Titlebook: Cubic Fields with Geometry; Samuel A. Hambleton,Hugh C. Williams Book 2018 Springer Nature Switzerland AG 2018 binary cubic forms.cubic fi

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The , and Polish Partisan Warfare, 1939–43d relate these to the work of Godwin. We give a few algorithms for finding units of a cubic field of negative discriminant inspired by what we learn here. The main theme of this chapter is the applications of Diophantine approximation to problems associated with cubic fields.

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Construction of All Cubic Fields of a Fixed Fundamental Discriminant (Renate Scheidler),n of Shanks’ method due toFung found generating polynomials of all 364 cubic fields with a 19-digit discriminant. This chapter presents the never before published Shanks-Fung algorithm and, for completeness, concludes with a brief summary ofBelabas’ fast technique for tabulating all cubic fields of bounded discriminant.

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