How to solve system of iinequalities?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1049] How to solve system of iinequalities?
• From: jeff at econ.berkeley.edu
• Date: Wed, 10 May 1995 08:55:38 -0400
• Organization: University of California, Berkeley

```Hi.  I have a system of linear inequlities specified symbolically.
I want to test whether they are consistent.  (i.e. whether the
solution region is non-empty).  I don't see how to do this and
it is not covered in Wolfram's book.

For example, I can surely type

In[1] 1<0

and get back the expected

Out[1] False

But if I enter

In[2] y<x && x<y

Out[2] y < x && x < y

Apparently Mathematica cannot deduce that this is impossible.
Is there any way to get Mathematica to tell me when a series of
inequalities is logically consistent?  The workaround I tried
was to use ConstrainedMin which returns an error when the
Constraint inequalities have empty solution region.  The problem
is that I need to enforce the inequalities to be strict and
Constrained seems to be willing to assume weak inequalites when
necessary.  For example

In[3] ConstrainedMin[x,{x<y,y<x},{x,y}]

returns

Out[3] {0, {x->0, y->0}}

which is not what I wanted.

There has got to be a simple way to do this, right?

Jeff

ps I am sending this from my brand new Linux box and may not have
jeff at econ.berkeley.edu

```

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