• Macaulay2

  • Referenced in 1841 articles [sw00537]
  • supporting research in algebraic geometry and commutative algebra, whose creation has been funded ... core algorithms for computing Gröbner bases and graded or multi-graded free resolutions of modules ... over quotient rings of graded or multi-graded polynomial rings with a monomial ordering ... integral closure of rings, and more. Computer algebra system...
  • Geometer's Sketchpad

  • Referenced in 227 articles [sw04858]
  • gives students at all levels—from third grade through college—a tangible, visual ... school students can build their readiness for algebra by exploring ratio and proportion, rate...
  • C-AMS

  • Referenced in 13 articles [sw18051]
  • paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow ... compared against an industrial-grade Algebraic MultiGrid (AMG) solver. Results of this comparison illustrate that...
  • ANICK

  • Referenced in 10 articles [sw18779]
  • Yoneda product in the noncommutative graded algebras...
  • PurityFiltration

  • Referenced in 10 articles [sw07656]
  • grade filtration can be explicitly characterized by means of elementary methods of homological algebra ... literature of algebraic analysis. Efficient implementations dedicated to the computation of grade filtration can then ... standard computer algebra systems. Moreover, this characterization of grade filtration is shown to induce ... standard PDE solvers of computer algebra systems such as Maple...
  • CodepthThree

  • Referenced in 4 articles [sw12131]
  • carries the structure of a differential graded algebra, and the induced algebra structure...
  • GradedLieAlgebras

  • Referenced in 2 articles [sw27126]
  • package for doing computations in graded Lie algebras. This package provides routines for doing computations ... graded Lie algebras. The package relies on algorithmic theory on graded Lie algebras developed ... Nonnilpotent 1-2-Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle...
  • Poincare_Series

  • Referenced in 12 articles [sw06953]
  • respectively. The algebras ℐ d and 𝒞 d are graded subalgebras ... dimensions of the multihomogeneous components of the algebras. First he presents an analogue...
  • autgradalg.lib

  • Referenced in 1 article [sw27091]
  • software package to compute automorphisms of graded algebras. We present a library autgradalg.lib ... integral, finitely generated C-algebras that are graded pointedly by a finitely generated abelian group...
  • T-algebra

  • Referenced in 1 article [sw34177]
  • exercises in four areas of school algebra (Grades 4-8): calculation of the values ... systems; operations with monomials and polynomials. T-algebra implements 61 task types. The student solves...
  • Schubert2

  • Referenced in 4 articles [sw16709]
  • equations. Instead, one gives its graded intersection ring of algebraic cycle classes modulo numerical equivalence...
  • CONTRACTIONS

  • Referenced in 1 article [sw17828]
  • computer calculation of graded contractions of Lie algebras and their representations. We present a computer ... defining equations for grading preserving contractions of Lie algebras of any type, and their representations ... perform contractions of Lie algebras and/or representations for which the grading is either generic...
  • STRATIFY

  • Referenced in 1 article [sw18775]
  • computing the intersection of (some) graded structures of commutative algebra and computing the stratification ... finitely many disjoint basic open semi-algebraic sets, called strata. A set of fundamental invariants ... finitely generated graded subalgebras, which can be specialized to compute invariants of algebraic groups ... intersection of graded submodules, which can be specialized to compute equivariants of algebraic groups. Moreover...
  • DGAlgebras

  • Referenced in 1 article [sw16716]
  • types and basic functions on differential graded (DG) Algebras. This package is used to define...
  • FieldsX

  • Referenced in 1 article [sw34826]
  • Fierz identities, invariant tensors on Lie algebras, arbitrary gradings and left and right variational derivatives...
  • CHAMP

  • Referenced in 4 articles [sw08494]
  • Verma modules for restricted rational Cherednik algebras. Part of this package ... simple modules as graded G-modules for generic restricted rational Cherednik algebras for around half...
  • clifford

  • Referenced in 2 articles [sw32631]
  • linear algebra and several other independent mathematical systems. Scalars, vectors, and higher-grade entities...
  • ncfactor.lib

  • Referenced in 1 article [sw23797]
  • polynomials are implemented for three types of algebras, all generated ... shift and graded polynomials in n’th q-Weyl algebras) over a field K. More...
  • ncHilb

  • Referenced in 2 articles [sw27177]
  • computation of multigraded Hilbert series to algebras that are invariant under the action ... efficient and complete implementation of (standard) graded and multigraded Hilbert series that has been developed ... kernel of the computer algebra system {sc Singular}. A large set of tests provides...
  • LIESUPER

  • Referenced in 2 articles [sw15674]
  • symbolic computations in (free) Lie (super)algebras. For this purpose we will introduce ... liebracket, which satisfies the bilinearity and the (graded) skew-symmetry of the liebracket. Moreover...