Abstract
The Minkowski method of unit search is applied to particular types of parallelotopes permitting to discover algebraic integers of bounded norm in a given algebraic number field of degree n at will by solving successively 2 n 2n linear inequalities for one unknown each. Application is made to the unit search for all totally real number fields of minimal discriminant for n ⩽ 7 n \leqslant 7 .
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