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<head><title>isQuism -- Test to see if the ChainComplexMap is a quasiisomorphism.</title>
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<div><h1>isQuism -- Test to see if the ChainComplexMap is a quasiisomorphism.</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>isChainComplexMap(phi)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>phi</tt>, </span></li>
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<li><div class="single">Outputs:<ul><li><span>Boolean</span></li>
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<div class="single"><h2>Description</h2>
<div>A quasiisomorphism is a chain map that is an isomorphism in homology.Mapping cones currently do not work properly for complexes concentratedin one degree, so isQuism could return bad information in that case.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : kRes = res coker vars R
1 3 3 1
o2 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o2 : ChainComplex</pre>
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<tr><td><pre>i3 : multBya = extend(kRes,kRes,matrix{{a}})
1 1
o3 = 0 : R <--------- R : 0
| a |
3 3
1 : R <----------------- R : 1
{1} | a b c |
{1} | 0 0 0 |
{1} | 0 0 0 |
3 3
2 : R <----- R : 2
0
1 1
3 : R <----- R : 3
0
4 : 0 <----- 0 : 4
0
o3 : ChainComplexMap</pre>
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<tr><td><pre>i4 : isQuism(multBya)
o4 = false</pre>
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<tr><td><pre>i5 : F = extend(kRes,kRes,matrix{{1_R}})
1 1
o5 = 0 : R <--------- R : 0
| 1 |
3 3
1 : R <----------------- R : 1
{1} | 1 0 0 |
{1} | 0 1 0 |
{1} | 0 0 1 |
3 3
2 : R <----------------- R : 2
{2} | 1 0 0 |
{2} | 0 1 0 |
{2} | 0 0 1 |
1 1
3 : R <------------- R : 3
{3} | 1 |
4 : 0 <----- 0 : 4
0
o5 : ChainComplexMap</pre>
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<tr><td><pre>i6 : isQuism(F)
o6 = true</pre>
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<div class="waystouse"><h2>Ways to use <tt>isQuism</tt> :</h2>
<ul><li>isQuism(ChainComplexMap)</li>
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