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The correspondence is explicitly provided by Minkowski's question-mark function. That article also reviews tools that make it easy to work with such continued fractions. Consider first the purely periodic part
:This can, in fact, be written as
:with the being integers, and satisfying Explicit values can be obtained by writing
:which is termed a "shift", so that
:and similarly a reflection, given by
:so that . Both of these matrices are unimodular,

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