Mathematica for UNIX

The following is the method to run Mathematica as a batch job:

math -batchinput -batchoutputm < infile > outfile

( Here please note < , > )

There is a man page available for Mathematica. To read the manual page type:

man math

Mathematica does not provide help within the math command. There is a command called mathbook which will allow you to access a Mathematica reference of available functions.

Inside Mathematica you can use the following three methods to get information on functions.

?function       Gives a brief description of the function

function        Gives a extended description of the function

?Ab*            Shows all functions starting with "Ab"

?*					Shows all functions

1. Arguments to functions are given in square brackets.

2. The first letter of build in functions are upper case

3. Multiplication can also be represented by spaces.

4. Powers are denoted by ^.

5. Complex numbers

   x + Iy  => The complex number (x+iy)
   Re[z], Im[z], Conjugate[z], Abs[z], Arg[z]

6. Using previous results

   %               => The last generated results
   %%              => Next to last
   %n              => The result of the n-th line
   

7. Manipulating Variables

   x = value,      x = y = value,
   x = .   or      Clear[x]
   x y   means    xy
   x^2y   means (x^2)y  not  x^(2y)
   

8. List:
   When you collect together a bunch of entries and treat them as a single entry, then it's named as a list.

   Ex:   ln[1]  :=  {3, 5, 1}
   Accessing or Manipulating a single elemnet
   Part[list,i], or list[[i]]

Mathematica has the ability to handle both numeric and symbolic calculations. This allows users to enter algebraic formulas. This has the added advantage of being able to enter the values as they are read, and be able to evaluate results for different values.

Replacing variables with values

EX: Replacing 'x'
           exp   /.  x -> value
    Several replacements
           exp  /.  { x -> xval, y -> yval }

Some important functions to manipulate equations

Expand, Factor, Simplify, ExpandAll

Together, Apart, Cancel, Collect

Expand[exp, Trig -> True]

Factor[exp, Trig -> True]

ComplexExpand, PowerExpand

Derivatives

D[f,x], D[f,x1,x2,...], D[f, {x,n}], Dt[f], Dt[f,x]

Intergration

Intergrat[f,x], Intergrate[f, {x, xmin, xmax}],
Intergrate[f, {x, xmin, xmax}, {y, ymin, ymax}]

Sums & Products

Sum[exp, {i, imin, imax}], Sum[ exp, {i, imin, imax}, {j, jmin, jmax}]
Product[exp, {i, imin, imax}]

Solving Equations

Solve[lhs == rhs, x]

Creating functions

Just as mathematica has built-in fuctions, users can also create their own functions.

Ex: f[x_] := exp        (Defines the function f)
You can use "?f" to show the definition of f, &
Clear[f] clears the definition of f.
Look at  the following example of transformation rules for functions.

Ex: 1+ f[x] + f[y]

The three transformation rules shown below transforms the expression differently.
x -> value
f[x] -> exp (or value)
f[t_] -> exp

Lists and lists of lists are used in mathematica to represent vectors and matrixes.

{a, b, c}               => vector(a, b, c)
{{a,b,c}, {c,d,e}}      => matrix(a b c)
                                 (c d e)

Useful functions

Array, IdentityMatrix, DiagonalMatrix, Part

Dimensions, MatrixForm,

Inverse, MatrixPower, Det, Transpose

EigenValue, EigenVector

Unlike some other programs, Mathematica allows it's users to plot actual algebraic functions. One can do 2-d and 3-d plots with a cutomized view port. Also, users have the freedom to change the settings in graphs to customize them accordingly.

Ploting functions (2-D)

Plot[f, {x, xmin, xmax}]
Plot[f1,f2,...., {x, xmin, xmax}]

More examples can be found on page 136.

In general mathematica selects the suitable options for the graph, but if one wants, the option command is there to change the choices.

Important options

Axes, AxesLabel, AxesOrigin, DefaultFont, DisplayFunction

Frame, FrameLabel, FrameTicks, GridLines, PlotLabel

PlotRange, Ticks, DisplayFunction

(options that cannot be used with 'show') PlotStyle,

PlotPoints, MaxBend, PlotDivision, Compiled

Ploting functions (3-D)

The command for 3-D plots is Plot3D. After a plot, the command show can be used for redrawing and changing options.

Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}]

Important Options

Axes, AxesLabel, Boxed, ColorFunction, DefaultFont

DisplayFunction,  FaceGrids, HiddenSurface, Lighting

Mesh, PlotRange, Shading, ViewPoint

Default View point = {1.3, -2.4, 2}

Ploting lists of Data

The following functions are awailable for ploting of lists.

ListPlot, ListPlot3D, ListContourPlot, ListDensityPlot

NOTE:

1. Mathematica also has the ability to do parametric plots. More information on parametric plots can be found on page 169.

2. There is a command show available in mathematica that can be used to redraw plots, and to change the options after the initial plot.

3. There are a lot more different plotting functions available with mathematica, such as animation plots. If these functions are not loaded at startup one may need to explicitly load them before calling a function.

<< Graphics'Graphics'  load a package with additional graphics function

LogPlot, LogLogPlot, LogListPlot, LogLogListPlot

PolarPlot, ErrorListPlot, TestListPlot,

BarChart, PieChart, PlotvectorField, SphericalPlot3D

<< Graphics'Animation'  load animation package

<< name          Reads in a plaintext file.

expr >> name    Outputs 'expr' to a file as plaintext.

expr >>> name   DAappend 'expr' to file.

!!name          Display content of plain text file.

Save:   Save[" name", f,g,...] save definition for variable




Dump:   In systems such as unix, one has the ability to save the

complete state of mathematica.

Dump[" namefile"]

math -x < filename>  to start from dump file.

NOTE:
1. Dump creates a huge binary file, therefore one may run out of quota, when trying to run Dump command.

2. For more information on generation of c,fortqran code, Tex input or spicing files please refer to page 182 through page 186 of Mathematica book.