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# 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 $Q$.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2:298:0.