isNormal(Ring) -- determine if a reduced ring is normal

Synopsis

Function: isNormal
Usage:

isNormal R
Inputs:
- R, a ring, a reduced equidimensional ring
Outputs:
- a Boolean value, whether R is normal, that is, whether it satisfies Serre's conditions S2 and R1

Description

This function computes the jacobian of the ring which can be costly for larger rings. Therefore it checks the less costly S2 condition first and if true, then tests the R1 condition using the jacobian of R.

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);

i2 : isNormal R

o2 = false

i3 : isNormal(integralClosure R)

o3 = true

Caveat

The ring R must be an equidimensional ring. If R is a domain, then sometimes computing the integral closure of R can be faster than this test.

Ways to use this method: