Or (unexpectedly much simpler) :
```
sage: mathematica.Reduce(Sys, Vars)
False
```
Le jeudi 3 mars 2022 à 15:09:27 UTC+1, Emmanuel Charpentier a écrit :
> And, BTW :
>
> sage: mathematica("Sys = {%s}"%", ".join([u._mathematica_init_() for u in
> Sys]))
> {-B^2 + A*EE + EE^2 - B*F == 1, A*II + II^2 - B*J + RR^2 == -1/2,
> A*RR + 2*II*RR - B*T == 0, B*II - EE*J + II*J + RR*T == 0,
> -(B*RR) - J*RR + EE*T - II*T == 0, EE*II - F*J + J^2 + T^2 == 1/2,
> -(EE*RR) + F*T - 2*J*T == 0, II^2 - J^2 - RR^2 + T^2 == -1}
> sage: mathematica("Vars = {%s}"%", ".join([u._mathematica_init_() for u in
> Vars]))
> {A, B, EE, F, II, J, RR, T}
> sage: mathematica("Reduce[Sys, Vars]")
> False
>
> HTH,
>
> Le jeudi 3 mars 2022 à 15:01:46 UTC+1, Emmanuel Charpentier a écrit :
>
>> 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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>>>> https://groups.google.com/d/msgid/sage-support/47695a04-777d-4fbb-af5d-7371db01a31an%40googlegroups.com.
>>>>
>>>>
>>>> >
>>>> >
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>>>>
>>>>
>>>>
>>>
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