# Singular Book 1.3.13 -- computation in quotient rings

In Macaulay2, we define a quotient ring using the usual mathematical notation.
 i1 : R = ZZ/32003[x,y,z]; i2 : Q = R/(x^2+y^2-z^5, z-x-y^2) o2 = Q o2 : QuotientRing i3 : f = z^2+y^2 2 o3 = z - x + z o3 : Q i4 : g = z^2+2*x-2*z-3*z^5+3*x^2+6*y^2 2 o4 = z - x + z o4 : Q i5 : f == g o5 = true
Testing for zerodivisors in Macaulay2:
 i6 : ann f o6 = ideal () o6 : Ideal of Q
This is the zero ideal, meaning that $f$ is not a zero divisor in the ring $Q$.