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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