On Mon, Feb 28, 2022 at 7:24 AM cyrille.piate...@univ-orleans.fr
<cyrille.piate...@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.wil...@octoengineering.ca>
> À: sage-support <sage-support@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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