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gs.txt
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Introduction
This package includes two TI basic programs.  One performs Gram-Schmidt
orthogonalization on a vector space, the other performs Gram-Schmidt
orthogonalization on a polynomial space.

Be aware that these programs produce orthogonal subspaces, not orthonormal
subspaces.  If you require orthonormal subspaces, you must normalize them
yourself.

If you don't know what Gram-Schmidt orthogonalization is, go read a linear
algebra textbook.  There also _might_ be explanation on the [synthetic realms]
webpage (bottom of file).  No gurantees, though.
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Package Contents
GS4POLY.82P             GS4POLY ready to be uploaded to a TI-82 or TI-83.
GS4POLY.SRC             TI Basic source to GS4POLY.
GS4VECT.82P             GS4VECT ready to be uploaded to a TI-82 or TI-83.
GS4VECT.SRC             TI Basic source to GS4VECT.
GS.TXT                  This file.
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Getting the programs on your calculator
The easy thing to do is to use a computer link to upload the *.82P files to
your TI-82 or TI-82.  Computer links are available from TI, or you can make
your own.  Go to the synthetic realms webpage to find links on how to make
links.  The address is at the bottom of this text file.

The other way is to enter the *.SRC into your calculator using the TI basic
editor.  Not suggested obviously.  It is, however, the only way to do it
right now if you don't have a TI-82 or TI-83.  If you aren't using a TI-82
or a TI-83, you might have to make some changes to it.  If you do make a port,
I would be interested in getting it to distribute it.
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Using GS4VECT

GS4VECT performs Gram-Schmidt orthogonalization on a vector space.

Note: GS4VECT uses <a,b>=ab.  That is to say, the inner product is equal
to the dot product of the two vectors.  This is what you see almost all the
time.  It should be what you will see all the time at the undergraduate level.

To use it, enter the vectors into matrix [A] as row vectors.  The vectors may
be up to 6d, and you may have up to six vectors.

Now run GS4VECT.

GS4VECT will display the orthogonalized [A] on screen.  The answer will also
be stored in matrix [B] for later reference.

GS4VECT obviously consumes [A] and [B].  It will also destroy L1 (list 1),
and a handful of reals.
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Using GS4POLY

GS4POLY performs Gram-Schmidt orthogonalization on a polynomial space.

Note: GS4POLY uses <f(x), g(x)> = A
                                    f(x)g(x) dx
                                  B
A and B can be entered everytime the program is run.
This should be what you see almost all the time.  It should be what you see all
the time at the undergraduate level.

To use it, enter the polynomial coefficients as row vectors into matrix [A].
The terms should be in ascending power, that is the first column contains
X^0 coefficients, the second column contains X^1 coefficients, etc.
You may enter up to six polynomials of up to fifth degree (p5 or p6, depending
upon your textbook and professor).

Now run GS4POLY.  Enter appropriate values for A and B.  A is the lower limit
of the integral, B is the upper limit of the integral.

Now wait.  Due to the large number of integrals that must be performed, this
can take a while.  There's a progress indicator at the bottom of the screen
that shows how complete the process.

GS4POLY will display the orthogonalized [A] on screen.  The answer will also
be stored in matrix [B] for later reference.

GS4POLY obviously consumes [A] and [B].  It will also destroy L1 (list 1),
and Y9 and Y0 (Y functions 9 and 10), and a handful of reals.
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contact
These programs were created by
Geoffrey Wossum (aka Maxon / [synthetic realms])
gpw0341@omega.uta.edu
http://www.fastlane.net/~gpwossum
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standard disclaimer
The author of GS4POLY and GS4VECT assumes no responsibility for any damages,
coincidental or incidental from the use of misuse of these programs.
These programs were intended to be used to check your answers.  If you would
rather use them instead of learning Gram-Schmidt, that's your own problem.
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end of gs.txt
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