Re: Finding Solution to Set of Equations with Inequality Constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg19485] Re: Finding Solution to Set of Equations with Inequality Constraints
• Date: Sat, 28 Aug 1999 15:53:11 -0400
• Organization: Wolfram Research, Inc.
• References: <7pl60t\$cd2@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Version 4 of Mathematica contains an implementation of the Cylindrical
Algebraic Decomposition algorithm which allows finding solution sets of
systems of real algebraic equations and inequalities.

For a logical combination of algebraic equations and inequalities ineqs
in
variables vars, Experimental`CylindricalAlgebraicDecomposition[ineqs,
vars],
or InequalitySolve[ineqs, vars]  (from Algebra`InequalitySolve` package)

give a full description of the solution set.

In[1]:=  ineqs = x^2+y^2+z^2==8 && x-y^3==1 && 1<x+y<z;
In[2]:= <<Algebra`InequalitySolve`

In[3]:= InequalitySolve[ineqs, {x, y, z}]

2       3        4     6
Out[3]= 1 < x < Root[-63 - 14 #1 + 61 #1  + 2 #1  - 14 #1  + #1  & , 2]
&&

3                          2    2
>    y == Root[1 - x + #1  & , 1] && z == Sqrt[8 - x  - y ]

If all you need is just one solution, you can use
Developer`InequalityInstance

In[4]:= Developer`InequalityInstance[ineqs, {x, y, z}]

403        Sqrt[7747041556806895623]       1139192651
Out[4]= {y -> ----, z -> -------------------------, x -> ----------}
1024              1073741824               1073741824

Best Regards,

Wolfram Research

Herbert Gintis wrote:

> Is there a Mathematica program that takes a set of equations
> (multivariate polynomial) and finds a solution that satisfies certain
> inequality constraints? The number of equations is less than the
> number of unknowns, so there is a nonlinear manifold of solutions to
> the equations. I just want a few that satisfy the inequalities.
>
> Thanks!
>
> Best Regards,
>
> Herbert M Gintis
> Professor of Economics
> University of Massachusetts
> 413-586-7756 (Home/Office)
> 413-586-6014 (Fax)
> gintis at econs.umass.edu
> http://www-unix.oit.umass.edu/~gintis

```

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