
Re: Automatic solving of unprepared polynomial equation systems?
Posted:
Mar 31, 2013 10:06 PM


In sci.math.symbolic IV <ivgroups@onlinehome.de> wrote: > 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=c3A, C=AB], 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.
Well, in FriCAS:
(19) > solve([c1=A*B/C, c2=C*A/D, D=c3A, C=AB], [D, B, C, A])
(19) [ 2 2 c2 c3  A c2 + A c1  A  c2 c3 + A c2 + A [D= c3  A, B= , C= , c1 c1 2 3 ( c1  A)c2 c3 + (A c1 + A )c2 + A = 0] ] Type: List(List(Equation(Fraction(Polynomial(Integer)))))
The last line is the cubic to determine A, and the other variables are expressed int term of A.
The only trick is that I put A as _last_ variable. Using natural order with D last everything is expressed in terms of D.
As other posters mentioned Mathematica and Maple also can solve it. > > Is a mathematical algorithm or a computer algorithm known for such equation > systems?
Two standard approaches are Groebner bases and triangular systems.  Waldek Hebisch hebisch@math.uni.wroc.pl

