# Mathematica and Geometry Hints

## Books

Here are some books that I recommend. You should not think of Mathematica as
a program but rather as a language. Just as you would not try to learn C
without a book, neither should you expect to learn Mathematica just from the
online help.
AUTHOR Blachman, Nancy R.
TITLE Mathematica, a practical approach / Nancy Blachman.
PUBLISHED Englewood Cliffs, N.J. : Prentice Hall, c1992.
DESCRIPTION xv, 363 p. : ill. ; 23 cm.
SERIES Prentice Hall series in innovative technology.
NOTE(S) Includes index.
SUBJECT(S) Mathematica (Computer file)
Mathematics --Computer programs.
ISBN 0135638267.

This is an excellent book to start with. I am still looking things up in it.
AUTHOR Wickham-Jones, Tom, 1958-
TITLE Mathematica graphics : techniques & applications / Tom Wickham-
Jones.
PUBLISHED Santa Clara, Calif. : TELOS, c1994.
DESCRIPTION xiii, 721 p. : ill. (some col.) ; 24 cm. + 1 computer disk (3 1/2
in.)
NOTE(S) System requirements for computer disk using IBM-compatible PC:
DOS or Windows; Mathematica; high-density disk drive. Files may
also be read by Macintosh, Unix, and NeXT systems.
BIBLIOGRAPHY Includes bibliographical references and index.
SUBJECT(S) Computer graphics.

This is really necessary if you want to get into graphics with any
sophistication.

## How to write vectors and covectors in Mma.

You can manipulate lists of numbers as if they were vectors, like say
{1,2,3}, but this will not let you separate the vector types from the
covector types.
Mma writes matrices as lists of lists, and you should treat vectors and
covectors as 1xn matrices. Thus the vectors might be written

{{1},{2},{3}}

and the covectors as

{{1,2,3}}

You can see the output written properly as matrices if you ask for
MatrixForm

{{1},{2},{3}} // MatrixForm

The Euclidean metric operator maps vectors into covectors, and is here
represented by the Transpose[] operator. This is actually an important
observation: the transpose operator implies the choice of a geometry.

The spacetime geometry operator would instead flip the sign of the first
component (if that is where you have decided to put the timelike components)
provided that you are working in orthonormal coordinates.