We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift...

We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending translation, our connection allows for the exchange of arbitrary information between the two systems. We show how to make use of the Lean metaprogramming framework to v...

We provide an introduction to automated theorem proving for the Mathematica community. Specifically, we show how to implement, in Mathematica, the Davis-Putnam algorithm, as modified in [3]. We then apply our program to show by computer, that in any group, a left inverse is also a right inverse, a problem that was left unsolved in [3] because the computers that were available at the time lacked...

Modelica is a new object-oriented multi-domain modeling language based on algebraic and differential equations. In this paper we present an environment that integrates different phases of the Modelica development lifecycle. This is achieved by using the Mathematica environment and its structured documents, “notebooks”. Simulation models are represented in the form of structured documents, which...

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the supe...

We call our approach geometrical as instead of considering 6-fold integral in abstract space we consider random triangle (RT) inside the plane rectangle when all possible cases are explicitly apparent. Area of triangle with vertices p1=(x1,y1), p2=(x2,y2), p3=(x3,y3) is equal to s = 1 2 (x1(y2− y3) + x2 (−y1 + y3) + x3 (y1− y2)). (1) Let points p1, p2, p3 are randomly (with constant differentia...

Coloring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring graphs by using webMathematica which is the new web-based technology. In this paper, we describe some web-based interactive examples on graph coloring with webMathematica.

In this paper, we present an implementation of the harmonic polylog-arithm of Remiddi and Vermaseren [1] for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Man...