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<head><title>SPACE -- blank operator; often used for function application, making polynomial rings</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="___S__P__A__C__E.html" title="blank operator; often used for function application, making polynomial rings">SPACE</a></div>
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<div><h1>SPACE -- blank operator; often used for function application, making polynomial rings</h1>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Function_sp__Thing.html" title="function application">Function Thing</a> -- function application</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>SPACE</tt> :</h2>
<ul><li><span>BettiTally Array, 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>BettiTally ZZ, 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__Array.html" title="degree shift">ChainComplex Array</a> -- degree shift</span></li>
<li><span><a href="___Chain__Complex__Map_sp__Array.html" title="degree shift">ChainComplexMap Array</a> -- degree shift</span></li>
<li><span><a href="___Coherent__Sheaf_sp__Z__Z.html" title="canonical twist of a coherent sheaf">CoherentSheaf ZZ</a> -- canonical twist of a coherent sheaf</span></li>
<li><span>SheafOfRings ZZ, see <span><a href="___Coherent__Sheaf_sp__Z__Z.html" title="canonical twist of a coherent sheaf">CoherentSheaf ZZ</a> -- canonical twist of a coherent sheaf</span></span></li>
<li><span>Command Thing, see <span><a href="___Command.html" title="the class of all commands">Command</a> -- the class of all commands</span></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="___Function_sp__Thing.html" title="function application">Function Thing</a> -- function application</span></li>
<li><span><a href="___Graded__Module_sp__Array.html" title="degree shift">GradedModule Array</a> -- degree shift</span></li>
<li><span>HeaderType List, see <span><a href="___Header__Type.html" title="a class of lists with abbreviated constructors">HeaderType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span>HeaderType Sequence, see <span><a href="___Header__Type.html" title="a class of lists with abbreviated constructors">HeaderType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span>CoherentSheaf LowerBound, see <span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
<li><span>SheafOfRings LowerBound, see <span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
<li><span>Manipulator Database, see <span><a href="___Manipulator.html" title="the class of all file manipulators">Manipulator</a> -- the class of all file manipulators</span></span></li>
<li><span>Manipulator File, see <span><a href="___Manipulator.html" title="the class of all file manipulators">Manipulator</a> -- the class of all file manipulators</span></span></li>
<li><span>Manipulator Nothing, see <span><a href="___Manipulator.html" title="the class of all file manipulators">Manipulator</a> -- the class of all file manipulators</span></span></li>
<li><span><a href="___Module_sp__Array.html" title="make a chain complex from a module">Module Array</a> -- make a chain complex from a module</span></li>
<li><span>Manipulator NetFile, see <span><a href="___Net__File.html" title="the class of all net files">NetFile</a> -- the class of all net files</span></span></li>
<li><span><a href="___Projective__Hilbert__Polynomial_sp__Z__Z.html" title="value of polynomial">ProjectiveHilbertPolynomial ZZ</a> -- value of polynomial</span></li>
<li><span>InexactFieldFamily Array, see <span><a href="___Ring_sp__Array.html" title="the standard way to make a polynomial ring">Ring Array</a> -- the standard way to make a polynomial ring</span></span></li>
<li><span><a href="___Ring_sp__Array.html" title="the standard way to make a polynomial ring">Ring Array</a> -- the standard way to make a polynomial ring</span></li>
<li><span><a href="___Ring_sp__List.html" title="make a local polynomial ring">Ring List</a> -- make a local polynomial ring</span></li>
<li><span><a href="___Ring_sp__Ordered__Monoid.html" title="make a polynomial ring">Ring OrderedMonoid</a> -- make a polynomial ring</span></li>
<li><span><a href="___Ring__Element_sp__Array.html" title="substitution of variables">RingElement Array</a> -- substitution of variables</span></li>
<li><span>RingMap ChainComplex, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span>RingMap Ideal, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span>RingMap Matrix, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span>RingMap Module, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></li>
<li><span>RingMap Vector, see <span><a href="___Ring__Map_sp__Ring__Element.html" title="apply a ring map">RingMap RingElement</a> -- apply a ring map</span></span></li>
<li><span>ScriptedFunctor Thing, see <span><a href="___Scripted__Functor.html" title="the class of all scripted functors">ScriptedFunctor</a> -- the class of all scripted functors</span></span></li>
<li><span>SelfInitializingType Thing, see <span><a href="___Self__Initializing__Type.html" title="the class of all self initializing types">SelfInitializingType</a> -- the class of all self initializing types</span></span></li>
<li><span>WrapperType List, see <span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span>WrapperType Sequence, see <span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></span></li>
<li><span>WrapperType Thing, see <span><a href="___Wrapper__Type.html" title="a class of lists with abbreviated constructors">WrapperType</a> -- a class of lists with abbreviated constructors</span></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___S__P__A__C__E.html" title="blank operator; often used for function application, making polynomial rings">SPACE</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 SPACE 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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