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.
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