Combinatorica extends Mathematica by over 450 functions in combinatorics and graph theory. It includes functions for constructing graphs and other combinatorial objects, ...

SquareFreeQ, PrimePowerQ, KroneckerSymbol, ChineseRemainder and PrimitiveRoot have been added to the built-in Mathematica kernel functions. NextPrime and PreviousPrime are ...

Fibonacci[n] gives the Fibonacci number F_n. Fibonacci[n, x] gives the Fibonacci polynomial F_n (x).

LQEstimatorGains[ss, {w, v}] gives the optimal estimator gain matrix for the StateSpaceModel object ss with process and measurement noise covariance matrices w and ...

SeriesCoefficient[series, n] finds the coefficient of the n\[Null]\[Null]^th-order term in a power series in the form generated by Series. SeriesCoefficient[f, {x, x_0, n}] ...

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

MatrixPlot[m] generates a plot that gives a visual representation of the values of elements in a matrix.

While DSolve usually returns the correct solution to a differential equation it is given, it is common practice to verify the solution returned by any differential equation ...

ImageCompose[image, overlay] gives the result of overlaying overlay onto image. ImageCompose[image, {overlay, \[Alpha]}] gives the result of alpha blending overlay into image ...

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...