Short Representation of Quadratic Integers
Let O be a real quadratic order of discriminant Δ. For elements α in O we develop a compact representation whose binary length is polynomially bounded in log log H(α), log N(α) and log Δ where H(α) is the height of α and N(α) is the norm of α. We show that using compact representations we can in polynomial time compute norms, signs, products, and inverses of numbers in O and principal ideals generated by numbers in O. We also show how to compare numbers given in compact representation in polynomial time.
KeywordsPolynomial Time Polynomial Time Algorithm Standard Representation Class Number Compact Representation
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