RootOfUnityQ[a] yields True if a is a root of unity, and yields False otherwise.

ObservabilityGramian[ss] gives the observability Gramian of the StateSpaceModel object ss.

This package provides functions for performing a univariate Analysis of Variance (ANOVA) to examine the differences between groups of means. The function ANOVA can handle ...

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...

DifferentialRootReduce[expr, x] attempts to reduce expr to a single DifferentialRoot object as a function of x.DifferentialRootReduce[expr, {x, x_0}] takes the initial ...

Mathematica uses a large number of original algorithms to provide automatic systemwide support for inequalities and inequality constraints. Whereas equations can often be ...

Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of ...

SystemsModelDimensions[sys] gives the number of inputs and outputs of a StateSpaceModel or TransferFunctionModel object sys.

NumberFieldRootsOfUnity[a] gives the roots of unity for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Following are two examples of nonlinear systems of ODEs that can be solved symbolically using DSolve. The first three equations in this system of four nonlinear ODEs can be ...