Date: Mar 31, 2013 11:34 AM
Author: Scott Berg
Subject: Re: Automatic solving of unprepared polynomial equation systems?
"IV" <email@example.com> wrote in message
> 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
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
> What is with Buchberger algorithm and Gröbner basis? Maple's (version 11)
> Groebner[Solve] command could also not find the solutions of the equation
> 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?