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<head><title>** -- a binary operator, usually used for tensor product or Cartesian product</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_operators.html" title="">operators</a> > <a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a></div>
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<div><h1>** -- a binary operator, usually used for tensor product or Cartesian product</h1>
<div><!--empty documentation body--></div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_^_st_st.html" title="a binary operator, usually used for tensor or Cartesian power">^**</a> -- a binary operator, usually used for tensor or Cartesian power</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>**</tt> :</h2>
<ul><li><span><a href="___Affine__Variety_sp_st_st_sp__Ring.html" title="a binary operator, usually used for tensor product or Cartesian product">AffineVariety ** Ring</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span>BettiTally ** BettiTally, see <span><a href="___Betti__Tally.html" title="the class of all Betti tallies">BettiTally</a> -- the class of all Betti tallies</span></span></li>
<li><span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplex ** ChainComplex</a> -- tensor product</span></li>
<li><span>ChainComplex ** Module, see <span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplex ** ChainComplex</a> -- tensor product</span></span></li>
<li><span>Module ** ChainComplex, see <span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplex ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplex ** ChainComplexMap</a> -- tensor product</span></li>
<li><span>Module ** ChainComplexMap, see <span><a href="___Chain__Complex_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplex ** ChainComplexMap</a> -- tensor product</span></span></li>
<li><span><a href="___Chain__Complex_sp_st_st_sp__Graded__Module.html" title="tensor product">ChainComplex ** GradedModule</a> -- tensor product</span></li>
<li><span><a href="___Chain__Complex_sp_st_st_sp__Ring.html" title="a binary operator, usually used for tensor product or Cartesian product">ChainComplex ** Ring</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplexMap ** ChainComplex</a> -- tensor product</span></li>
<li><span>ChainComplexMap ** Module, see <span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex.html" title="tensor product">ChainComplexMap ** ChainComplex</a> -- tensor product</span></span></li>
<li><span><a href="___Chain__Complex__Map_sp_st_st_sp__Chain__Complex__Map.html" title="tensor product">ChainComplexMap ** ChainComplexMap</a> -- tensor product</span></li>
<li><span><a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html" title="tensor produce of coherent sheaves">CoherentSheaf ** CoherentSheaf</a> -- tensor produce of coherent sheaves</span></li>
<li><span>Expression ** Expression, see <span><a href="___Expression.html" title="the class of all expressions">Expression</a> -- the class of all expressions</span></span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Chain__Complex.html" title="tensor product">GradedModule ** ChainComplex</a> -- tensor product</span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Graded__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** GradedModule</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span><a href="___Graded__Module_sp_st_st_sp__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** Module</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<li><span>Module ** GradedModule, see <span><a href="___Graded__Module_sp_st_st_sp__Module.html" title="a binary operator, usually used for tensor product or Cartesian product">GradedModule ** Module</a> -- a binary operator, usually used for tensor product or Cartesian product</span></span></li>
<li><span><a href="___Matrix_sp_st_st_sp__Matrix.html" title="tensor product">Matrix ** Matrix</a> -- tensor product</span></li>
<li><span><a href="___Matrix_sp_st_st_sp__Module.html" title="tensor product">Matrix ** Module</a> -- tensor product</span></li>
<li><span>Module ** Matrix, see <span><a href="___Matrix_sp_st_st_sp__Module.html" title="tensor product">Matrix ** Module</a> -- tensor product</span></span></li>
<li><span><a href="___Matrix_sp_st_st_sp__Ring.html" title="tensor product">Matrix ** Ring</a> -- tensor product</span></li>
<li><span>Ring ** Matrix, see <span><a href="___Matrix_sp_st_st_sp__Ring.html" title="tensor product">Matrix ** Ring</a> -- tensor product</span></span></li>
<li><span><a href="___Matrix_sp_st_st_sp__Ring__Element.html" title="a binary operator, usually used for tensor product or Cartesian product">Matrix ** RingElement</a> -- a binary operator, usually used for tensor product or Cartesian product</span></li>
<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="___Module_sp_st_st_sp__Ring.html" title="tensor product">Module ** Ring</a> -- tensor product</span></li>
<li><span>Ring ** Module, see <span><a href="___Module_sp_st_st_sp__Ring.html" title="tensor product">Module ** Ring</a> -- tensor product</span></span></li>
<li><span><a href="___Monoid_sp_st_st_sp__Monoid.html" title="tensor product of monoids">Monoid ** Monoid</a> -- tensor product of monoids</span></li>
<li><span><a href="___Ring_sp_st_st_sp__Ring.html" title="tensor product">Ring ** Ring</a> -- tensor product</span></li>
<li><span><a href="___Ring__Map_sp_st_st_sp__Matrix.html" title="tensor product of a module map via a ring map">RingMap ** Matrix</a> -- tensor product of a module map via a ring map</span></li>
<li><span><a href="___Ring__Map_sp_st_st_sp__Module.html" title="tensor product of a module via a ring map">RingMap ** Module</a> -- tensor product of a module via a ring map</span></li>
<li><span><a href="___Set_sp_st_st_sp__Set.html" title="Cartesian product">Set ** Set</a> -- Cartesian product</span></li>
<li><span><a href="___Tally_sp_st_st_sp__Tally.html" title="Cartesian product of tallies">Tally ** Tally</a> -- Cartesian product of tallies</span></li>
<li><span><a href="___Vector_sp_st_st_sp__Vector.html" title="tensor product">Vector ** Vector</a> -- tensor product</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a> is <span>a <a href="___Keyword.html">keyword</a></span>.</p>
<div><div><p>This operator may be used as a binary operator in an expression like <tt>x**y</tt>.  The user may install <a href="_binary_spmethods.html" title="">binary methods</a> for handling such expressions with code such as</p>
<pre>         X ** Y := (x,y) -> ...</pre>
<p>where <tt>X</tt> is the class of <tt>x</tt> and <tt>Y</tt> is the class of <tt>y</tt>.</p>
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