When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

Reduce[expr, vars] reduces the statement expr by solving equations or inequalities for vars and eliminating quantifiers. Reduce[expr, vars, dom] does the reduction over the ...

CirculantGraph[n, j] gives the circulant graph with n vertices and jump j C_n (j).CirculantGraph[n, {j_1, j_2, ...}] gives the circulant graph with n vertices and jumps j_1, ...

Waveform[type, freq, dur] creates a Sound object that is a standard waveform of type type, having a fundamental frequency of freq hertz, and a duration of dur seconds.

EconomizedRationalApproximation[expr, {x, {x_0, x_1}, m, n}] gives the economized rational approximation to expr that is good over the interval x_0 to x_1, with numerator ...

BoxLabels is an option for BoxWhiskerPlot which specifies labels to be given for each of the datasets.

ParameterRanges[] gives the intervals over which each the of the parameters in the default coordinate system may range. ParameterRanges[coordsys] gives the ranges for each of ...

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. ...

Long the standard for high-quality function and surface visualization, Mathematica incorporates a host of original numeric, symbolic, and geometric algorithms that automate ...