FWIW, executing :
reset()
# Don't scratch Sage's predefined identifiers, for sanity's sake...
Vars= var('A B EE F II J RR T')
eq1 = A*EE-B^2-B*F+EE^2==1
eq4 = A*II-B*J+II^2+RR^2==-1/2
eq5 = A*RR-B*T+2*RR*II==0
eq6 = B*II-EE*J+II*J+RR*T==0
eq8 = -B*RR+EE*T-RR*J-II*T==0
eq9 = EE*II-F*J+J^2+T^2==1/2
eq11 = -EE*RR+F*T-2*T*J==0
eq12 = II^2-RR^2-J^2+T^2==-1
Sys = [eq1,eq4,eq5,eq6,eq8,eq9,eq11,eq12]
# Build an equivalent polynomial system
# Ring
R1 = PolynomialRing(QQbar, len(Vars), "u")
R1.inject_variables()
# Conversion dictionary
D = dict(zip(Vars, R1.gens()))
# Polynomial system
PSys = [R1((u.lhs()-u.rhs()).subs(D)) for u in Sys]
# Try to solve
J1 = R1.ideal(PSys)
# Check
print(J1.dimension())
prints
Defining u0, u1, u2, u3, u4, u5, u6, u7
-1
According to J1.dimension? : If the ideal is the total ring, the dimension
is -1 by convention.
No bloody solution…
Le mardi 1 mars 2022 à 18:23:19 UTC+1, Scott Wilson a écrit :
> Thanks all. I believe Dima is correct. These are inconsistent.
>
> On Monday, February 28, 2022 at 1:59:58 AM UTC-8 [email protected] wrote:
>
>> On Mon, Feb 28, 2022 at 7:24 AM [email protected]
>> <[email protected]> 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 <[email protected]>
>> > À: sage-support <[email protected]>
>> > 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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>>
>> >
>> >
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>>
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