2 citations · 5 across the 5 of their papers we have counts for
5 papers
Exact -adic computation in Magma
Christopher Doris
We describe a new arithmetic system for the Magma computer algebra system for working with -adic numbers exactly, in the sense that numbers are represented lazily to infinite $p…
Computing the Galois group of a polynomial over a -adic field
Christopher Doris
We present a family of algorithms for computing the Galois group of a polynomial defined over a -adic field. Apart from the "naive" algorithm, these are the first general algori…
ExactpAdics: An exact representation of p-adic numbers
Christopher Doris
We describe two new packages ExactpAdics and ExactpAdicsII for the Magma computer algebra system for working with p-adic numbers exactly, in the sense that numbers are represented…
On enumerating extensions of p-adic fields with given invariants
Christopher Doris
We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons of Eisenstein polynomials over p-adic fields, their associated residual polynomials a…
3-torsion and conductor of genus 2 curves
Tim Dokchitser, Christopher Doris
We give an algorithm to compute the conductor for curves of genus 2. It is based on the analysis of 3-torsion of the Jacobian for genus 2 curves over 2-adic fields.