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.
|<<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 |
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
should be used.
This evaluates the gradient of
in the spherical coordinate system.
|<<VariationalMethods`||load the variational methods package|
|VariationalD[f,y[x],x]||find the variational derivative of f|
This loads the variational methods package.
This finds the functional derivative of
|<<Quaternions`||load the quaternions package|
|Quaternion[a,b,c,d]||the quaternion |
This loads the quaternions package.
This finds the principal square root of a quaternion.