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<head><title>typeA -- Type A reflection arrangement</title>
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<div><h1>typeA -- Type A reflection arrangement</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>typeA(n) or typeA(n,R) or typeA(n,k)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the rank</span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span>, a polynomial (coordinate) ring in n+1 variables</span></li>
<li><span><tt>k</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, a coefficient ring; by default, <tt>QQ</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Arrangement.html">hyperplane arrangement</a></span>, the A_n reflection arrangement</span></li>
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<div class="single"><h2>Description</h2>
<div>The hyperplane arrangement with hyperplanes x_i-x_j.<table class="examples"><tr><td><pre>i1 : A3 = typeA(3)
o1 = {x - x , x - x , x - x , x - x , x - x , x - x }
1 2 1 3 1 4 2 3 2 4 3 4
o1 : Hyperplane Arrangement </pre>
</td></tr>
<tr><td><pre>i2 : describe A3
o2 = {x - x , x - x , x - x , x - x , x - x , x - x }
1 2 1 3 1 4 2 3 2 4 3 4</pre>
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<tr><td><pre>i3 : ring A3
o3 = QQ[x , x , x , x ]
1 2 3 4
o3 : PolynomialRing</pre>
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Alternatively, one may specify a coordinate ring,<table class="examples"><tr><td><pre>i4 : S = ZZ[w,x,y,z];</pre>
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<tr><td><pre>i5 : A3' = typeA(3,S)
o5 = {w - x, w - y, w - z, x - y, x - z, y - z}
o5 : Hyperplane Arrangement </pre>
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<tr><td><pre>i6 : describe A3'
o6 = {w - x, w - y, w - z, x - y, x - z, y - z}</pre>
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or a coefficient ring:<table class="examples"><tr><td><pre>i7 : A4 = typeA(4,ZZ/3)
o7 = {x - x , x - x , x - x , x - x , x - x , x - x , x - x , x - x , x - x , x - x }
1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 3 5 4 5
o7 : Hyperplane Arrangement </pre>
</td></tr>
<tr><td><pre>i8 : ring A4
ZZ
o8 = --[x , x , x , x , x ]
3 1 2 3 4 5
o8 : PolynomialRing</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_type__B.html" title="Type B reflection arrangement">typeB</a> -- Type B reflection arrangement</span></li>
<li><span><a href="_type__D.html" title="Type D reflection arrangement">typeD</a> -- Type D reflection arrangement</span></li>
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<div class="waystouse"><h2>Ways to use <tt>typeA</tt> :</h2>
<ul><li>typeA(ZZ)</li>
<li><span><a href="_type__A_lp__Z__Z_cm__Polynomial__Ring_rp.html" title="A_n arrangement with specified coordinate ring">typeA(ZZ,PolynomialRing)</a> -- A_n arrangement with specified coordinate ring</span></li>
<li><span><a href="_type__A_lp__Z__Z_cm__Ring_rp.html" title="A_n reflection arrangement with specified coefficient ring">typeA(ZZ,Ring)</a> -- A_n reflection arrangement with specified coefficient ring</span></li>
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