Complex Polynomial Systems (Mathematica Tutorial)

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

Notebook Basics (Mathematica Guide)

From simple calculations to full publishable documents and sophisticated dynamic interfaces, everything you can do with Mathematica's standard interactive interface is done ...

CUDALink Overview (CUDALink Overview)

CUDALink allows Mathematica to use the CUDA parallel computing architecture on Graphical Processing Units (GPUs). It contains functions that use CUDA-enabled GPUs to boost ...

Part (Built-in Mathematica Symbol)

expr[[i]] or Part[expr, i] gives the i\[Null]^th part of expr. expr[[-i]] counts from the end. expr[[i, j, ...]] or Part[expr, i, j, ...] is equivalent to expr[[i]][[j]] .... ...

ContourPlot (Built-in Mathematica Symbol)

ContourPlot[f, {x, x_min, x_max}, {y, y_min, y_max}] generates a contour plot of f as a function of x and y. ContourPlot[f == g, {x, x_min, x_max}, {y, y_min, y_max}] plots ...

Numerical Functions (Mathematica Guide)

Throughout Mathematica there is support not only for approximate real numbers, but also for exact numbers represented in algebraic or symbolic form. Functions like Floor, ...

Advanced Numerical Differential ... (Mathematica Tutorial)

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...

Rational Functions (Mathematica Guide)

Mathematica can efficiently handle both univariate and multivariate rational functions, with built-in functions immediately implementing standard algebraic transformations.

Solving Linear Systems (Mathematica Tutorial)

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

Cryptographic Number Theory (Mathematica Guide)

Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language make it uniquely suited to both research ...