Packages for Symbolic Mathematics

There are many Wolfram Language packages that implement symbolic mathematical operations. Here are a few examples drawn from the standard set of packages distributed with the Wolfram System. As discussed in "Wolfram Language Packages", some copies of the Wolfram Language may be set up so that the functions described here are automatically loaded into the Wolfram Language if they are ever needed.

Variational Methods

Variational methods.

This loads the variational methods package:

<<VariationalMethods`

This finds the functional derivative of y(x)(Sqrt[y'(x)]):

VariationalD[y[x] Sqrt[y'[x]],y[x],x]

Quaternions

Quaternions.

This loads the quaternions package:

<<Quaternions`

This finds the principal square root of a quaternion:

Sqrt[Quaternion[1,1,1,0]]