Abstract
A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt--Picard group of such an order is a certain group of ideal classes that is closely related to the...
Highlights
An order is a commutative ring of which the additive group is isomorphic toZn for some n â Zâ„0
In algorithms one specifies an automorphism of an order by means of its matrix on the same Z-basis α1, . . . , αn that was used for the bijk
An A-lattice L is invertible if the values of the map ÏL of Proposition 4.1 all lie in A and the map ÏL : L âA L â A is an isomorphism of A-modules
Summary
The group of roots of unity in A might be too large to even write down in polynomial time, so the set of short vectors in L and the set of all A-isomorphisms from L to A might be too large to enumerate Our work on this subject was inspired by an algorithm of Gentry and Szydlo (Section 7 of [4]), and is related to our work on lattices with symmetry [11, 12].
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