icPIdeal -- compute the integral closure in prime characteristic of a principal ideal

Synopsis

• Usage:
icPIdeal (a, D, N)
• Inputs:
• a, an element in R
• D, a non-zerodivisor of R that is in the conductor
• N, the number of steps in icFracP to compute the integral closure of R, by using the conductor element D
• Outputs:
• the integral closure of the ideal (a).

Description

The main input is an element a which generates a principal ideal whose integral closure we are seeking. The other two input elements, a non-zerodivisor conductor element D and the number of steps N are the pieces of information obtained from icFracP(R, Verbosity => true). (See the Singh--Swanson paper, An algorithm for computing the integral closure, Remark 1.4.)
 i1 : R=ZZ/3[u,v,x,y]/ideal(u*x^2-v*y^2); i2 : icFracP(R, Verbosity => 1) Number of steps: 3, Conductor Element: x^2 u*x o2 = {1, ---} y o2 : List i3 : icPIdeal(x, x^2, 3) o3 = ideal (x, v*y) o3 : Ideal of R

Caveat

The interface to this algorithm will likely change eventually