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Topic: Automatic solving of unprepared polynomial equation systems?
Replies: 9   Last Post: Apr 1, 2013 9:08 AM

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Peter Pein

Posts: 1,147
Registered: 5/4/05
Re: Automatic solving of unprepared polynomial equation systems?
Posted: Mar 31, 2013 7:11 PM
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Am 31.03.2013 16:15, schrieb IV:
> Hallo,
>
> I'm not a mathematician. I'm a natural scientist.
>
> It seems that computer algebra systems like Maple (version 11) and
> Mathematica (version 7) can not solve all simply solvable equation
> systems automatically. 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. ....

Just for completeness:

to get the cubic equation for a in dependence of the ci, type into
Mathematica:
eqfora =
Eliminate[{c1 == a b/c, c2 == c a/d, d == c3 - a, c == a - b},
{b, c, d}]

to get
(a + c1) c2 c3 == a (a^2 + a c2 + c1 c2)

Peter



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