# [Maxima] equivalent to Mathematica's Reduce?

Richard Fateman fateman at cs.berkeley.edu
Mon Apr 20 18:50:58 CDT 2009

```Reduce takes an equation or an  inequality and tries to simplify,
eliminating quantifiers

e.g.
Reduce[x^2 + y^2 < 1, {x, y}] -->     -1 < x < 1 && -Sqrt[1 - x^2] < y <
Sqrt[1 - x^2]

Has anyone written something like this?

It is related to solve, eliminate, ..

How does solve and reduce differ?
From the documentation..

The general question of whether a set of equations has any consistent
solution is quite a subtle one. For example, for most values of a, the
equations {x==1,x==a} are inconsistent, so there is no possible solution
for x. However, if a is equal to 1, then the equations do have a
solution. Solve is set up to give you generic solutions to equations. It
discards any solutions that exist only when special constraints between
parameters are satisfied.

If you use Reduce instead of Solve, Mathematica will however keep all
the possible solutions to a set of equations, including those that
require special conditions on parameters.

RJF

```