Related papers: S@M, a Mathematica Implementation of the Spinor-He…
We give a comprehensive review of recent developments on using the pure spinor formalism to compute massless superstring scattering amplitudes at tree level. The main results of the pure spinor computations are placed into the context of…
Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools.…
The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R.…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…
We present a method for symbolic evaluation of Feynman amplitudes. We construct special polarization basis for spinor particles which produces compact expressions for tensor products of basis spinors.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We propose a 2-categorical formalism for describing classical information, quantum systems, and their interactions, based on the principle that classical information can be encoded as correlations between quantum systems. Applying this in…
As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with…
We give a spinorial set of Hamiltonian variables for General Relativity in any dimension greater than 2. This approach involves a study of the algebraic properties of spinors in higher dimension, and of the elimination of second-class…
We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and…
Number sequences with wide-ranging applications in mathematics, physics, medicine, and engineering remain an active research topic. This study examines these sequences through the general framework of Horadam numbers and their special cases…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
We introduce an intrinsic filtration to the magnitude chain complex of a metric space, and study basic properties of the associated spectral sequence of the magnitude homology. As an application, the third magnitude homology of the circle…
Pointer arithmetic is widely used in low-level programs, e.g. memory allocators. The specification of such programs usually requires using pointer arithmetic inside inductive definitions to define the common data structures, e.g. heap lists…
I present a simple dynamic programming algorithm for the evaluation of operators in a wide range of superconformal algebras. Special care is taken to describe the computation of the Gram matrix. A Mathematica package, Weaver.m, is provided…
A class of smoothing methods is proposed for solving mathematical programs with equimibrium constraints. We introduce new and very simple regularizations of the complementarity constraints. Some estimate distance to optimal solution and…
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to…
As helioseismology matures and turns into a precision science, modeling finite-frequency, geometric and systematical effects is becoming increasingly important. Here we introduce a general formulation for treating perturbations of arbitrary…
Using a new proposal for the "picture lowering" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type…