When fitting models to data, it is often useful to analyze how well the model fits the data and how well the fitting meets the assumptions of the model. For a number of ...

Exact global optimization problems can be solved exactly using Minimize and Maximize. This computes the radius of the circle, centered at the origin, circumscribed about the ...

CylindricalDecomposition[ineqs, {x_1, x_2, ...}] finds a decomposition of the region represented by the inequalities ineqs into cylindrical parts whose directions correspond ...

Mathematica is built to handle arbitrarily large computations—limited only by computer time and memory—and provides a collection of convenient global safety features to ...

Mathematica supports zeta and polylogarithm functions of a complex variable in full generality, performing efficient arbitrary-precision evaluation and implementing extensive ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Combinatorial functions. The factorial function n! gives the number of ways of ordering n objects. For non-integer n, the numerical value of n! is obtained from the gamma ...

These "How tos" give step-by-step instructions for common tasks related to algebraic computation in Mathematica .

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...

SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.