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Showing 1 to 5 of 5 for “"Ideal Class Group"”.
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Improved Arithmetic in the Ideal Class Group of Imaginary Quadratic Number Fields with an Application to Integer Factoring
… to arithmetic and exponentiation in the ideal class group of imaginary quadratic number fields for the Intel x64 architecture. This is useful in tabulating the class number and class group structure, but also as an application to a novel integer factoring algorithm called “SuperSPAR”. …
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Function Field Arithmetic and Related Algorithms
… the Jacobian of this curve is isomorphic to the ideal class group of K[C], the ring of regular functions on C. By exploiting the structure of ideals in K[C] as K[x] modules, we are able to produce a very efficient algorithm for performing group operations in the Jacobian which heuristically …
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On the Computation of Invariants in non-Normal, non-Pure Cubic Fields and in Their Normal Closures
… prove general results relating the ranks of the ideal class groups of the rings of integers of these cubic fields to those of their normal closures.
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Steinitz Classes of Tamely Ramified Nonabelian Extensions of Algebraic Number Fields of Degree P(3)
… - 1$ copies of ${\cal D}\sb{k}$ and a fractional ideal ${\cal J}$ of k. The class $c\ell({\cal J})$ of ${\cal J}$ in the ideal class group C(k) of k is the Steinitz class C(L,k) of ${\cal D}\sb{L}$. Now let G be a finite group of order n. As L varies over all normal extensions of k such that …
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On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures
… known. Some work has been done on the units, classnumbers and other invariants of the bicubic fields and their normal closures by Parry but no method is available for calculating those invariants. This dissertation provides an algorithm for calculating the number theoretic invariants of the …