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

Synopsis

Usage:
isNormal R
Function: isNormal
Inputs:
- R, a ring, a reduced ring
Outputs:
- a Boolean value, whether R is normal, i.e., whether the Serre conditions R1 and S2 hold

i1 : R = ZZ/101[x,y,z]/ideal(x^6-z^6-y^2*z^4);

i2 : isNormal R

o2 = false

i3 : S = ZZ/101[a_7,a_6,x,y,z]/ideal(x^2-a_6*z,a_6*x-a_7*z,a_6^2-a_7*x,a_7^2-y^2-z^2)

o3 = S

o3 : QuotientRing

i4 : isNormal S

o4 = true

In the example above S is the integral closure of R given in the form T/J where T is a polynomial ring and J is an ideal.