```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.>>>
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