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
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
the reply-to set correctly so if replying by mail, reply to
jeff at econ.berkeley.edu