Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
An algorithm for computing genera of ternary and quaternary quadratic forms
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Lattice basis reduction for indefinite forms and an application
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Computing isometries of lattices
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Subexponential algorithms for class group and unit computations
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Factoring polynomials over finite fields: a survey
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the second Magma conference
Factoring polynominals over algebraic number fields
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Rational Points Near Curves and Small Nonzero |x3-y2| via Lattice Reduction
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
How to generate random integers with known factorization
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Quadratic forms and quaternion algebras: algorithms and arithmetic
Quadratic forms and quaternion algebras: algorithms and arithmetic
Enumeration of totally real number fields of bounded root discriminant
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Computing Hilbert modular forms over fields with nontrivial class group
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Computing CM points on shimura curves arising from cocompact arithmetic triangle groups
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.