Computational Aspects of NUCOMP
In 1989, Shanks introduced the NUCOMP algorithm  for computing the reduced composite of two positive definite binary quadratic forms of discriminant Δ. Essentially by applying reduction before composing the two forms, the intermediate operands are reduced from size O(Δ) to O(Δ 1/2) in most cases and at worst to O(Δ 3/4). Shanks made use of this to extend the capabilities of his hand-held calculator to computations involving forms with discriminants with as many as 20 decimal digits, even though his calculator had only some 10 digits precision. Improvements by Atkin (described in , ) have also made NUCOMP very effective for computations with forms of larger discriminant.
KeywordsCommunication Partner Computational Aspect Quadratic Number Binary Quadratic Form Ideal Arithmetic
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