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Analytical beam optics deals with the basic properties of the magnetic modules which compose particle accelerators in the same way as light optics was developed for telescopes, microscopes, or other instruments. The difference between photon and charged-particle optics lies in the nature of the field which acts upon the particle. The magnets of accelerators do not have the rotational symmetry of glass lenses and the computational problems are much more difficult. For this reason, the symbolic program BeamOptics has been written to assist the user in finding the parameters of systems whose complexity is better treated by computer than by hand. Symbolic results may be hard to interpret. Thin-lens models have been adopted because their description is algebraic and emphasis has been put on the existence of solutions, the number of solutions, and simple yet unknown special schemes. The program can also be applied to real machines with long elements. In that case, it works with numerical data but the results are accessible through continuous functions which provide the machine parameters at arbitrary positions along the reference orbit. The code is organized to be implemented in accelerator controls and has functions to correct all the first-order perturbations using a universal procedure.
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