Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica >
Mathematica TutorialFunctions »|Tutorials »

Packages for Symbolic Mathematics

There are many Mathematica packages which 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 f of f in the coordinate system chosen
Div[f]evaluate the divergence f of the list f
Curl[f]evaluate the curl f of the list f
Laplacian[f]evaluate the Laplacian 2f of f

Vector analysis.

This loads the vector analysis package. In some versions of Mathematica, you may not need to load the package explicitly.
In[2]:=
Click for copyable input
This specifies that a spherical coordinate system with coordinate names r, theta and phi should be used.
In[3]:=
Click for copyable input
Out[3]=
This evaluates the gradient of r2sin () in the spherical coordinate system.
In[4]:=
Click for copyable input
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.
In[5]:=
Click for copyable input
This finds the functional derivative of .
In[6]:=
Click for copyable input
Out[6]=

Quaternions

<<Quaternions`load the quaternions package
Quaternion[a,b,c,d]the quaternion a+bi+cj+dk

Quaternions.

This loads the quaternions package.
In[7]:=
Click for copyable input
This finds the principal square root of a quaternion.
In[8]:=
Click for copyable input
Out[8]=
© 2013 Wolfram Research, Inc. Japanese
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team