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

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

Synopsis

Description

Caveat

See also

Ways to use icPIdeal:

For the programmer