Root[f, k] represents the exact k\[Null]^th root of the polynomial equation f[x] == 0. Root[{f, x_0}] represents the exact root of the general equation f[x] == 0 near x = ...

Many calculations involve solving systems of linear equations. In many cases, you will find it convenient to write down the equations explicitly, and then solve them using ...

The Mathematica function NDSolve is a general numerical differential equation solver. It can handle a wide range of ordinary differential equations (ODEs) as well as some ...

Introduction to Differential Equation Solving with DSolve Classification of Differential Equations Ordinary Differential Equations (ODEs)

NullSpace[m] gives a list of vectors that forms a basis for the null space of the matrix m.

HermiteDecomposition[m] gives the Hermite normal form decomposition of an integer matrix m.

Mathematica handles both integers and real numbers with any number of digits, automatically tagging numerical precision when appropriate. Mathematica internally uses several ...

Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly-optimized algorithms. Using many original methods, ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...