# icFracP(...,Verbosity=>...) -- Prints out the conductor element and the number of intermediate modules it computed.

## Synopsis

• Usage:
icFracP(R, Verbosity => ZZ)

## Description

The main use of the extra information is in computing the integral closure of principal ideals in R, via icPIdeal.
 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 : S = ZZ/3[x,y,u,v]; i4 : R = S/kernel map(S,S,{x-y,x+y^2,x*y,x^2}); i5 : icFracP(R, Verbosity => 1) Number of steps: 4, Conductor Element: x*u*v^2-x*v^3 u - v x + y - v o5 = {-----, ---------, 1} x x + 1 o5 : List

## Further information

• Default value: 0
• Function: icFracP -- compute the integral closure in prime characteristic
• Option key: Verbosity -- an optional argument

## Functions with optional argument named Verbosity :

• icFracP(...,Verbosity=>...) -- Prints out the conductor element and the number of intermediate modules it computed.
• "idealizer(...,Verbosity=>...)" -- see idealizer -- compute Hom(I,I) as a quotient ring
• integralClosure(...,Verbosity=>...) -- display a certain amount of detail about the computation
• "isPrime(Ideal,Verbosity=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
• "makeS2(...,Verbosity=>...)" -- see makeS2 -- compute the S2ification of a reduced ring
• "decompose(Ideal,Verbosity=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "minimalPrimes(...,Verbosity=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "ringFromFractions(...,Verbosity=>...)" -- see ringFromFractions -- find presentation for f.g. ring