       A Reduce question

• To: mathgroup at smc.vnet.net
• Subject: [mg46207] A Reduce question
• From: "Tony Harker" <a.harker at ucl.ac.uk>
• Date: Thu, 12 Feb 2004 07:15:38 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```This query concerns the application of Reduce to a simple pair of
simultaneous equations, as follows.
eq = {a x + b y == 0,
c x + d y == 0};
red = Reduce[eq, {x, y}];

Why does the program recognise only one of the special cases in which one
coefficient is nonzero and the others are zero?

We find that if we apply Reduce to the equations and ask it to consider x
and y as variables we get  one result, the same process with only x as a
variable gives  something similar, but with y as the variable  we get a
different number of special cases from the one with x as the variable:

So the first question is why the treatments of x and y are different, and
the second is why, if we look at the x,y case, several special cases are
missing. For example, it is clear that if nonzero a and all other
coeficients zero is a special case, there are three similar special cases.
Are we meant to infer these ourselves from the symmetry of the equations?
Presumably not, as (0,0,c,d) and (a,b,0,0) are both given explicitly.

What is the recipe, then, for interpreting the output of Reduce?

These results are from Mathematica version 5.0.0.0.

Tony Harker
Department of Physics and Astronomy
University College London
January 30th 2004

```

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