Class Number and Regulator Computation in Purely Cubic Function Fields of Unit Rank Two

@inproceedings{Fontein2010ClassNA,
  title={Class Number and Regulator Computation in Purely Cubic Function Fields of Unit Rank Two},
  author={Felix Fontein and Eric Landquist and Renate Scheidler},
  year={2010}
}
We describe and give computational results of a procedure to compute the divisor class number and regulator of most purely cubic function fields of unit rank 2. Our implementation is an improvement to Pollard's Kangaroo method in infrastructures, using distribution results of class numbers as well as information on the congruence class of the divisor class number, and an adaptation that efficiently navigates these torus-shaped infrastructures. Moreover, this is the first time that an efficient… CONTINUE READING