isDomain -- whether a ring is a domain

Synopsis

This function returns true if R is an integral domain, otherwise it returns false. It simply checks whether the zero ideal is prime.

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

o1 = R

o1 : QuotientRing

i2 : isDomain(R)

o2 = true

i3 : S = ZZ/5[x,y]/ideal(x^2*y^3)

o3 = S

o3 : QuotientRing

i4 : isDomain(S)

o4 = false