Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...

ClearNotations[] will remove all notations, symbolizations and infix notations.

IntegerDigits[n] gives a list of the decimal digits in the integer n. IntegerDigits[n, b] gives a list of the base b digits in the integer n. IntegerDigits[n, b, len] pads ...

RotationMatrix[\[Theta]] gives the 2D rotation matrix that rotates 2D vectors counterclockwise by \[Theta] radians.RotationMatrix[\[Theta], w] gives the 3D rotation matrix ...

Evaluate[expr] causes expr to be evaluated even if it appears as the argument of a function whose attributes specify that it should be held unevaluated.

Converting to and from character codes. Mathematica assigns every character that can appear in a string a unique character code. This code is used internally as a way to ...

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

LinkRead[link] reads one expression from the specified MathLink connection. LinkRead[link, h] wraps h around the expression read before evaluating it.

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, ...

This package provides an interactive tool for investigating the solutions of differential equations as well as other types of equations that have solutions that can be viewed ...