Computing the unit group and class group of a number field are two of the main tasks in computational algebraic number theory. Factoring integers reduces to solving Pell's eq...
The best practical algorithm for class group computations in imaginary quadratic number fields (such as group structure, class number, discrete logarithm computations) is a varian...
This paper analyzes the complexity of problems from class field theory. Class field theory can be used to show the existence of infinite families of number fields with constant ro...
Using a new regulator bound we determine unit groups and class groups of the 289040 quintic algebraic number fields with absolute discriminant less than 2 × 107 (totally real fi...