Re: How to solve system of inequalities?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1099] Re: How to solve system of inequalities?
• From: bientin at cli.di.unipi.it (Paolo Bientinesi)
• Date: Sun, 14 May 1995 22:31:35 -0400
• Organization: Dipartimento di Informatica, Universita' di Pisa

```jeff at econ.berkeley.edu wrote:
: 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

: I get back the unhelpful

: 	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

The matter of your question is TYPE.
When you write 1 < 0, MMA works well because
understands you're are speaking about integers, in the same way
if you write 1. < 0. MMA knows you're speaking about reals.
The expression x < y && y < x is meaningless if you don't define
the type of variables. If x,y would be boolean, any ordinal expression
is without sense. Again, exist sets and operat r for which one
element could be "less" and "more" than another at the same time.
This is WHY Mathematica doesn't work, but I can't tell you
HOWhto solveosooolve the problem.
I wait with you for a solution.

Paul Dj.

```

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