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 $Q$.