I have a quantity ds2
which is expressed in term of a set of 5 variables (let's call them t, r, θ, φ, ψ
). I have 5 equations (let’s label them eqi
where i
=1, 2..5) relating those variables to another set of variables (let’s those T, y, Θ, Φ, Ψ
). How can I express my original quantity solely using the second set?
I have tried the following pieces of code:
- Solve
Solve[{ds2==bla bla bla, eq1 && eq2 && eq3 && eq4 && eq5}, ds2, {T, y, Θ, Φ, Ψ}, Reals]
-> "Solve: This system cannot be solved with the methods available to Solve."
- Eliminate
Eliminate[{ds2= bla bla bla, eq1, eq2,eq3, eq4, eq5}, {T, y, Θ, Φ, Ψ}]
-> "Eliminate: Inverse functions are being used by Eliminate, so some solutions may not be found;
use Reduce for complete solution information."
Edit: Below are the explicit quantites/equations
eq1 = Xi[a] y^2 Sin[Θ]^2 == (r^2 + a^2) Sin[θ]^2;
eq2 = Φ == φ + a t/l^2;
eq3 = T == t;
eq4 = Xi[b] y^2 Cos[Θ]^2 == (r^2 + b^2) Cos[θ]^2;
eq5 = Ψ == ψ + b t/l^2;
ds2 = Sin[Θ]^2;
The actual ds
is much more complicated, but even this simple case does not work and give the aforementioned error messages.
D[]
is reserved for the derivative, so don't use it here. $\endgroup$ds2
with a much simpler case however. Could you let me know what I could do in this case if you know? $\endgroup$