isNormal Ring -- determine if a reduced ring is normal

isNormal Ring -- determine if a reduced ring is normal

Synopsis:

Usage: isNormal R

Function: isNormal

Input:

R, an instance of class Ring: reduced ring

Output:

an instance of class Boolean: is R1 and S2 and false otherwise.

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.