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GELDA
GELDA is a Fortran77 software package for the numerical integration of general linear differential-algebraic equations (DAE) with variable coefficients of arbitrary index. The implementation of GELDA is based on the construction of the discretization scheme, which first determines all the local invariants and then transforms the linear DAE into an equivalent strangeness-free DAE with the same solution set. The resulting strangeness-free system is allowed to have nonuniqueness in the solution set or inconsistency in the initial values or inhomogeneities. In the case that the DAE is found to be uniquely solvable, GELDA is able to compute a consistent initial value and apply the well-known integration schemes for DAEs. In GELDA the BDF methods and Runge-Kutta schemes are implemented.
More informationGEOMS
GEOMS is a Fortran77 software package for the numerical integration of general model equations (equations of motion) of multibody systems. The code combines a regularization technique with the Runge-Kutta method of type Radau IIa of order 5. This regularization technique reduces the index under preservation of all information of the solution manifold and, therefore, allows a robust numerical integration of the system.
More informationNormaliz
Normaliz is a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Its input data can be specified in terms of a system of generators or vertices or a system of linear homogeneous Diophantine equations, inequalities and congruences or a binomial ideal. Normaliz computes the dual cone of a rational cone (in other words, given generators, Normaliz computes the defining hyperplanes, and vice versa), a placing (or lexicographic) triangulation of a vector configuration (resulting in a triangulation of the cone generated by it), the Hilbert basis of a rational cone, the lattice points of a lattice polytope, the normalization of an affine monoid, the Hilbert (or Ehrhart) series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example, for rational polytopes), NEW: generalized (or weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description of the cone and lattice under consideration by a system of inequalities, equations and congruences
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