InequalityInstance bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg26560] InequalityInstance bug?
• From: Gianluca Gorni <gorni at dimi.uniud.it>
• Date: Fri, 5 Jan 2001 22:22:57 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello!

I am using Mathematica version 4.0. With ineqs and vars defined below
I get the following unexpected output:

In:  Developer`InequalityInstance[ ineqs, vars ]

Out:{r[4, 4] -> 1, r[4, 3] -> -1, r[3, 3] -> 2, r[4, 2] -> 0,
r[4, 1] -> 1, r[3, 4] -> -1, r[3, 2] -> -1, r[3, 1] -> -1,
r[2, 4] -> 0, r[2, 3] -> True,
r[2, 2] -> 1, r[2, 1] -> 0, r[1, 4] -> True,
r[1, 3] -> -1, r[1, 2] -> 0,  r[1, 1] -> 1}

Notice the values for r[2,3] and r[1,4]. I thought that perhaps
True meant "arbitrary", but it is not so: the equations require
that r[2,3] = -1, r[1,4] = 1.

What happens with version 4.1?

All best wishes for a new millennium with fewer bugs!

Gianluca Gorni

ineqs = {r[1, 2] - r[2, 1] == 0, r[2, 1] ==
-r[1, 1] - r[3, 1], -r[1, 2] + r[2, 1] == 0,
r[2, 2] == -r[1, 2] - r[3, 2],
r[2, 3] == -r[1, 3] - r[3, 3],
r[2, 4] == -r[1, 4] - r[3, 4],
r[1, 3] - r[3, 1] == 0, -r[1, 3] + r[3, 1] == 0,
r[2, 3] - r[3, 2] == 0, -r[2, 3] + r[3, 2] == 0,
r[1, 4] - r[4, 1] == 0, r[4, 1] == r[1, 1],
-r[1, 4] + r[4, 1] == 0, r[2, 4] - r[4, 2] == 0,
r[4, 2] == r[1, 2], -r[2, 4] + r[4, 2] == 0,
r[3, 4] - r[4, 3] == 0, r[4, 3] == r[1, 3],
-r[3, 4] + r[4, 3] == 0, r[4, 4] == r[1, 4],
(-(r[1, 2]*r[3, 1]) + r[1, 1]*r[3, 2])^2 +
(-(r[1, 3]*r[3, 1]) + r[1, 1]*r[3, 3])^2 +
(-(r[1, 3]*r[3, 2]) + r[1, 2]*r[3, 3])^2 +
(-(r[1, 4]*r[3, 1]) + r[1, 1]*r[3, 4])^2 +
(-(r[1, 4]*r[3, 2]) + r[1, 2]*r[3, 4])^2 +
(-(r[1, 4]*r[3, 3]) + r[1, 3]*r[3, 4])^2 > 0,
r[1, 1] >= 0, -(r[1, 2]*r[2, 1]) +
r[1, 1]*r[2, 2] >= 0,
-(r[1, 3]*r[2, 2]*r[3, 1]) + r[1, 2]*r[2, 3]*
r[3, 1] + r[1, 3]*r[2, 1]*r[3, 2] -
r[1, 1]*r[2, 3]*r[3, 2] - r[1, 2]*r[2, 1]*
r[3, 3] + r[1, 1]*r[2, 2]*r[3, 3] >= 0,
r[1, 4]*r[2, 3]*r[3, 2]*r[4, 1] -
r[1, 3]*r[2, 4]*r[3, 2]*r[4, 1] -
r[1, 4]*r[2, 2]*r[3, 3]*r[4, 1] +
r[1, 2]*r[2, 4]*r[3, 3]*r[4, 1] +
r[1, 3]*r[2, 2]*r[3, 4]*r[4, 1] -
r[1, 2]*r[2, 3]*r[3, 4]*r[4, 1] -
r[1, 4]*r[2, 3]*r[3, 1]*r[4, 2] +
r[1, 3]*r[2, 4]*r[3, 1]*r[4, 2] +
r[1, 4]*r[2, 1]*r[3, 3]*r[4, 2] -
r[1, 1]*r[2, 4]*r[3, 3]*r[4, 2] -
r[1, 3]*r[2, 1]*r[3, 4]*r[4, 2] +
r[1, 1]*r[2, 3]*r[3, 4]*r[4, 2] +
r[1, 4]*r[2, 2]*r[3, 1]*r[4, 3] -
r[1, 2]*r[2, 4]*r[3, 1]*r[4, 3] -
r[1, 4]*r[2, 1]*r[3, 2]*r[4, 3] +
r[1, 1]*r[2, 4]*r[3, 2]*r[4, 3] +
r[1, 2]*r[2, 1]*r[3, 4]*r[4, 3] -
r[1, 1]*r[2, 2]*r[3, 4]*r[4, 3] -
r[1, 3]*r[2, 2]*r[3, 1]*r[4, 4] +
r[1, 2]*r[2, 3]*r[3, 1]*r[4, 4] +
r[1, 3]*r[2, 1]*r[3, 2]*r[4, 4] -
r[1, 1]*r[2, 3]*r[3, 2]*r[4, 4] -
r[1, 2]*r[2, 1]*r[3, 3]*r[4, 4] +
r[1, 1]*r[2, 2]*r[3, 3]*r[4, 4] >= 0};

vars = {r[1, 1], r[1, 2], r[1, 3], r[1, 4], r[2, 1],
r[2, 2], r[2, 3], r[2, 4],
r[3, 1], r[3, 2], r[3, 3], r[3, 4], r[4, 1],
r[4, 2], r[4, 3], r[4, 4]}

--

+---------------------------------+
| Gianluca Gorni                  |
| Universita` di Udine            |
| Dipartimento di Matematica      |
|   e Informatica                 |
| via delle Scienze 208           |
| I-33100 Udine UD                |
| Italy                           |
+---------------------------------+
| Ph.: (39) 0432-558422           |
| Fax: (39) 0432-558499           |
| mailto:gorni at dimi.uniud.it      |
| http://www.dimi.uniud.it/~gorni |
+---------------------------------+

```

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