On Sun, Feb 27, 2022 at 9:08 PM Scott Wilson
<scott.wil...@octoengineering.ca> wrote:
>
> 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)
One should not use a generic solver for polynomial equations.
One can set this up easily:
sage: P.<A, B, E, F, I, J, R, T>=QQ[]
sage: 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
....: eq6 = B*I-E*J+I*J+R*T
....: eq8 = -B*R+E*T-R*J-I*T
....: eq9 = E*I-F*J+J^2+T^2-1/2
....: eq11 = -E*R+F*T-2*T*J
....: eq12 = I^2-R^2-J^2+T^2+1
sage: sy=P.ideal(eq1,eq4,eq5,eq6,eq8,eq9,eq11,eq12)
and see that this ideal contains 1, i.e. your system has no solutions,
even no complex solutions, assuming I didn't make an error while
converting:
sage: sy.groebner_basis()
[1]
HTH,
Dima
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