sw12903]
  • CWRESU and CWRESX, which compute the residuals of the differential algebraic equations (DAE) system obtained ... must be applied, for example, a BDF method such as implemented in the DAE solvers...