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<head><title>Vector ** Vector -- tensor product</title>
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<div><h1>Vector ** Vector -- 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>v ** w</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>v</tt>, <span>a <a href="___Vector.html">vector</a></span></span></li>
<li><span><tt>w</tt>, <span>a <a href="___Vector.html">vector</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Vector.html">vector</a></span>, the tensor product of v and w</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>v</tt> is in the module <tt>M</tt>, and <tt>w</tt> is in the module <tt>N</tt>, then <tt>v**w</tt> is in the module <tt>M**N</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ[a..d];</pre>
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<tr><td><pre>i2 : F = R^3
3
o2 = R
o2 : R-module, free</pre>
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<tr><td><pre>i3 : G = coker vars R
o3 = cokernel | a b c d |
1
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : v = (a-37)*F_1
o4 = | 0 |
| a-37 |
| 0 |
3
o4 : R</pre>
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<tr><td><pre>i5 : v ** G_0
o5 = | 0 |
| -37 |
| 0 |
o5 : cokernel | a b c d 0 0 0 0 0 0 0 0 |
| 0 0 0 0 a b c d 0 0 0 0 |
| 0 0 0 0 0 0 0 0 a b c d |</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>
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