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<head><title>exteriorPower(ZZ,Matrix) -- exterior power of a matrix</title>
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<div><h1>exteriorPower(ZZ,Matrix) -- exterior power of a matrix</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>exteriorPower(i,f)</tt><br/><tt>exteriorPower_i f</tt></div>
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<li><span>Function: <a href="_exterior__Power.html" title="exterior power">exteriorPower</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, the <tt>i</tt>-th exterior power of <tt>f</tt>.</span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_exterior__Power_lp..._cm_sp__Strategy_sp_eq_gt_sp..._rp.html">Strategy => ...</a>, -- choose between Bareiss and Cofactor algorithms</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/2[x,y];</pre>
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<tr><td><pre>i2 : f = random(R^3,R^{3:-1})
o2 = | x+y 0 0 |
| y y 0 |
| 0 0 x |
3 3
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : exteriorPower_2 f
o3 = | xy+y2 0 0 |
| 0 x2+xy 0 |
| 0 xy xy |
3 3
o3 : Matrix R <--- R</pre>
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The matrix may be a more general homomorphism of modules. For example,<table class="examples"><tr><td><pre>i4 : g = map(coker matrix {{x^2},{x*y},{y^2}}, R^3, id_(R^3))
o4 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
o4 : Matrix</pre>
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<tr><td><pre>i5 : g2 = exteriorPower(2,g)
o5 = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
o5 : Matrix</pre>
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<tr><td><pre>i6 : target g2
o6 = cokernel | xy x2 0 |
| y2 0 x2 |
| 0 y2 xy |
3
o6 : R-module, quotient of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_exterior__Power_lp__Z__Z_cm__Module_rp.html" title="exterior power of a module">exteriorPower(ZZ,Module)</a> -- exterior power of a module</span></li>
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