Engineering↗
Computing the Structure of Residue Rings
The structure of the unit group of a residue ring of the maximal order, and its computation by decomposition and lifting.
Every page in the KEVOS library tagged Conductor. 5 pages.
The structure of the unit group of a residue ring of the maximal order, and its computation by decomposition and lifting.
Reduction of an elliptic curve modulo a prime, the classification of bad reduction types, and Tate's algorithm.
Cyclic cubic and pure cubic fields as parametrised families, with closed-form invariants that avoid general algorithms.
Orders as subrings that are full-rank lattices, the equation order, the maximal order, and the index that separates them.
Computing minimal Weierstrass models, Tate's algorithm for reduction type and conductor, torsion subgroup determination, heights, and descent for rank computation.