# KASH3 Ref - RationalReconstruction

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### Function

RationalReconstruction ( elt-res^rat x ) -> elt-alg^boo, elt-fld^rat

### Optional Arguments

Results | elt-ord^rat |  | 1 <= Results <= 2

### Description

<shortdoc> Given an element x of the ring of integers mod M, return true and the unique rational r = (n / d) if such exists with the absolute values of n and d less than or equal to Isqrt(M div 2); return false otherwise. </shortdoc>

### Examples

x_Z3:=IntegerRing(3); x_a:=Coerce(x_Z3,5); RationalReconstruction(x_a);

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