Given an ideal I returns a non-zerodivisor in I with small coefficients (in the LLL sense). This is achieved by randomly picking an element with small coefficients in a LLL-reduced basis (wrt the T2 norm as a Z-lattice).
Given a fractional R-ideal I, it returns an isomorphic ideal a .I, and the element a,
such that a .I is a subset of R, and the cardinality of R/aI is small.
This is achieved by computing the ShortElement a of (R:I).
Note that if I is invertible R/aI is isomorphic to (R:I)/aR.
V2.29, 26 September 2025