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 $Q$.