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I have the function:

[tex] x(\phi) = \left[(\phi - \phi_0)\frac{72~000}{360^\circ} + x_0\right]~\textrm{mod}~72~000 [/tex]

and I'm wondering how to invert it in order to get [itex] \phi(x) [/itex]? Also, the modulus operator is not exactly what I'm looking for here, because if x goes below 0, I want it to wrap around so that [itex] -1 \longrightarrow 71~999 [/itex], and [itex] -2 \longrightarrow 71~998 [/itex] etc. How do I express that mathematically?

Finally, the angle [itex] \phi [/itex] is restricted between values that cover a range < 360 degrees, leading me to believe this function should be one-to-one. [itex] \phi_0 [/itex] also lies in this range. [itex] x_0 [/itex] is arbitrary but should be between 0 and 71999.

EDIT: I should also mention that x is in the set of integers (which I guess means that step sizes in [itex]\phi[/itex] of less than 18 arsec don't occur).

[tex] x(\phi) = \left[(\phi - \phi_0)\frac{72~000}{360^\circ} + x_0\right]~\textrm{mod}~72~000 [/tex]

and I'm wondering how to invert it in order to get [itex] \phi(x) [/itex]? Also, the modulus operator is not exactly what I'm looking for here, because if x goes below 0, I want it to wrap around so that [itex] -1 \longrightarrow 71~999 [/itex], and [itex] -2 \longrightarrow 71~998 [/itex] etc. How do I express that mathematically?

Finally, the angle [itex] \phi [/itex] is restricted between values that cover a range < 360 degrees, leading me to believe this function should be one-to-one. [itex] \phi_0 [/itex] also lies in this range. [itex] x_0 [/itex] is arbitrary but should be between 0 and 71999.

EDIT: I should also mention that x is in the set of integers (which I guess means that step sizes in [itex]\phi[/itex] of less than 18 arsec don't occur).

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