• Aligator

  • Referenced in 10 articles [sw00029]
  • software package Aligator for automatically inferring polynomial loop invariants. The package combines algorithms from symbolic ... loop variables, computing the ideal of polynomial invariants by variable elimination, invariant filtering and completeness...
  • SADE

  • Referenced in 19 articles [sw07076]
  • classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE’s (previously ... determination of quasi-polynomial first-integrals, Lie symmetries and invariant surfaces. Examples...
  • QPSI

  • Referenced in 4 articles [sw09344]
  • determination of quasi-polynomial symmetries and invariants We present the quasi-polynomial symmetries and invariants ... systematic determination of quasi-polynomial symmetries, invariants and invariant tensor fields for dynamical systems...
  • Aligator.jl

  • Referenced in 3 articles [sw26257]
  • software package for automatically generating all polynomial invariants of the rich class of extended ... variables and infer the ideal of polynomial invariants by variable elimination based on Gröbner basis...
  • FourTiTwo

  • Referenced in 8 articles [sw07615]
  • Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals This paper ... chains of lattice ideals in polynomial rings that are invariant under a symmetric group action ... polynomial rings are increasing in Krull dimension. Underlying many computations is the fact that ... nice orderings, the authors show that invariant chains of Laurent lattice ideals stabilize...
  • posets

  • Referenced in 18 articles [sw07773]
  • computing various poset invariants, such as Möbius functions or h-polynomials. Also included...
  • ObservabilityTest

  • Referenced in 20 articles [sw36921]
  • algorithm to test local algebraic observability in polynomial time. The following questions are often encountered ... model letting the inputs and the outputs invariant. We present a probabilistic seminumerical algorithm that ... proposes a solution to this problem in polynomial time. A bound for the necessary number...
  • DISCOVERER

  • Referenced in 55 articles [sw07719]
  • work of complete discrimination systems of polynomials [33,31],, we invented new theories and algorithms ... including SAS-solving itself, termination analysis and invariant generation of programs, and reachability computation...
  • ProjectionCAD

  • Referenced in 8 articles [sw09911]
  • respect to equational constraint and truth-table invariant. There are also commands for choosing ... McCallum’s delineating polynomials and the only package to offer order-invariant output. [England13b] describes...
  • GrIP

  • Referenced in 1 article [sw32821]
  • based package that computes the Group Invariant Polynomial of (super)fields. The user needs...
  • Flow*

  • Referenced in 22 articles [sw20162]
  • model-based flowpipe construction for non-linear (polynomial) hybrid systems. Flow* combines well-known Taylor ... combination of approaches for handling mode invariants and discrete transitions. Flow* supports a wide variety...
  • symmChainGens

  • Referenced in 8 articles [sw06689]
  • study chains of lattice ideals that are invariant under a symmetric group action ... ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus...
  • Mint

  • Referenced in 1 article [sw16342]
  • just the sum of Symanzik polynomials. The relevant topological invariant...
  • InvariantRing

  • Referenced in 1 article [sw12134]
  • describing the invariant ring of finite group actions on polynomial rings in characteristic zero...
  • GENOM3CK

  • Referenced in 2 articles [sw07655]
  • singularity, the Alexander polynomial of each algebraic link, the delta-invariant of each singularity...
  • ABC

  • Referenced in 7 articles [sw09721]
  • Iteration bounds are obtained from the inferred invariants, by replacing variables with bounds on their ... derived symbolic bounds express non-trivial polynomial relations over loop variables. We also report...
  • KnotTwister

  • Referenced in 1 article [sw34526]
  • computes twisted Alexander polynomials of knots which are isotopy invariants. Some help can be found...
  • MapDE

  • Referenced in 1 article [sw35022]
  • vector fields leaving R invariant. For systems of exact differential polynomials R, ^R our algorithm ... that map the infinitesimals of the Lie invariance algebra for R to those...