We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space ...

The area of numerical computation tends to break somewhat naturally into three subareas which, for want of better terms, we will call sampling, linear algebra, and theory. ...

Spin and spatial tensor manipulations are frequently required to describe the theory of NMR experiments. A Mathematica package is presented here, which provides some of the ...

We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well ...

The Mathematica quantum computer simulation packages QDENSITY and QCWAVE are updated for Mathematica 9-10.3. An overview is given of the new QDensity, QCWave, BTSystem and ...

In this article we will show how to use Mathematica in dealing with curves and surfaces in the three dimensional unit sphere S3 embedded in the four dimensional Euclidian ...

We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincare groups. Using these ...

The package NFourierListCoefficients is intended for calculation of list of Fourier coefficients for a given function. It is necessary in many applications when a ...

We use the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions ...

Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two ...