# [Maxima] 1/0? Why the error

Richard Hennessy rich.hennessy at verizon.net
Thu Apr 26 00:12:38 CDT 2012

```This is somewhat new to me but it suggests that the idea might be useful.
It reminds me of my Excel spreadsheet macro that rotates the eigenvector of
a rotation matrix.

Rich

-----Original Message-----
From: Henry Baker
Sent: Wednesday, April 25, 2012 3:46 PM
To: Richard Fateman
Cc: Stavros Macrakis ; maxima at math.utexas.edu
Subject: Re: [Maxima] 1/0? Why the error

Graphics people, including the Postscript language, utilize "homogeneous
coordinates" in 1 extra dimension in order to put off the possibility of
dividing by zero until the last minute.  Homogeneous coordinates also have
the advantage that conversion to proper perspective is done as the last
step, when the extra coordinate is divided out.

Lots of other types of computations are sometimes easier with "extra"
coordinates, which are only eliminated when absolutely necessary.  Examples
are homogeneous polynomials and the use of quaternions (which avoid
so-called "gimbal lock").

http://en.wikipedia.org/wiki/Gimbal_lock

With modern computers, doing a few extra arithmetic ops is not very
expensive, when compared with memory latency, so "redundant" calculation in
homogeneous coordinates is actually cheaper when it avoids branching.

At 05:36 PM 4/24/2012, Richard Fateman wrote:
>There is at least one proposal as to how to extend the rational numbers
>0/0, 1/0, and -1/0.  They correspond in most respects to the floating-point
>objects in the IEEE standard of NotANumber, Infinity, and negative
>Infinity.
>
>As a consequence, one can look in the literature for reasonable definitions
>for (say) expt, log, cosine, addition, multiplication, ... of these
>objects.
>Unfortunately this does not always lead to consistency  (in IEEE .. as
>well).
>
>Just patching one spot to leave 1/0 alone may have some momentary appeal,
>but if you think about it a little, it requires a lot of work and
>considerable thought
>to make such a feature work.
>
>RJF
>
>ps
>
>www.cs.berkeley.edu/~fateman/papers/extrat.ps

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