solve equtions in maxima (algorithms, description ofimplementation in clisp)

Hi, all.

If we try to solve equations of kind: (x+a)/(x+a)=1, a - fixed number,
then the answer should be "all numbers, excepting x=-a". Maxima outputs the result "all", it does not exclude wrong solution x=-a. As I understand,
Maxima simplifies expression and (x+a)/(x+a) and gets 1=1. So it answers "all".

Could you advise how to avoid this error? Maybe could you tell me functions that do this simplification (is it possible to torn off such simplification)?

Best regards,
Mihail D

---------------------------
-----Original Message-----
From: Barton Willis <willisb at unk.edu>
To: ?????? ????????? <mihail_denisenko at mail.ru>
Date: Mon, 12 Oct 2009 10:15:39 -0500
Subject: Re: [Maxima] solve equtions in maxima (algorithms,	description of
implementation in clisp)

> For exact solutions, Maxima has three equation solvers. For numerical
> solutions there are a few more (mnewton is the one I know the most
> about, but there are others). For the exact solvers:
> 
> (1) The built in function solve mostly works with polynomial equations
> and some trigonometric-like equations.
> 
> (2) The optional package to_poly_solve works by trying to convert a
> system of equations into polynomial form. You can learn something
> about this solver in the document
> http://www.unk.edu/uploadedFiles/facstaff/profiles/willisb/solve-talk(3).pdf
> 
> A quick demo:
> 
> (%i198) load(to_poly_solver)$
> 
> (%i199) to_poly_solve([max(x,y) + min(x,2*y) = 1, x - abs(y) = 23],[x,y]);
> (%o199) %union([x=45,y=-22])
> (%i201) to_poly_solve(sin(x)*cos(x)=1/2,x);
> (%o201) %union([x=-(-2*%pi*%z25-%pi/2)/2])
> 
> (3) I don't know much about the optional package "solver."  The solver
> package is documented in share\algebra\solver\solver1.pdf . To use
> it, load(solver).
> 
> If you wrote some code, maybe you could make it available.
> 
> Barton
> 
> maxima-bounces at math.utexas.edu wrote on 10/12/2009 07:35:17 AM:
> 
> > [image removed] 
> > 
> > [Maxima] solve equtions in maxima (algorithms, description of 
> > implementation in clisp)
> > 
> > ?????? ????????? 
> > 
> > to:
> > 
> > maxima
> > 
> > 10/12/2009 07:35 AM
> > 
> > Sent by:
> > 
> > maxima-bounces at math.utexas.edu
> > 
> > Please respond to ?????? ????????? 
> > 
> > Hi,
> >  I work with Maxima to solve equations consist of elementary 
> > functions (polynomials, rational expressions, logarithm, 
> > trigonometric functions, exponentiation). It is significant to 
> > define domain of definition of equation and critical points of the 
> > equation. There are not any similar functionality in the developed 
> > Maxima project. I have try to add necessary functions to Maxima 
> > source code. But I have to understand structure and working logic of
> > the maxima_solve subsystem. Is it possible to get some informations 
> > about solve functions in Maxima? Could you tell me about algorithms 
> > that were used in the implementation of the functionality for 
> > solving equations (maybe articles, books, etc.)?
> > 
> > Best regards,
> > 
> > Mihail D.
> > _______________________________________________
> > Maxima mailing list
> > Maxima at math.utexas.edu
> > http://www.math.utexas.edu/mailman/listinfo/maxima
> 
>