Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

The function NDSolve discussed in "Numerical Differential Equations" allows you to find numerical solutions to differential equations. NDSolve handles both single ...

StirlingS1[n, m] gives the Stirling number of the first kind S_n^(m).

MorphologicalEulerNumber[image] computes the morphological Euler number of regions in a binary image.MorphologicalEulerNumber[image, t] treats values above t as foreground.

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

Algebraic is now available as the newly added built-in Mathematica kernel function AlgebraicNumber. ToCommonField and ToNumberFieldElement are now available as the newly ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

You can use most of the list operations discussed in "Lists" on any kind of Mathematica expression. By using these operations, you can manipulate the structure of expressions ...

VectorPoints is an option to VectorPlot, ListVectorPlot, and related functions that determines how many field vectors to draw.

When you use //N to get a numerical result, Mathematica does what a standard calculator would do: it gives you a result to a fixed number of significant figures. You can also ...