• Kenzo

  • Referenced in 54 articles [sw04861]
  • called the Fundamental Theorem of Algebraic Topology. The first version of the program, called...
  • FeynArts

  • Referenced in 79 articles [sw06474]
  • platform for topology editing. Computer algebra system...
  • CHomP

  • Referenced in 27 articles [sw09358]
  • that these techniques be computationally efficient. Algebraic Topology is the classical mathematical tool ... large datasets can be reduced to compact algebraic expressions that provide insight into underlying geometric ... develop and apply efficient and effective topologically based methods to the analysis of nonlinear systems...
  • insulate

  • Referenced in 17 articles [sw21729]
  • exact computation of the topology of real algebraic curves. We consider the problem of computing ... those polynomials are algebraic numbers. Various algebraic approaches for this real root finding and counting ... case of computing the topology of a single real algebraic curve. Even this prototypical implementation...
  • fKenzo

  • Referenced in 5 articles [sw01156]
  • user interface for computations in algebraic topology. fKenzo is an integral assistant for research ... subset of) Algebraic Topology. The ”integral” adjective means that this assistant not only provides...
  • Homology

  • Referenced in 23 articles [sw04871]
  • algorithms Geometric properties of topological spaces are conveniently expressed by algebraic invariants of the space...
  • Axel

  • Referenced in 21 articles [sw06457]
  • curves, singularities of algebraic curves or surfaces, certified topology of curves and surfaces...
  • Reduze

  • Referenced in 33 articles [sw10354]
  • topologies and integrals. Reduze uses GiNaC or, optionally, Fermat to perform manipulations of algebraic expressions...
  • HAP

  • Referenced in 27 articles [sw04870]
  • library for use with the GAP computer algebra system, and is still under development ... regular CW-complexes in the context of topological data analysis...
  • GENOM3CK

  • Referenced in 2 articles [sw07655]
  • computing the genus of a plane complex algebraic curve using knot theory. The library also ... singularities of the curve, the topological type (algebraic link) of each singularity, the Alexander polynomial...
  • Sheafhom 2.0

  • Referenced in 1 article [sw00854]
  • applications. The package is motivated by algebraic topology, and provides partial support for items from...
  • SimplicialVIEW

  • Referenced in 1 article [sw21821]
  • simplicial approximation theorem of algebraic topology to develop the theoretical foundation, and put it into...
  • Globular

  • Referenced in 2 articles [sw18031]
  • formalization of proofs from logic, topology and algebra which are not formalizable by other methods...
  • Zeta

  • Referenced in 4 articles [sw13746]
  • Zeta provides methods for computing topological zeta functions arising from the enumeration of subalgebras, ideals ... submodules, and representations of suitable algebraic structures. For theoretical background and descriptions of the methods...
  • PolyMesher

  • Referenced in 26 articles [sw13340]
  • codes that use linear convex polygons. In topology optimization, polygonal discretizations have been shown ... construct a large class of domains via algebraic expressions. Examples are provided to illustrate...
  • TituRel

  • Referenced in 6 articles [sw08501]
  • many explorative investigations: games, (bi-)simulations, topology, qualitative fuzzy considerations, theory extraction, social choice, decision ... support via interval orderings, etc. TituRel supports algebraic visualizations, proofs and transformations. Its generic construction...
  • SARAG

  • Referenced in 3 articles [sw00826]
  • with: theory of signed sub-resultants, linear algebra, gcd computation, real roots counting, real roots ... sign determination, Thom encodings, study of the topology of curves. At the moment SARAG...
  • Parsol

  • Referenced in 20 articles [sw00684]
  • presents user with the set of linear algebra objects (multidimentional arrays, vectors, sparse and dense ... adding several lines of code (initialization, topology specification and data exchange). The parallel version should...
  • Bertini_real

  • Referenced in 5 articles [sw09933]
  • dimensional complex irreducible algebraic set in any reasonable number of variables. Using numerical homotopy continuation ... using isosingular deflation. This decomposition captures the topological information and can be used for further...
  • VFC package

  • Referenced in 3 articles [sw16729]
  • algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves. We develop ... applications as foundations for invariants in symplectic topology arising from “counting” pseudo-holomorphic curves ... prove appropriate gluing theorems. We require only topological gluing theorems, that is, smoothness ... approach to virtual fundamental cycles is algebraic rather than geometric (in particular...