The theory of Gröbner bases is the basis of Mathematica's Solve and related functions. This article gives an introduction to the theory via three applications: solving ...

The general scheme, suggested in [1] using a basis of an infinite-dimensional space and allowing to construct finite-dimensional orthogonal systems and interpolation ...

Getting a smooth curve through some data points is not always enough. Sometimes it is critical to preserve the general shape suggested by the data.

A simple method has been developed in order to get a contour plot in an element with given nodal values. The contour lines are obtained by solving a differential equation ...

Parton Distribution Functions (PDFs) are essential non-perturbative inputs for calculation of any observable with hadronic initial states. These PDFs are released by ...

A Mathematica package for solving functional equations of the form is presented. The use of the package is illustrated with two applications, to conditional specification of ...

Spiral-shaped inclusion trails are visible as curves within sections of metamorphic garnet crystals. They are sections of surfaces rich in aligned inclusions of other ...

Obtaining finite difference approximations using function values at equally spaced sample points is an important problem in numerical analysis. A familiar example is ...

This is a column of programming tricks and techniques, most of which, we hope, will be contributed by our readers, either directly as submissions to The Mathematica Journal ...

A finite element method for numerical solutions of the systems governed by distributed models of Hopfield-type neural network equations is studied. When time keeps continuous ...