MaximalIndependentVertexSet[g] gives a maximal independent vertex set of an undirected graph g.MaximalIndependentVertexSet[g, w] gives a maximal independent vertex set of g ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Mathematica can run its calculations on other computers that have Mathematica installed. Passing computations to other, potentially more powerful, machines can increase the ...

LogicalExpand[expr] expands out logical combinations of equations, inequalities, and other functions.

ContourPlot3D[f, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}] produces a three-dimensional contour plot of f as a function of x, y, and z. ContourPlot3D[f == g, ...

Root[f, k] represents the exact k\[Null]^th root of the polynomial equation f[x] == 0. Root[{f, x_0}] represents the exact root of the general equation f[x] == 0 near x = ...

If you experience internet connectivity problems, such as trouble using Mathematica's integrated data functions, try following the troubleshooting techniques described below. ...

Mathematica's unified symbolic architecture allows arbitrary extensibility in the output and input of notation.

Sparse representations of matrices are useful because they do not store every element. If one particular value appears very frequently it can be very advantageous to use a ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.