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

o2 = {1, ---}

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 eventually

See also

Ways to use icPIdeal :

For the programmer

The object icPIdeal is a method function.