In the fictional Star Trek universe, a holodeck is an enclosed room with force-fields, the same sort of thing as shields and deflector fields, onto which light is projected allowing three dimensional surfaces of objects.
Considering how often the holodeck malfunctioned, it is surprising they were not all disabled and removed.
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... the formula should be understood as "either of those element(s) of the field whose square equals b2 - 4ac". In some fields, some elements have no square roots ...