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<head><title>presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring</title>
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<div><h1>presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>presentation B</tt><br/><tt>presentation(A,B)</tt></div>
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<li><span>Function: <a href="_presentation.html" title="presentation of a module or ring">presentation</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>A</tt>, <span>a <a href="___Polynomial__Ring.html">polynomial ring</a></span></span></li>
<li><span><tt>B</tt>, <span>a <a href="___Quotient__Ring.html">quotient ring</a></span>, a quotient ring of A</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, whose image is the ideal of <tt>A</tt> defining <tt>B</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>If A is not present, then it is understood to be the ultimate ambient polynomial ring of B. In general, A may be any ring of which B is a quotient.<p/>
In the examples below, A is the ultimate ambient polynomial ring of A, B and C.<table class="examples"><tr><td><pre>i1 : A = QQ[a..d];</pre>
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<tr><td><pre>i2 : B = A/(a^2,b^3);</pre>
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<tr><td><pre>i3 : C = B/(a*b*c,b*c*d, b^2);</pre>
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<tr><td><pre>i4 : presentation A
o4 = 0
1
o4 : Matrix A <--- 0</pre>
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<tr><td><pre>i5 : presentation B
o5 = | a2 b3 |
1 2
o5 : Matrix A <--- A</pre>
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<tr><td><pre>i6 : presentation C
o6 = | abc bcd b2 a2 b3 |
1 5
o6 : Matrix A <--- A</pre>
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<tr><td><pre>i7 : presentation(B,C)
o7 = | abc bcd b2 |
1 3
o7 : Matrix B <--- B</pre>
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<tr><td><pre>i8 : presentation(A,C)
o8 = | abc bcd b2 a2 b3 |
1 5
o8 : Matrix A <--- A</pre>
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<tr><td><pre>i9 : minimalPresentation C
QQ[a, b, c, d]
o9 = --------------------------
2 3 2
(a , b , a*b*c, b*c*d, b )
o9 : QuotientRing</pre>
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<div class="single"><h2>Caveat</h2>
<div>The given presentation is often not minimal</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_minimal__Presentation.html" title="compute a minimal presentation">minimalPresentation</a> -- compute a minimal presentation</span></li>
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