One of the unique strengths of Mathematica's core language is its powerful and succinct—yet highly readable—symbolic pattern language. Convenient both for immediate use in ...

Permutations are among the most basic elements of discrete mathematics. They can be used to represent discrete groups of transformations and in particular play a key role in ...

Mathematica allows convenient automated selection of plotting and image regions using a family of specially developed robust algorithms, as well as allowing detailed manual ...

With its core symbolic paradigm and immediate access to sophisticated numerical, symbolic and geometric algorithms, Mathematica is able to provide a uniquely flexible and ...

Mathematica provides unified graphics support for 2D and 3D polygons, allowing all standard Mathematica colors and transparency to be used for both faces and edges, as well ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

As with integers, operations related to division are key to many computations with polynomials. Mathematica includes not only highly optimized univariate polynomial-division ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...