Packages for Symbolic Mathematics

Variational MethodsQuaternions
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
<<VariationalMethods`
load the variational methods package
VariationalD[f,y[x],x]
find the variational derivative of f
Variational methods.
This loads the variational methods package:
This finds the functional derivative of :
Quaternions
<<Quaternions`
load the quaternions package
Quaternion[a,b,c,d]
the quaternion a+bi+cj+dk
Quaternions.
This loads the quaternions package:
This finds the principal square root of a quaternion: