Table: Make a list or array of values or expressions

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Table[expr, {i, imax}] generates a list of the values of expr when i runs from 1 to imax. Table[expr, {i, imin, imax}] starts with i = imin. Table[expr, {i, imin, imax, di}] uses steps di. Table[expr, {i, {i1, i2, ...}}] uses the successive values i1, i2, .... Table[expr, {i, imin, imax}, {j, jmin, jmax}, ...] gives a nested list. 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class="TI">n</span></span> copies of <span class="IF"><span class="TI">expr</span></span>. </p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/Table.en/usage_2.txt"> <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">max</span></sub><span class="closebrace">}</span><span class="closebracket">]</span></span> </p> <p class="code-description">generates a list of the values of <span class="IF"><span class="TI">expr</span></span> when <span class="IF"><span class="TI">i</span></span> runs from 1 to <span class="IF"><span class="TI">i</span><sub><span class="TI">max</span></sub></span>. </p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/Table.en/usage_3.txt"> <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">min</span></sub><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">max</span></sub><span class="closebrace">}</span><span class="closebracket">]</span></span> </p> <p class="code-description">starts with <span class="IF"><span class="TI">i</span>=<span class="TI">i</span><sub><span class="TI">min</span></sub></span>. </p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/Table.en/usage_4.txt"> <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">min</span></sub><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">max</span></sub><span class="comma">,</span><span class="TI">di</span><span class="closebrace">}</span><span class="closebracket">]</span></span> </p> <p class="code-description">uses steps <span class="IF"><span class="TI">di</span></span>. </p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/Table.en/usage_5.txt"> <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><sub><span class="TR">1</span></sub><span class="comma">,</span><span class="TI">i</span><sub><span class="TR">2</span></sub><span class="comma">,</span><span class="TR"><span class="special-character Ellipsis">…</span></span><span class="closebrace">}</span><span class="closebrace">}</span><span class="closebracket">]</span></span> </p> <p class="code-description">uses the successive values <span class="IF"><span class="TI">i</span><sub><span class="TR">1</span></sub></span>, <span class="IF"><span class="TI">i</span><sub><span class="TR">2</span></sub></span>, <span class="IF"><span class="special-character Ellipsis">…</span></span>.</p> </div> <div class="functionIntro"> <p class="code clipboard-inline" data-code="Files/Table.en/usage_6.txt"> <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">i</span><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">min</span></sub><span class="comma">,</span><span class="TI">i</span><sub><span class="TI">max</span></sub><span class="closebrace">}</span><span class="comma">,</span><span class="openbrace">{</span><span class="TI">j</span><span class="comma">,</span><span class="TI">j</span><sub><span class="TI">min</span></sub><span class="comma">,</span><span class="TI">j</span><sub><span class="TI">max</span></sub><span class="closebrace">}</span><span class="comma">,</span><span class="TR"><span class="special-character Ellipsis">…</span></span><span class="closebracket">]</span></span> </p> <p class="code-description">gives a nested list. The list associated with <span class="IF"><span class="TI">i</span></span> is outermost.<a href="#25318" class="ExampleButtonLink"> <span class="special-character RightGuillemet">»</span></a></p> </div> </div><section id="DetailsAndOptions"><div class="inner"> <h1 class="toggle">Details</h1> <div class="NotesThumbnails"> <img src="Files/Table.en/details_1.png" height="57" width="171" alt="" /> </div> <div class="hideable"> <ul class="functionList"> <li><a name="13000"></a>You can use <span class="IF"><a href="/language/ref/Table.html">Table</a></span> to build up vectors, matrices, tensors, and other arrays. </li> <li><a name="12212"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> uses the standard Wolfram Language iteration specification. </li> <li><a name="21100"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> evaluates its arguments in a nonstandard way.</li> <li><a name="7551"></a><span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">spec</span><span class="closebracket">]</span></span> first evaluates <span class="IF"><span class="TI">spec</span></span>, then localizes the variable specified and successively assigns values to it, each time evaluating <span class="IF"><span class="TI">expr</span></span>.</li> <li><a name="25476"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> effectively uses <span class="IF"><a href="/language/ref/Block.html">Block</a></span> to localize values or variables.</li> <li><a name="6379"></a><span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">spec</span><sub><span class="TR">1</span></sub><span class="comma">,</span><span class="TI">spec</span><sub><span class="TR">2</span></sub><span class="closebracket">]</span></span> is effectively equivalent to <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span>Table<span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">spec</span><sub><span class="TR">2</span></sub><span class="closebracket">]</span><span class="comma">,</span><span class="TI">spec</span><sub><span class="TR">1</span></sub><span class="closebracket">]</span></span>.</li> <li><a name="1912970455"></a><span class="IF"><a href="/language/ref/Parallelize.html">Parallelize</a><span class="openbracket">[</span>Table<span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">iter</span><span class="closebracket">]</span><span class="closebracket">]</span></span> or <span class="IF"><a href="/language/ref/ParallelTable.html">ParallelTable</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">iter</span><span class="closebracket">]</span></span> computes <span class="IF"><a href="/language/ref/Table.html">Table</a><span class="openbracket">[</span><span class="TI">expr</span><span class="comma">,</span><span class="TI">iter</span><span class="closebracket">]</span></span> in parallel on all subkernels.<a href="#574066102" class="ExampleButtonLink"> <span class="special-character RightGuillemet">»</span></a></li> </ul> </div> </div></section><section id="Examples"><h1 id="191012613" class="toggle open">Examples</h1><span class="open-all on">open all</span><span class="close-all">close all</span><div class="hideable"> <div> <h2 id="2008418073" class="toggle open">Basic Examples<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(6)</span></h2> <div class="hideable"> <p><a name="14504"></a>A table of the first 10 squares:</p> <div id="12946" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_1.png" data-in-width="109" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-j9w" data-code="Files/Table.en/i_1.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_1.png" data-out-width="183" data-out-height="18" ></div> <div class="ExLine"><a name="20308"></a></div> <p><a name="12157"></a>A table with <span class="IM"><img src="Files/Table.en/1.png" height="15" width="5" alt="" /></span> running from 0 to 20 in steps of 2:</p> <div id="1430" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_2.png" data-in-width="135" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-bd0" data-code="Files/Table.en/i_2.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_2.png" data-out-width="302" data-out-height="18" ></div> <div class="ExLine"><a name="6464"></a></div> <p><a name="4074"></a>A list of 10 <span class="IM"><img src="Files/Table.en/2.png" height="15" width="8" alt="" /></span>'s:</p> <div id="4346" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_3.png" data-in-width="74" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-dm0" data-code="Files/Table.en/i_3.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_3.png" data-out-width="125" data-out-height="18" ></div> <div class="ExLine"><a name="1981"></a></div> <p><a name="25318"></a>Make a 4<span class="special-character Times">×</span>3 matrix:</p> <div id="26611" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_4.png" data-in-width="156" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-uth" data-code="Files/Table.en/i_4.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_4.png" data-out-width="267" data-out-height="18" ></div> <div id="17591" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_5.png" data-in-width="94" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-nux" data-code="Files/Table.en/i_5.txt" ></div> <div class="clipboard-output" data-out=" " data-out-num="" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_5.png" data-out-width="72" data-out-height="65" ></div> <div class="ExLine"><a name="27123"></a></div> <p><a name="6461"></a>Plot a table:</p> <div id="16991" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_6.png" data-in-width="194" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-nd9" data-code="Files/Table.en/i_6.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_6.png" data-out-width="151" data-out-height="95" ></div> <div class="ExLine"><a name="27330"></a></div> <p><a name="28498"></a>Arrange a table in a column:</p> <div id="17369" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_7.png" data-in-width="187" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-nor" data-code="Files/Table.en/i_7.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_7.png" data-out-width="14" data-out-height="82" ></div> </div> </div> <div> <h2 id="14179" class="toggle">Scope<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(6)</span></h2> <div class="hideable"> <p><a name="24117"></a>The index in the table can run backward:</p> <div id="2317" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_8.png" data-in-width="152" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-b2n" data-code="Files/Table.en/i_8.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_8.png" data-out-width="214" data-out-height="18" ></div> <div class="ExLine"><a name="1595"></a></div> <p><a name="1441"></a>Make a triangular array:</p> <div id="5936" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_9.png" data-in-width="152" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-eu6" data-code="Files/Table.en/i_9.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_9.png" data-out-width="333" data-out-height="18" ></div> <div id="7028" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_10.png" data-in-width="89" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-fpi" data-code="Files/Table.en/i_10.txt" ></div> <div class="clipboard-output" data-out=" " data-out-num="" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_10.png" data-out-width="175" data-out-height="82" ></div> <div class="ExLine"><a name="27909"></a></div> <p><a name="13973"></a>Make a 3<span class="special-character Times">×</span>2<span class="special-character Times">×</span>4 array, or tensor:</p> <div id="17981" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_11.png" data-in-width="240" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-n5r" data-code="Files/Table.en/i_11.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_11.png" data-out-width="471" data-out-height="35" ></div> <div class="ExLine"><a name="66821681"></a></div> <p><a name="38249001"></a>Iterate over an existing list:</p> <div id="1028220083" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_12.png" data-in-width="188" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ragly9" data-code="Files/Table.en/i_12.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_12.png" data-out-width="55" data-out-height="18" ></div> <div class="ExLine"><a name="74435587"></a></div> <p><a name="154543735"></a>Make an array from existing lists:</p> <div id="126626299" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_13.png" data-in-width="239" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-cdobrh" data-code="Files/Table.en/i_13.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_13.png" data-out-width="178" data-out-height="22" ></div> <div class="ExLine"><a name="1119339338"></a></div> <p><a name="779506046"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> evaluates the expression separately each time:</p> <div id="1224037689" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_14.png" data-in-width="187" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ui1ns7" data-code="Files/Table.en/i_14.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_14.png" data-out-width="267" data-out-height="18" ></div> </div> </div> <div> <h2 id="26569" class="toggle">Generalizations & Extensions<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(3)</span></h2> <div class="hideable"> <p><a name="6816"></a>The table index can have symbolic values:</p> <div id="1883" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_15.png" data-in-width="188" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-bql" data-code="Files/Table.en/i_15.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_15.png" data-out-width="417" data-out-height="19" ></div> <div class="ExLine"><a name="5385"></a></div> <p><a name="28402"></a>The variables need not just be symbols:</p> <div id="5230" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_16.png" data-in-width="129" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ebk" data-code="Files/Table.en/i_16.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_16.png" data-out-width="113" data-out-height="18" ></div> <div id="28681" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_17.png" data-in-width="248" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-wez" data-code="Files/Table.en/i_17.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_17.png" data-out-width="175" data-out-height="18" ></div> <div class="ExLine"><a name="59599520"></a></div> <p><a name="574066102"></a><span class="IF"><a href="/language/ref/ParallelTable.html">ParallelTable</a></span> computes <span class="IF"><a href="/language/ref/Table.html">Table</a></span> in parallel:</p> <div id="853692330" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_18.png" data-in-width="231" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-oejvh4" data-code="Files/Table.en/i_18.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_18.png" data-out-width="336" data-out-height="18" ></div> <p><a name="621200611"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> can be parallelized automatically, effectively using <span class="IF"><a href="/language/ref/ParallelTable.html">ParallelTable</a></span>:</p> <div id="1011524870" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_19.png" data-in-width="257" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-q0irvc" data-code="Files/Table.en/i_19.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_19.png" data-out-width="336" data-out-height="18" ></div> </div> </div> <div> <h2 id="1866" class="toggle">Applications<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(4)</span></h2> <div class="hideable"> <p><a name="3687"></a>Make a table of graphics:</p> <div id="13171" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_20.png" data-in-width="258" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-kf5" data-code="Files/Table.en/i_20.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_20.png" data-out-width="514" data-out-height="68" ></div> <div class="ExLine"><a name="31245"></a></div> <p><a name="32764"></a>Generate the corners of a polygon:</p> <div id="6238" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_21.png" data-in-width="393" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-e3k" data-code="Files/Table.en/i_21.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_21.png" data-out-width="151" data-out-height="144" ></div> <div class="ExLine"><a name="27311"></a></div> <p><a name="32657"></a>Make Pascal's triangle:</p> <div id="1405" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_22.png" data-in-width="329" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-bdb" data-code="Files/Table.en/i_22.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_22.png" data-out-width="151" data-out-height="151" ></div> <div class="ExLine"><a name="7171"></a></div> <p><a name="942181648"></a>Compare font sizes from 10 points to 20 points:</p> <div id="20580" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_23.png" data-in-width="205" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-p5y" data-code="Files/Table.en/i_23.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_23.png" data-out-width="341" data-out-height="19" ></div> </div> </div> <div> <h2 id="22530" class="toggle">Properties & Relations<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(13)</span></h2> <div class="hideable"> <div> <h3 id="13675" class="toggle">Display of Tables<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h3> <div class="hideable"> <p><a name="286480952"></a>Use <span class="IF"><a href="/language/ref/ListPlot.html">ListPlot</a></span>, <span class="IF"><a href="/language/ref/ListLinePlot.html">ListLinePlot</a></span> and similar functions to visualize numeric tables:</p> <div id="24320" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_24.png" data-in-width="295" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-s1u" data-code="Files/Table.en/i_24.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_24.png" data-out-width="241" data-out-height="159" ></div> <div class="ExLine"><a name="13377"></a></div> <p><a name="1912160822"></a>Use <span class="IF"><a href="/language/ref/Grid.html">Grid</a></span> to format a two-dimensional table:</p> <div id="10998" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_25.png" data-in-width="194" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-irs" data-code="Files/Table.en/i_25.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_25.png" data-out-width="33" data-out-height="168" ></div> <div class="ExLine"><a name="21604"></a></div> <p><a name="269479993"></a>Two-dimensional numeric tables can be visualized with <span class="IF"><a href="/language/ref/ArrayPlot.html">ArrayPlot</a></span> and <span class="IF"><a href="/language/ref/MatrixPlot.html">MatrixPlot</a></span>:</p> <div id="4489" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_26.png" data-in-width="250" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-dqz" data-code="Files/Table.en/i_26.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_26.png" data-out-width="151" data-out-height="151" ></div> <div class="ExLine"><a name="29744"></a></div> <p><a name="8388"></a>Print the values of the table index while the table is being generated:</p> <div id="26610" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_27.png" data-in-width="162" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-utg" data-code="Files/Table.en/i_27.txt" ></div> <div class="Print"> <a name="418866746"></a> <img src="Files/Table.en/Image_3.gif" height="17" width="7" class="FlushInput" /> </div> <div class="Print"> <a name="91382881"></a> <img src="Files/Table.en/Image_4.gif" height="17" width="7" class="FlushInput" /> </div> <div class="Print"> <a name="763995336"></a> <img src="Files/Table.en/Image_5.gif" height="17" width="7" class="FlushInput" /> </div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_27.png" data-out-width="132" data-out-height="18" ></div> <div class="ExLine"><a name="47400043"></a></div> <p><a name="622989007"></a>Monitor the values by showing them in a temporary cell:</p> <div id="198921070" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_28.png" data-in-width="240" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-dkpurk" data-code="Files/Table.en/i_28.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_28.png" data-out-width="132" data-out-height="18" ></div> </div> </div> <div> <h3 id="21479" class="toggle">Relations to Other Functions<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(5)</span></h3> <div class="hideable"> <p><a name="22716"></a><span class="IF"><a href="/language/ref/Range.html">Range</a></span> gives the sequence of values of a table iterator:</p> <div id="6300" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_29.png" data-in-width="93" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-e5a" data-code="Files/Table.en/i_29.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_29.png" data-out-width="67" data-out-height="18" ></div> <div id="16853" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_30.png" data-in-width="122" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-naf" data-code="Files/Table.en/i_30.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_30.png" data-out-width="67" data-out-height="18" ></div> <div class="ExLine"><a name="20830"></a></div> <p><a name="24593"></a><span class="IF"><a href="/language/ref/Do.html">Do</a></span> evaluates the same sequence of expressions as <span class="IF"><a href="/language/ref/Table.html">Table</a></span>, but does not return them:</p> <div id="30806" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_31.png" data-in-width="120" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-x10" data-code="Files/Table.en/i_31.txt" ></div> <div class="Print"> <a name="29849"></a> <img src="Files/Table.en/Image_6.gif" height="17" width="7" class="FlushInput" /> </div> <div class="Print"> <a name="14854"></a> <img src="Files/Table.en/Image_7.gif" height="17" width="7" class="FlushInput" /> </div> <div class="Print"> <a name="24272"></a> <img src="Files/Table.en/Image_8.gif" height="17" width="13" class="FlushInput" /> </div> <div id="26160" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_32.png" data-in-width="98" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ugy" data-code="Files/Table.en/i_32.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_31.png" data-out-width="48" data-out-height="18" ></div> <div class="ExLine"><a name="12054"></a></div> <p><a name="26333"></a><span class="IF"><a href="/language/ref/Sum.html">Sum</a></span> effectively applies <span class="IF"><a href="/language/ref/Plus.html">Plus</a></span> to results from <span class="IF"><a href="/language/ref/Table.html">Table</a></span>:</p> <div id="146" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_33.png" data-in-width="95" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ec" data-code="Files/Table.en/i_33.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_32.png" data-out-width="51" data-out-height="18" ></div> <div id="10471" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_34.png" data-in-width="101" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ic5" data-code="Files/Table.en/i_34.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_33.png" data-out-width="50" data-out-height="19" ></div> <div class="ExLine"><a name="10559"></a></div> <p><a name="22241"></a><span class="IF"><a href="/language/ref/Array.html">Array</a></span> iterates over successive integers:</p> <div id="29421" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_35.png" data-in-width="141" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-wzj" data-code="Files/Table.en/i_35.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_34.png" data-out-width="201" data-out-height="18" ></div> <div id="16366" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_36.png" data-in-width="213" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-mww" data-code="Files/Table.en/i_36.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_35.png" data-out-width="201" data-out-height="18" ></div> <div id="26685" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_37.png" data-in-width="147" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-uvj" data-code="Files/Table.en/i_37.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_36.png" data-out-width="201" data-out-height="18" ></div> <div class="ExLine"><a name="128619277"></a></div> <p><a name="84895798"></a><span class="IF"><a href="/language/ref/Map.html">Map</a></span> applies a function to successive elements in a list:</p> <div id="665105309" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_38.png" data-in-width="173" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-k99str" data-code="Files/Table.en/i_38.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_37.png" data-out-width="132" data-out-height="18" ></div> <div id="129933737" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_39.png" data-in-width="226" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-cfm7sr" data-code="Files/Table.en/i_39.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_38.png" data-out-width="132" data-out-height="18" ></div> <p><a name="68446400"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> can substitute successive elements in a list into an expression:</p> <div id="268498511" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_40.png" data-in-width="241" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ep4419" data-code="Files/Table.en/i_40.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_39.png" data-out-width="132" data-out-height="18" ></div> </div> </div> <div> <h3 id="25329" class="toggle">Nested Tables<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(1)</span></h3> <div class="hideable"> <p><a name="32261"></a>Using multiple iteration specifications is equivalent to nesting <span class="IF"><a href="/language/ref/Table.html">Table</a></span> functions: </p> <div id="22860" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_41.png" data-in-width="135" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-rxa" data-code="Files/Table.en/i_41.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_40.png" data-out-width="104" data-out-height="18" ></div> <div id="8982" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_42.png" data-in-width="178" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-g7s" data-code="Files/Table.en/i_42.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_41.png" data-out-width="104" data-out-height="18" ></div> </div> </div> <div> <h3 id="32506" class="toggle">Programmatic Table Construction<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(2)</span></h3> <div class="hideable"> <p><a name="6878"></a>Feed in parameters for tables:</p> <div id="11979" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_43.png" data-in-width="235" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ji1" data-code="Files/Table.en/i_43.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_42.png" data-out-width="367" data-out-height="18" ></div> <div id="7887" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_44.png" data-in-width="216" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-gdd" data-code="Files/Table.en/i_44.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_43.png" data-out-width="367" data-out-height="18" ></div> <div class="ExLine"><a name="14469"></a></div> <p><a name="30783"></a>Use <span class="IF"><a href="/language/ref/Apply.html">Apply</a></span> to splice a complete iterator specification into <span class="IF"><a href="/language/ref/Table.html">Table</a></span>:</p> <div id="17540" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_45.png" data-in-width="141" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-nti" data-code="Files/Table.en/i_45.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_44.png" data-out-width="134" data-out-height="18" ></div> <div id="7266" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_46.png" data-in-width="158" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-fv4" data-code="Files/Table.en/i_46.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_45.png" data-out-width="360" data-out-height="18" ></div> <p><a name="13509"></a><span class="IF"><a href="/language/ref/With.html">With</a></span> can insert the specification for a single iterator:</p> <div id="24557" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_47.png" data-in-width="183" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-s8f" data-code="Files/Table.en/i_47.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_46.png" data-out-width="80" data-out-height="18" ></div> </div> </div> </div> </div> <div> <h2 id="32053" class="toggle">Possible Issues<span class="special-character NonBreakingSpace"> </span><span class="special-character NonBreakingSpace"> </span><span class="total-examples">(6)</span></h2> <div class="hideable"> <p><a name="959781159"></a>For some step sizes, output from <span class="IF"><a href="/language/ref/Table.html">Table</a></span> may not include the upper limit given:</p> <div id="251244227" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_48.png" data-in-width="128" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-efvbkl" data-code="Files/Table.en/i_48.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_47.png" data-out-width="55" data-out-height="18" ></div> <div class="ExLine"><a name="12258"></a></div> <p><a name="2593"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> requires list iterator specifications to be given explicitly:</p> <div id="17843" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_49.png" data-in-width="84" data-in-height="39" data-link="https://wolfram.com/xid/0gisaa-n1x" data-code="Files/Table.en/i_49.txt" ></div> <div class="Message"> <img src="Files/Table.en/9.gif" height="19" width="404" alt="" /> </div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_48.png" data-out-width="65" data-out-height="19" ></div> <p><a name="583682388"></a>Forcing early evaluation of the list resolves the issue:</p> <div id="18140" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_50.png" data-in-width="147" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-n96" data-code="Files/Table.en/i_50.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_49.png" data-out-width="80" data-out-height="18" ></div> <p><a name="1526841987"></a>Alternatively, using <span class="IF"><a href="/language/ref/With.html">With</a></span> to lexically replace <span class="IF"><span class="TI">p</span></span> with its list form:</p> <div id="12937" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_51.png" data-in-width="193" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-j9n" data-code="Files/Table.en/i_51.txt" ></div> <div class="clipboard-output" data-out="Out[3]=" data-out-num="3" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_50.png" data-out-width="80" data-out-height="18" ></div> <div class="ExLine"><a name="2512"></a></div> <p><a name="6097"></a><span class="IF"><a href="/language/ref/Table.html">Table</a></span> normally reevaluates at each step:</p> <div id="9551" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_52.png" data-in-width="157" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-hnl" data-code="Files/Table.en/i_52.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_51.png" data-out-width="258" data-out-height="18" ></div> <div id="21817" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_53.png" data-in-width="220" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-q4b" data-code="Files/Table.en/i_53.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_52.png" data-out-width="277" data-out-height="18" ></div> <div class="ExLine"><a name="21292"></a></div> <p><a name="20237"></a>The <span class="IF"><a href="/language/ref/Evaluate.html">Evaluate</a></span> is needed to force evaluation of the table before it is fed to <span class="IF"><a href="/language/ref/Plot.html">Plot</a></span>:</p> <div id="27530" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_54.png" data-in-width="321" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-vi0" data-code="Files/Table.en/i_54.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_53.png" data-out-width="226" data-out-height="131" ></div> <p><a name="1416735721"></a>Compare with:</p> <div id="31369872" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_55.png" data-in-width="258" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-synfm" data-code="Files/Table.en/i_55.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_54.png" data-out-width="241" data-out-height="140" ></div> <div class="ExLine"><a name="25296"></a></div> <p><a name="21710"></a>Values of <span class="IF"><a href="/language/ref/Table.html">Table</a></span> variables do not get substituted inside held expressions:</p> <div id="32389" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_56.png" data-in-width="123" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-y9z" data-code="Files/Table.en/i_56.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_55.png" data-out-width="215" data-out-height="18" ></div> <p><a name="5809"></a>Use <span class="IF"><a href="/language/ref/With.html">With</a></span> to insert values:</p> <div id="28786" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_57.png" data-in-width="199" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-whw" data-code="Files/Table.en/i_57.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_56.png" data-out-width="231" data-out-height="18" ></div> <div class="ExLine"><a name="18840"></a></div> <p><a name="8182"></a>Formatting wrappers such as <span class="IF"><a href="/language/ref/Grid.html">Grid</a></span> give expressions that are no longer lists:</p> <div id="28569" class="clipboard-input" data-in="In[1]:=" data-in-num="1" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_58.png" data-in-width="163" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-wbv" data-code="Files/Table.en/i_58.txt" ></div> <div class="clipboard-output" data-out="Out[1]=" data-out-num="1" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_57.png" data-out-width="56" data-out-height="65" ></div> <div id="27393" class="clipboard-input" data-in="In[2]:=" data-in-num="2" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_59.png" data-in-width="33" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ve7" data-code="Files/Table.en/i_59.txt" ></div> <div class="clipboard-output" data-out="Out[2]=" data-out-num="2" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_58.png" data-out-width="75" data-out-height="65" ></div> <div id="14962" class="clipboard-input" data-in="In[3]:=" data-in-num="3" data-in-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/I_60.png" data-in-width="88" data-in-height="19" data-link="https://wolfram.com/xid/0gisaa-ltw" data-code="Files/Table.en/i_60.txt" ></div> <div class="clipboard-output" data-out=" " data-out-num="" data-out-src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="Files/Table.en/O_59.png" data-out-width="304" data-out-height="18" ></div> </div> </div> <div class="clear"></div> </div></section><section id="SeeAlso" class="related-links"><div class="inner"> <h1>See Also</h1> <p class="inlineFunctionList"><span class="IF"><a href="/language/ref/Range.html">Range</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/DiagonalMatrix.html">DiagonalMatrix</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/IdentityMatrix.html">IdentityMatrix</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/Array.html">Array</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/Do.html">Do</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/Sum.html">Sum</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/Product.html">Product</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/NestList.html">NestList</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/NestWhileList.html">NestWhileList</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/SparseArray.html">SparseArray</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/RecurrenceTable.html">RecurrenceTable</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/BooleanTable.html">BooleanTable</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/DiscretePlot.html">DiscretePlot</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/ParallelTable.html">ParallelTable</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/ConstantArray.html">ConstantArray</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/StringRepeat.html">StringRepeat</a></span><span class="special-character NonBreakingSpace"> </span><span class="inlineSeparator"></span> <span class="IF"><a href="/language/ref/FindRepeat.html">FindRepeat</a></span></p> </div></section><section id="Tutorials" class="related-links"><div class="inner"> <h1>Tech Notes</h1> <ul class="functionList"> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/tutorial/FunctionsAndPrograms.html#3565">Repetitive Operations</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/tutorial/Lists.html#23192">Making Tables of Values</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/tutorial/EvaluationOfExpressions.html#16334">Evaluation in Iteration Functions</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/tutorial/Lists.html#2534">Vectors and Matrices</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/tutorial/LinearAlgebra.html#20229">Tensors</a> </li> </ul> </div></section><section id="RelatedGuides" class="related-links"><div class="inner"> <h1>Related Guides</h1> <ul class="functionList"> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ConstructingMatrices.html">Constructing Matrices</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/OperationsOnVectors.html">Operations on Vectors</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ConstructingLists.html">Constructing Lists</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/Tensors.html">Tensors</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/ListManipulation.html">List Manipulation</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/IntegerSequences.html">Integer Sequences</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/CreatingAndImportingSignals.html">Creating & Importing Signals</a> </li> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/guide/HandlingArraysOfData.html">Handling Arrays of Data</a> </li> </ul> </div></section><section id="RelatedWorkflows" class="related-links"><div class="inner"> <h1>Related Workflows</h1> <ul class="functionList"> <div class="RelatedWorkflowsSection">Related Workflows</div> <span class="special-character FilledVerySmallSquare">▪</span> <li> <a href="/language/workflow/CreateAMatrix.html">Create a Matrix</a> </li> </ul> </div></section><section id="RelatedLinks" class="related-links"><div class="inner"> <h1>Related Links</h1> <ul class="functionList"> <li class="fast-intro"> <a href="http://www.wolfram.com/language/fast-introduction-for-programmers/lists/">Fast Introduction for Programmers: Lists</a> </li> <li class="fast-intro"> <a href="http://www.wolfram.com/language/fast-introduction-for-programmers/iterators/">Fast Introduction for Programmers: Iterators</a> </li> <li class="elementary-intro"> <a href="https://www.wolfram.com/language/elementary-introduction/06-making-tables.html">An Elementary Introduction to the Wolfram Language</a> <a href="https://www.wolfram.com/language/elementary-introduction/06-making-tables.html">: Operations on Lists</a> </li> <li class="nks"> <a href="http://www.wolframscience.com/nks/search/?q=Table">NKS|Online</a> <a href="http://www.wolframscience.com/nks/"> (<em>A New Kind of Science</em>)</a> </li> </ul> </div></section><section id="History" class="related-links"><div class="inner"> <h1>History</h1> <p class="inlineFunctionList"> <span class="history-text">Introduced in 1988 <span class="history-version">(1.0)</span></span> <span class="HistoryDelimiter"> | </span> <span class="history-text"><a href="/language/guide/SummaryOfNewFeaturesIn102">Updated in 2015 <span class="history-version">(10.2)</span></a></span> </p> </div></section><section id="Citations" class="citations"><div class="inner"> <div class="citation"> <span class="citation-tooltip"><button type="button" class="citation-tooltip-button"><span class="citation-text">Cite this as:</span></button><span class="citation-default clipboard-inlineblock clipboard-hover">Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).</span><span class="citation-tooltip-content"><button class="x-close-svg"><img src="/language-assets/img/CitationCloseButton.svg" height="10px" width="10px" /></button><h4>Text</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Research (1988), Table, Wolfram Language function, https://reference.wolfram.com/language/ref/Table.html (updated 2015).</p><h4>CMS</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Language. 1988. "Table." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/Table.html.</p><h4>APA</h4><p class="clipboard-inlineblock clipboard-hover">Wolfram Language. (1988). Table. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Table.html</p><h4>BibTeX</h4><p class="clipboard-inlineblock clipboard-hover citation-timestamp">@misc{reference.wolfram_2024_table, author="Wolfram Research", title="{Table}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/Table.html}", note=[Accessed: 23-November-2024 ]}</p><h4>BibLaTeX</h4><p class="clipboard-inlineblock clipboard-hover citation-timestamp">@online{reference.wolfram_2024_table, organization={Wolfram Research}, title={Table}, year={2015}, url={https://reference.wolfram.com/language/ref/Table.html}, note=[Accessed: 23-November-2024 ]}</p></span><span class="citation-overlay"></span></span> </div> </div></section> </div> <section class="feedback-wrapper"> <div class="inner"> <div class="feedback-content"> <button class="feedback"><span class="give">Give</span> Feedback</button><a class="toplink" href="#top"><span class="top">Top</span></a> <iframe id="feedback" height="440" 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Table: Make a list or array of values or expressions—Wolfram Documentation