Thanks all. I believe Dima is correct. These are inconsistent.
On Monday, February 28, 2022 at 1:59:58 AM UTC-8 dim...@gmail.com wrote:
> On Mon, Feb 28, 2022 at 7:24 AM cyrille....@univ-orleans.fr
> <cyrille....@univ-orleans.fr> wrote:
> >
> > I am not a mathematician but what seems obvious is that you have 8
> equations with 8 variables. You could conjecture there is at least a real
> solution even if there could be 8. But, your system is highly nonlinear.
>
> Generically, one might expect up to 2^8 solutions here (8 variables, 8
> equations of degree 2).
> This is called Bezout theorem.
> No guarantee that any solution is real, though.
>
>
>
> So you can not expect a solution by quadrature. You must try to solve
> you system numerically.
> >
> >
> > ----- Mail d’origine -----
> > De: Scott Wilson <scott....@octoengineering.ca>
> > À: sage-support <sage-s...@googlegroups.com>
> > Envoyé: Sun, 27 Feb 2022 20:40:43 +0100 (CET)
> > Objet: [sage-support] nonlinear equation system
> >
> > Hello, I am new to sage math and tried to get the solution to the
> following nonlinear equation system. Sage has been working on this since
> yesterday and I am wondering how long I should typically wait. All comments
> are appreciated. Thanks in advance.
> >
> > var('A B E F I J R T')
> >
> > eq1 = A*E-B^2-B*F+E^2==1
> > eq4 = A*I-B*J+I^2+R^2==-1/2
> > eq5 = A*R-B*T+2*R*I==0
> > eq6 = B*I-E*J+I*J+R*T==0
> > eq8 = -B*R+E*T-R*J-I*T==0
> > eq9 = E*I-F*J+J^2+T^2==1/2
> > eq11 = -E*R+F*T-2*T*J==0
> > eq12 = I^2-R^2-J^2+T^2==-1
> >
> > solve([eq1,eq4,eq5,eq6,eq8,eq9,eq11,eq12],A,B,E,F,I,J,R,T)
> >
> >
> >
> >
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