Invariant simplices for subtractive algorithms

Affine Invariant Contractions of Simplices

It is known that every hyperbolic Iterated Function System containing affine mappings can be represented in barycentric form by which it becomes affine invariant. Some properties were surveyed and some new ones were established. Examples of fractal sets supplement the theory.

Veriication of Ieee Compliant Subtractive Division Algorithms

A parameterized deenition of subtractive oating point division algorithms is presented and veriied using PVS. The general algorithm is proven to satisfy a formal deenition of an IEEE standard for oating point arithmetic. The utility of the general speciication is illustrated using a number of diierent instances of the general algorithm.

Verification of IEEE Compliant Subtractive Division Algorithms

A parameterized deenition of subtractive oating point division algorithms is presented and veriied using PVS. The general algorithm is proven to satisfy a formal deenition of an IEEE standard for oating point arithmetic. The utility of the general speciication is illustrated using a number of diierent instances of the general algorithm.

Algorithms for Transposition Invariant String

Euclidean Simplices and Invariants of Three-manifolds: a Modification of the Invariant for Lens Spaces

It is well-known that any two triangulations of a piecewise-linear three-manifold can be transformed into each other using local “Pachner moves”. If we construct an algebraic expression depending on some values ascribed to a manifold triangulation and invariant under these moves, we get a value that does not depend on a specific triangulation. It is natural to call such value an invariant of th...