Date: Mar 31, 2013 11:34 AM
Author: Scott Berg
Subject: Re: Automatic solving of unprepared polynomial equation systems?

"IV" <ivgroups@onlinehome.de> wrote in message

news:kj9ge6$272$1@news.albasani.net...

> Hallo,

>

> I'm not a mathematician. I'm a natural scientist.

you admit right off the bat that your math is poopy.

>

> It seems that computer algebra systems like Maple (version 11) and

> Mathematica (version 7) can not solve all simply solvable equation systems

> automatically.

if they are "simply solvable" then it is simple to solve them.

>Let us look e.g. at the equation system [c1=A*B/C, c2=C*A/D, D=c3-A,

>C=A-B], where c1, c2 and c3 are real or complex constants, A, B, C and D

>are real or complex variables, and the solutions for the variable A are

>wanted. The equation system forms a cubic equation in A, and the solutions

>of the equation system are the solutions of this cubic equation. But the

>solve command can find neither the cubic equation nor its solutions. I

>think, the equation system has to be somehow prepared to yield a normal

>form of equation systems. Is a normal form for polynomial equation systems

>known?

>

> What is with Buchberger algorithm and GrÃ¶bner basis? Maple's (version 11)

> Groebner[Solve] command could also not find the solutions of the equation

> system.

>

> We know when we have a system of equations with several variables, then we

> have to insert the various equations skillfully into the other equations

> to eliminate single variables. But what is the best way to do that, and

> how can this be done automatically? Is there an automatic algorithm for

> the insertion - for the elimination of variables?

>

> Why can computer algebra systems not do that? What have I to do that Maple

> and Mathematica solve such equation systems automatically?

>

> I have a raw idea for an algorithm. I let determine the variables in each

> equation. If there is a variable that is only in one equation, I let solve

> this equation for this variable. If there is a variable that is only in

> two equations, I let solve this two equations for this variable and link

> both solutions with an equal sign. But what if after that still one

> variable is in more than two equations? Which two equations should you

> choose? Should one try all ways?

it is simple, as you pointed out above.

>

> Is a mathematical algorithm or a computer algorithm known for such

> equation systems?

>

> Thanks.

>

>

>