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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
: the reply-to set correctly so if replying by mail, reply to
: 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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