SymmetricReduction[f, {x_1, ..., x_n}] gives a pair of polynomials {p, q} in x_1, ..., x_n such that f == p + q, where p is the symmetric part and q is the ...

Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

LayeredGraphPlot attempts to draw the vertices of a graph in a series of layers, placing dominant vertices at the top, and vertices lower in the hierarchy progressively ...

Mathematica handles formulas of all types, from polynomials with millions of terms to complex combinations of higher mathematical functions. It provides powerful general ...

Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.

"Manipulating Elements of Lists" shows how you can pick out elements of lists based on their positions. Often, however, you will need to select elements based not on where ...

Built into Mathematica are state-of-the-art constrained nonlinear fitting capabilities, conveniently accessed with models given directly in symbolic form. Mathematica also ...

Mathematica 6.0 fundamentally redefined Mathematica and introduced a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

If you have a list of elements, it is often important to be able to apply a function separately to each of the elements. You can do this in Mathematica using Map. This ...