- 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)`.

- the integral closure of the ideal

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 |

The interface to this algorithm will likely change in Macaulay2 1.4

- icFracP -- compute the integral closure in prime characteristic

- icPIdeal(RingElement,RingElement,ZZ)