## 1.5.14 Packages for Symbolic Mathematics

There are many Mathematica packages which implement symbolic mathematical operations. This section gives a few examples drawn from the standard set of packages distributed with Mathematica. As discussed in Section 1.3.10, some copies of Mathematica may be set up so that the functions described here are automatically loaded into Mathematica if they are ever needed.

### Vector Analysis

 <

Vector analysis.
This loads the vector analysis package. In some versions of Mathematica, you may not need to load the package explicitly.
 In[1]:=  <
This specifies that a spherical coordinate system with coordinate names r, theta and phi should be used.
 In[2]:=  SetCoordinates[Spherical[r, theta, phi]]
 Out[2]=
This evaluates the gradient of in the spherical coordinate system.
 In[3]:=  Grad[r^2 Sin[theta]]
 Out[3]=

### Variational Methods

 <

Variational methods.
This loads the variational methods package.
 In[1]:=  <
This finds the functional derivative of .
 In[2]:=  VariationalD[y[x] Sqrt[y'[x]], y[x], x]
 Out[2]=

### Quaternions

 <

Quaternions.
This loads the quaternions package.
 In[1]:=  <
This finds the principal square root of a quaternion.
 In[2]:=  Sqrt[Quaternion[1, 1, 1, 0]]
 Out[2]=

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