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<head><title>+ -- a unary or binary operator, usually used for addition</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="__pl.html" title="a unary or binary operator, usually used for addition">+</a></div>
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<div><h1>+ -- a unary or binary operator, usually used for addition</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>+y </tt><br/><tt> x+y</tt></div>
</dd></dl>
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</li>
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<div class="single"><h2>Description</h2>
<div>In most cases, this operator refers to standard addition.<p/>
In many cases, the integer 1 can be used as the identity, and scalars function as multiples of the identity. For example, the 1 below refers to the identity matrix and the 2 to twice the identity matrix.<table class="examples"><tr><td><pre>i1 : M = matrix{{1,2,3},{2,3,4},{3,4,6}}
o1 = | 1 2 3 |
| 2 3 4 |
| 3 4 6 |
3 3
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : M+1, M+2
o2 = (| 2 2 3 |, | 3 2 3 |)
| 2 4 4 | | 2 5 4 |
| 3 4 7 | | 3 4 8 |
o2 : Sequence</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_plus.html" title="addition">plus</a> -- addition</span></li>
<li><span><a href="_sum.html" title="compute the sum">sum</a> -- compute the sum</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>+</tt> :</h2>
<ul><li>+ CC</li>
<li>+ Constant</li>
<li>+ QQ</li>
<li>+ RR</li>
<li>+ ZZ</li>
<li>CC + CC</li>
<li>CC + QQ</li>
<li>CC + RR</li>
<li>CC + ZZ</li>
<li>ChainComplexMap + ChainComplexMap</li>
<li>ChainComplexMap + RingElement</li>
<li>ChainComplexMap + ZZ</li>
<li>Constant + Constant</li>
<li>Constant + InexactNumber</li>
<li>Constant + Number</li>
<li>GradedModuleMap + GradedModuleMap</li>
<li>GradedModuleMap + RingElement</li>
<li>Ideal + RingElement</li>
<li>InexactNumber + Constant</li>
<li>InfiniteNumber + InfiniteNumber</li>
<li>InfiniteNumber + ZZ</li>
<li>Matrix + Matrix</li>
<li>Matrix + Number</li>
<li>Matrix + RingElement</li>
<li>MonomialIdeal + MonomialIdeal</li>
<li>MutableMatrix + MutableMatrix</li>
<li>Number + Constant</li>
<li>Number + Matrix</li>
<li>ProjectiveHilbertPolynomial + ProjectiveHilbertPolynomial</li>
<li>QQ + CC</li>
<li>QQ + QQ</li>
<li>QQ + RR</li>
<li>QQ + ZZ</li>
<li>RingElement + ChainComplexMap</li>
<li>RingElement + GradedModuleMap</li>
<li>RingElement + Matrix</li>
<li>RingElement + RingElement</li>
<li>RR + CC</li>
<li>RR + QQ</li>
<li>RR + RR</li>
<li>RR + ZZ</li>
<li>Vector + Vector</li>
<li>ZZ + CC</li>
<li>ZZ + ChainComplexMap</li>
<li>ZZ + InfiniteNumber</li>
<li>ZZ + QQ</li>
<li>ZZ + RR</li>
<li>ZZ + ZZ</li>
<li><span>Constant + RingElement, see <span><a href="___Constant.html" title="">Constant</a></span></span></li>
<li><span>RingElement + Constant, see <span><a href="___Constant.html" title="">Constant</a></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="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></li>
<li><span>Ideal + MonomialIdeal, see <span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></span></li>
<li><span>MonomialIdeal + Ideal, see <span><a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a> -- sum of ideals</span></span></li>
<li><span><tt>InexactNumber + RingElement</tt> (missing documentation<!-- tag: (+,InexactNumber,RingElement) -->)</span></li>
<li><span><a href="___List_sp_pl_sp__List.html" title="sum of two vectors">List + List</a> -- sum of two vectors</span></li>
<li><span><a href="___Module_sp_pl_sp__Module.html" title="sum of submodules">Module + Module</a> -- sum of submodules</span></li>
<li><span><tt>RingElement + InexactNumber</tt> (missing documentation<!-- tag: (+,RingElement,InexactNumber) -->)</span></li>
<li><span><a href="___Set_sp_pl_sp__Set.html" title="set union">Set + Set</a> -- set union</span></li>
<li><span><a href="___Tally_sp_pl_sp__Tally.html" title="union of tallies">Tally + Tally</a> -- union of tallies</span></li>
<li><span><tt>VirtualTally + VirtualTally</tt> (missing documentation<!-- tag: (+,VirtualTally,VirtualTally) -->)</span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="__pl.html" title="a unary or binary operator, usually used for addition">+</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>
</div>
<div><p>This operator may be used as a prefix unary operator in an expression like <tt>+y</tt>. The user may <a href="_installing_spmethods.html">install a method</a> for handling such expressions with code such as</p>
<pre> + Y := (y) -> ...</pre>
<p>where <tt>Y</tt> is the class of <tt>y</tt>.</p>
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