
Macaulay2
 Referenced in 1963 articles
[sw00537]
 supporting research in algebraic geometry and commutative algebra, whose creation has been funded ... core algorithms for computing Gröbner bases and graded or multigraded free resolutions of modules ... over quotient rings of graded or multigraded polynomial rings with a monomial ordering ... integral closure of rings, and more. Computer algebra system...

Geometer's Sketchpad
 Referenced in 228 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...

CAMS
 Referenced in 14 articles
[sw18051]
 paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow ... compared against an industrialgrade 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 5 articles
[sw12131]
 carries the structure of a differential graded algebra, and the induced algebra structure...

GradedLieAlgebras
 Referenced in 3 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 12Presented Graded Hopf Algebra Whose Hilbert Series Converges in the Unit Circle...

Lie algebra gradings
 Referenced in 2 articles
[sw41558]
 Gradings for nilpotent Lie algebras. We present ... constructive approach to torsionfree gradings of Lie algebras. Our main result is the computation ... maximal grading. Given a Lie algebra, using its maximal grading we enumerate...

autgradalg.lib
 Referenced in 2 articles
[sw27091]
 software package to compute automorphisms of graded algebras. We present a library autgradalg.lib ... integral, finitely generated Calgebras that are graded pointedly by a finitely generated abelian group...

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...

Schubert2
 Referenced in 5 articles
[sw16709]
 equations. Instead, one gives its graded intersection ring of algebraic cycle classes modulo numerical equivalence...

Talgebra
 Referenced in 1 article
[sw34177]
 exercises in four areas of school algebra (Grades 48): calculation of the values ... systems; operations with monomials and polynomials. Talgebra implements 61 task types. The student solves...

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...

CHAMP
 Referenced in 6 articles
[sw08494]
 Verma modules for restricted rational Cherednik algebras. Part of this package ... simple modules as graded Gmodules for generic restricted rational Cherednik algebras for around half...

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 semialgebraic 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...

clifford
 Referenced in 2 articles
[sw32631]
 linear algebra and several other independent mathematical systems. Scalars, vectors, and highergrade 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 qWeyl 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...