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<div><h1>Matrix ** Module -- tensor product</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>f ** M</tt><br/><tt>M ** f</tt></div>
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<li><span>Operator: <a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___Matrix.html">matrix</a></span></span></li>
<li><span><tt>M</tt>, <span>a <a href="___Module.html">module</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>, formed by tensoring <tt>f</tt> with the identity map of <tt>M</tt></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y];</pre>
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<tr><td><pre>i2 : R^2 ** vars R
o2 = | x y 0 0 |
| 0 0 x y |
2 4
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : (vars R) ** R^2
o3 = | x 0 y 0 |
| 0 x 0 y |
2 4
o3 : Matrix R <--- R</pre>
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When <tt>N</tt> is a free module of rank 1 the net effect of the operation is to shift the degrees of <tt>f</tt>.<table class="examples"><tr><td><pre>i4 : R = ZZ/101[t];</pre>
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<tr><td><pre>i5 : f = matrix {{t}}
o5 = | t |
1 1
o5 : Matrix R <--- R</pre>
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<tr><td><pre>i6 : degrees source f
o6 = {{1}}
o6 : List</pre>
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<tr><td><pre>i7 : degrees source (f ** R^{-3})
o7 = {{4}}
o7 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Module_sp_st_st_sp__Module.html" title="tensor product">Module ** Module</a> -- tensor product</span></li>
<li><span><a href="___Matrix_sp_st_st_sp__Matrix.html" title="tensor product">Matrix ** Matrix</a> -- tensor product</span></li>
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