Related papers: Normaliz 2013-2016
Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of…
Normaliz is a program for solving linear systems of inequalities. In this paper we present the algorithms implemented in the program, starting with version 2.0.
We discuss the computation of automorphism groups and normal forms of cones and polyhedra in Normaliz, and indicate its implementation via nauty. The types of automorphisms include integral, rational, Euclidean and combinatorial, as well as…
We describe the implementation of algebraic polyhedra in Normaliz. In addition to convex hull computation/vertex enumeration, it is possible to compute triangulations, volumes, lattice points, face lattices and automorphism groups. The…
We describe the use of pyramid decomposition in Normaliz, a software tool for the computation of Hilbert bases and enumerative data of rational cones and affine monoids. Pyramid decomposition in connection with efficient parallelization and…
We study regular inclusions of finite-dimensional von Neumann algebras from a matrix-theoretic perspective. To this end, we introduce a new combinatorial invariant of an inclusion, called the normalizer matrix, which encodes the structure…
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…
The theory of associative $n$-categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant, this is potentially attractive, since it has the potential…
In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions…
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques…
We propose algebraic protocols that enable the definition of protocol templates and session types analogous to the definition of domain-specific types with algebraic datatypes. Parameterized algebraic protocols subsume all regular as well…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
We survey the computation of polytope volumes by the algorithms of Normaliz to which the Lawrence algorithm has recently been added. It has enabled us to master volume computations for polytopes from social choice in dimension $119$. This…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
We generalize a regularization method of Stumpf 1984 in the case of non-linear spinor field models to fourth order theories and to non-scalar interactions. The involved discrete symmetries can be connected with C,P,T transformations.
In our paper "On D-module of categories I", we provide two different methods of constructing D-module structures on the complex computing periodic cyclic homology associated to a family of stable infinity categories. One is based on a…
Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita-Takesaki modular theory and its applications to quantum field theory. In this article, inclusions of standard subspaces are studied…
Contents of this issue: Workshops on SPM themes; Second workshop on Coverings, Selections and Games in Topology (SPM05); Analysis and Descriptive Set Theory Workshop; Descriptive set theory: Effective methods, equivalence relations;…
In this paper, we introduces and undertake as a systematical investigation of the class $\mathcal{P}_{\mathcal{H}}^{0}(\alpha,M)$ of normalized harmonic mappings $f = h + \overline{g}$ in the unit disk $\mathbb{D}$, defined by the…