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<head><title>Singular Book 1.3.13 -- computation in quotient rings</title>
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<div><h1>Singular Book 1.3.13 -- computation in quotient rings</h1>
<div>In Macaulay2, we define a quotient ring using the usual mathematical notation.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[x,y,z];</pre>
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<tr><td><pre>i2 : Q = R/(x^2+y^2-z^5, z-x-y^2)
o2 = Q
o2 : QuotientRing</pre>
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<tr><td><pre>i3 : f = z^2+y^2
2
o3 = z - x + z
o3 : Q</pre>
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<tr><td><pre>i4 : g = z^2+2*x-2*z-3*z^5+3*x^2+6*y^2
2
o4 = z - x + z
o4 : Q</pre>
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<tr><td><pre>i5 : f == g
o5 = true</pre>
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Testing for zerodivisors in Macaulay2:<table class="examples"><tr><td><pre>i6 : ann f
o6 = ideal ()
o6 : Ideal of Q</pre>
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This is the zero ideal, meaning that <i>f</i> is not a zero divisor in the ring <i>Q</i>.</div>
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