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<head><title>eulers(Ring) -- list the sectional Euler characteristics</title>
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<div><h1>eulers(Ring) -- list the sectional Euler characteristics</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>eulers R</tt></div>
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<li><span>Function: <a href="_eulers.html" title="list the sectional Euler characteristics">eulers</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, the successive sectional Euler characteristics of a (sheaf of) ring(s).</span></li>
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<div class="single"><h2>Description</h2>
<div>Computes a list of the successive sectional Euler characteristics of a ring (sheaf of), the i-th entry in the list being the Euler characteristic of the i-th generic hyperplane restriction of <tt>R</tt><table class="examples"><tr><td><pre>i1 : S = ZZ/101[a,b,c];</pre>
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<tr><td><pre>i2 : I = ideal(a^3+b^3+c^3)
3 3 3
o2 = ideal(a + b + c )
o2 : Ideal of S</pre>
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<tr><td><pre>i3 : R = S/I
o3 = R
o3 : QuotientRing</pre>
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<tr><td><pre>i4 : eulers(R)
o4 = {0, 3}
o4 : List</pre>
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<tr><td><pre>i5 : J = substitute(ideal(b,a+c),R)
o5 = ideal (b, a + c)
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : eulers(R/J)
o6 = {1}
o6 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_genera.html" title="list of the successive linear sectional arithmetic genera">genera</a> -- list of the successive linear sectional arithmetic genera</span></li>
<li><span><a href="_genus.html" title="arithmetic genus">genus</a> -- arithmetic genus</span></li>
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