Rational Reconstruction

A family of algorithms to recover a rational number p/q from its image modulo an integer N or from an approximate modular residue, under size bounds on numerator and denominator, typically using continued fractions or the extended Euclidean algorithm.

A technique to recover an unknown rational number p/q from its modular image r modulo an integer M, typically by finding small numerator and denominator consistent with r via continued fractions or lattice-based methods.

A methodological procedure that reformulates informal, historical, or fragmentary beliefs, arguments, or practices into a systematic, more explicit structure (for example by making implicit premises explicit, formalizing inferences, or organizing conceptual assumptions) in order to clarify, evaluate, or improve the original material for analysis; it is an interpretive and analytic device, not a li