It seems you want to revert the Lorentz transformation:
https://en.wikipedia.org/wiki/Lorentz_factor#Occurrence
In this case you have a system of equations relating
the various quantities c, ga, t, tt, x, xx, v, where
- ga is the gamma factor, c is the speed of light,
- v is the relative speed of two inertial frames,
- t, x are spacetime coordinates in one inertial frame,
- tt, xx are spacetime coordinates in the other frame.
In Sage form, the system looks like:
tt == ga * (t - v*x/c^2)
xx == ga * (x - v*t)
It is a usual system of equations, not a system of
differential equations, so you want to use `solve`
and not `desolve` (note that "desolve is short for
"differential equation solve").
You could do this:
Define the variables (everything stays symbolic,
we don't give specific values to any variable):
sage: ga, t, tt, x, xx, v = SR.var("ga t tt x xx v")
Define the two equations:
sage: eq1 = tt == ga * (t - v*x/c^2)
sage: eq2 = xx == ga * (x - v*t)
Use `solve`, giving it a list of equations constituting
the system to be solved, and the variables for which to solve:
sage: solve([eq1, eq2], t, x)
[[t == (c^2*tt + v*xx)/(c^2*ga - ga*v^2),
x == (c^2*tt*v + c^2*xx)/(c^2*ga - ga*v^2)]]
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