[Maxima] Working with Inequalities

Barton Willis willisb at unk.edu
Sat Jan 28 08:12:22 CST 2012

```The optional package 'to_poly_solver' has a (very) limited ability to solve inequations.
When to_poly_solver is able to transform the inequations into a linear system, the solver
applies the Fourier elimination method.

(%i2) load(to_poly_solver)\$
Loading maxima-grobner \$Revision: 1.6 \$ \$Date: 2009-06-02 07:49:49 \$

(%i3) %solve([x^2 + 2*x=3, 7*x+2<-x-3],[x]);
(%o3) %union([x=-3])

To attempt conversion to a linear form, %solve doesn't introduce radicals:

(%i6) %solve([x^2 + 9*x=3, 7*x+2<-x-3],[x]);
(%o6) %union([x<-5/8,x^2+9*x-3=0])

So %solve handles x^2 + 2*x=3, 7*x+2<-x-3 OK, but don't expect great things from %solve.

--Barton (author of to_poly_solver).

-----maxima-bounces at math.utexas.edu wrote: -----
To: maxima at math.utexas.edu
From: "Thomas D. Dean"
Sent by: maxima-bounces at math.utexas.edu
Date: 01/28/2012 02:35AM
Subject: [Maxima] Working with Inequalities

How do I solve this?

x^2 + 2*x=3 and 7*x+2<-x-3

I found solve_rat_ineq.  That handles the inequality OK.

(%i1) solve(x^2 + 2*x=3,x);
(%o1) [x = - 3, x = 1]
(%i2) solve_rat_ineq(7*x+2<-x-3);
5
(%o2)                            [[x < - -]]
8

The solution is x = -3

Tom Dean
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