Packages for Symbolic Mathematics
There are many
Mathematica packages that implement symbolic mathematical operations. Here are a few examples drawn from the standard set of packages distributed with
Mathematica. As discussed in
"Mathematica Packages", 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
| <<VectorAnalysis` | load the vector analysis package |
| SetCoordinates[system[names]] | specify the coordinate system to be used (Cartesian, Cylindrical, Spherical, etc.), giving the names of the coordinates in that system |
| Grad[f] | evaluate the gradient  of  in the coordinate system chosen |
| Div[f] | evaluate the divergence  of the list  |
| Curl[f] | evaluate the curl  of the list  |
| Laplacian[f] | evaluate the Laplacian  of  |
Vector analysis.
This loads the vector analysis package. In some versions of
Mathematica, you may not need to load the package explicitly.
This specifies that a spherical coordinate system with coordinate names
,
, and
should be used.
| Out[3]= |  |
This evaluates the gradient of
in the spherical coordinate system.
| Out[4]= |  |
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
.
| Out[6]= |  |
Quaternions
| <<Quaternions` | load the quaternions package |
| Quaternion[a,b,c,d] | the quaternion  |
Quaternions.
This loads the quaternions package.
This finds the principal square root of a quaternion.
| Out[8]= |  |
