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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___Function.html" title="the class of all functions">Function</a></div>
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<div><h1>Function -- the class of all functions</h1>
<div><!--empty documentation body--></div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_using_spfunctions.html" title="">using functions</a></span></li>
<li><span><a href="_using_spfunctions_spwith_spoptional_spinputs.html" title="">using functions with optional inputs</a></span></li>
<li><span><a href="_making_spfunctions.html" title="">making functions</a></span></li>
<li><span><a href="_local_spvariables_spin_spa_spfunction.html" title="">local variables in a function</a></span></li>
<li><span><a href="_making_spfunctions_spwith_spa_spvariable_spnumber_spof_sparguments.html" title="">making functions with a variable number of arguments</a></span></li>
<li><span><a href="_making_spfunctions_spwith_spmultiple_spreturn_spvalues.html" title="">making functions with multiple return values</a></span></li>
<li><span><a href="_making_spnew_spfunctions_spwith_spoptional_sparguments.html" title="">making new functions with optional arguments</a></span></li>
</ul>
</div>
<div class="waystouse"><h2>Types of function :</h2>
<ul><li><span><a href="___Compiled__Function.html" title="the class of all compiled functions">CompiledFunction</a> -- the class of all compiled functions</span></li>
<li><span><a href="___Compiled__Function__Closure.html" title="the class of all compiled function closures">CompiledFunctionClosure</a> -- the class of all compiled function closures</span></li>
<li><span><a href="___Function__Closure.html" title="the class of all function closures">FunctionClosure</a> -- the class of all function closures</span></li>
</ul>
<h2>Functions and methods returning a function :</h2>
<ul><li><span><a href="___Function_sp_at_at_sp__Function.html" title="composition of functions">Function @@ Function</a> -- composition of functions</span></li>
<li><span><a href="___Function_sp_us_sp__Thing.html" title="attach the first argument to a function of two or more arguments">Function _ Thing</a> -- attach the first argument to a function of two or more arguments</span></li>
<li><span>Boolean >> Function, see <span><a href="___Option__Table_sp_gt_gt_sp__Function.html" title="attaching options to a function">OptionTable >> Function</a> -- attaching options to a function</span></span></li>
<li><span>List >> Function, see <span><a href="___Option__Table_sp_gt_gt_sp__Function.html" title="attaching options to a function">OptionTable >> Function</a> -- attaching options to a function</span></span></li>
<li><span><a href="___Option__Table_sp_gt_gt_sp__Function.html" title="attaching options to a function">OptionTable >> Function</a> -- attaching options to a function</span></li>
<li><span>profile(Function), see <span><a href="_profile.html" title="profile a function">profile</a> -- profile a function</span></span></li>
</ul>
<h2>Methods that use a function :</h2>
<ul><li><span><a href="_accumulate_lp__Function_cm__Thing_cm__Visible__List_rp.html" title="">accumulate(Function,Thing,VisibleList)</a></span></li>
<li><span><a href="_accumulate_lp__Function_cm__Visible__List_rp.html" title="">accumulate(Function,VisibleList)</a></span></li>
<li><span><a href="_accumulate_lp__Visible__List_cm__Function_rp.html" title="">accumulate(VisibleList,Function)</a></span></li>
<li><span><a href="_accumulate_lp__Visible__List_cm__Thing_cm__Function_rp.html" title="">accumulate(VisibleList,Thing,Function)</a></span></li>
<li><span><a href="_add__Hook_lp__Hash__Table_cm__Thing_cm__Function_rp.html" title="add a hook function to an object for later processing">addHook(HashTable,Thing,Function)</a> -- add a hook function to an object for later processing</span></li>
<li><span><a href="_add__Hook_lp__Symbol_cm__Function_rp.html" title="add a hook function to an object for later processing">addHook(Symbol,Function)</a> -- add a hook function to an object for later processing</span></li>
<li><span><a href="_all_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="whether all corresponding elements of a pair of lists satisfy a condition">all(BasicList,BasicList,Function)</a> -- whether all corresponding elements of a pair of lists satisfy a condition</span></li>
<li><span><a href="_all_lp__Basic__List_cm__Function_rp.html" title="whether all elements of a list satisfy a specified condition">all(BasicList,Function)</a> -- whether all elements of a list satisfy a specified condition</span></li>
<li><span>all(ZZ,Function), see <span><a href="_all_lp__Basic__List_cm__Function_rp.html" title="whether all elements of a list satisfy a specified condition">all(BasicList,Function)</a> -- whether all elements of a list satisfy a specified condition</span></span></li>
<li><span><a href="_all_lp__Hash__Table_cm__Function_rp.html" title="whether all key/value pairs in a hash table satisfy a specified condition">all(HashTable,Function)</a> -- whether all key/value pairs in a hash table satisfy a specified condition</span></li>
<li><span><a href="_any_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="whether any corresponding elements of a pair of lists satisfy a condition">any(BasicList,BasicList,Function)</a> -- whether any corresponding elements of a pair of lists satisfy a condition</span></li>
<li><span><a href="_any_lp__Basic__List_cm__Function_rp.html" title="whether any elements of a list satisfy a specified condition">any(BasicList,Function)</a> -- whether any elements of a list satisfy a specified condition</span></li>
<li><span>any(ZZ,Function), see <span><a href="_any_lp__Basic__List_cm__Function_rp.html" title="whether any elements of a list satisfy a specified condition">any(BasicList,Function)</a> -- whether any elements of a list satisfy a specified condition</span></span></li>
<li><span><a href="_any_lp__Hash__Table_cm__Function_rp.html" title="whether all key/value pairs in a hash table satisfy a specified condition">any(HashTable,Function)</a> -- whether all key/value pairs in a hash table satisfy a specified condition</span></li>
<li><span><a href="_apply_lp__Basic__List_cm__Basic__List_cm__Function_rp.html" title="apply a function to pairs of elements, one from each list">apply(BasicList,BasicList,Function)</a> -- apply a function to pairs of elements, one from each list</span></li>
<li><span><a href="_apply_lp__Basic__List_cm__Function_rp.html" title="apply a function to each element of a list">apply(BasicList,Function)</a> -- apply a function to each element of a list</span></li>
<li><span><a href="_apply_lp__Z__Z_cm__Function_rp.html" title="apply a function to {0,..., n-1}">apply(ZZ,Function)</a> -- apply a function to {0,..., n-1}</span></li>
<li><span>applyKeys(HashTable,Function), see <span><a href="_apply__Keys.html" title="apply a function to each key in a hash table">applyKeys</a> -- apply a function to each key in a hash table</span></span></li>
<li><span>applyPairs(HashTable,Function), see <span><a href="_apply__Pairs.html" title="apply a function to each pair in a hash table">applyPairs</a> -- apply a function to each pair in a hash table</span></span></li>
<li><span>applyValues(HashTable,Function), see <span><a href="_apply__Values.html" title="apply a function to each value">applyValues</a> -- apply a function to each value</span></span></li>
<li><span><a href="_fold_lp__Function_cm__Thing_cm__Visible__List_rp.html" title="">fold(Function,Thing,VisibleList)</a></span></li>
<li><span><a href="_fold_lp__Function_cm__Visible__List_rp.html" title="">fold(Function,VisibleList)</a></span></li>
<li><span><a href="_fold_lp__Visible__List_cm__Function_rp.html" title="">fold(VisibleList,Function)</a></span></li>
<li><span><a href="_fold_lp__Visible__List_cm__Thing_cm__Function_rp.html" title="">fold(VisibleList,Thing,Function)</a></span></li>
<li><span>frames(Function), see <span><a href="_frames.html" title="get the frames associated to a closure">frames</a> -- get the frames associated to a closure</span></span></li>
<li><span><a href="___Function_sp__Thing.html" title="function application">Function Thing</a> -- function application</span></li>
<li><span>Function \ Ideal, see <span><a href="___Ideal_sp_sl_sp__Function.html" title="apply a function to generators of an ideal">Ideal / Function</a> -- apply a function to generators of an ideal</span></span></li>
<li><span><a href="___Ideal_sp_sl_sp__Function.html" title="apply a function to generators of an ideal">Ideal / Function</a> -- apply a function to generators of an ideal</span></li>
<li><span>installAssignmentMethod(Symbol,HashTable,Function), see <span><a href="_install__Assignment__Method.html" title="install methods assignment to the value of an operator">installAssignmentMethod</a> -- install methods assignment to the value of an operator</span></span></li>
<li><span>installAssignmentMethod(Symbol,HashTable,HashTable,Function), see <span><a href="_install__Assignment__Method.html" title="install methods assignment to the value of an operator">installAssignmentMethod</a> -- install methods assignment to the value of an operator</span></span></li>
<li><span>localDictionaries(Function), see <span><a href="_local__Dictionaries.html" title="get local dictionaries">localDictionaries</a> -- get local dictionaries</span></span></li>
<li><span>locate(Function), see <span><a href="_locate.html" title="locate source code">locate</a> -- locate source code</span></span></li>
<li><span>new Manipulator from Function, 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="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Function_rp.html" title="make a map of chain complexes">map(ChainComplex,ChainComplex,Function)</a> -- make a map of chain complexes</span></li>
<li><span>map(GradedModule,GradedModule,Function), see <span><a href="_map_lp__Chain__Complex_cm__Chain__Complex_cm__Function_rp.html" title="make a map of chain complexes">map(ChainComplex,ChainComplex,Function)</a> -- make a map of chain complexes</span></span></li>
<li><span><a href="_map_lp__Module_cm__Module_cm__Function_rp.html" title="create a matrix by specifying a function that gives each entry">map(Module,Module,Function)</a> -- create a matrix by specifying a function that gives each entry</span></li>
<li><span><a href="_map_lp__Module_cm__Z__Z_cm__Function_rp.html" title="create a matrix from a free module by specifying a function that gives each entry">map(Module,ZZ,Function)</a> -- create a matrix from a free module by specifying a function that gives each entry</span></li>
<li><span>memoize(Function), see <span><a href="_memoize.html" title="record results of function evaluation for future use">memoize</a> -- record results of function evaluation for future use</span></span></li>
<li><span>memoize(Function,List), see <span><a href="_memoize.html" title="record results of function evaluation for future use">memoize</a> -- record results of function evaluation for future use</span></span></li>
<li><span><a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge(HashTable,HashTable,Function)</a> -- merge hash tables</span></li>
<li><span>mergePairs(BasicList,BasicList,Function), see <span><a href="_merge__Pairs.html" title="merge sorted lists of pairs">mergePairs</a> -- merge sorted lists of pairs</span></span></li>
<li><span><a href="_method__Options_lp__Function_rp.html" title="recover the options used when a method function was created">methodOptions(Function)</a> -- recover the options used when a method function was created</span></li>
<li><span><a href="_options_lp__Function_rp.html" title="get optional arguments and default values for a function that accepts them">options(Function)</a> -- get optional arguments and default values for a function that accepts them</span></li>
<li><span>package(Function), see <span><a href="_package.html" title="get containing package">package</a> -- get containing package</span></span></li>
<li><span>partition(Function,Tally), see <span><a href="_partition.html" title="partition a set or list by values of a function">partition</a> -- partition a set or list by values of a function</span></span></li>
<li><span>partition(Function,VisibleList), see <span><a href="_partition.html" title="partition a set or list by values of a function">partition</a> -- partition a set or list by values of a function</span></span></li>
<li><span>position(VisibleList,Function), see <span><a href="_position.html" title="find first element of a list satisfying a condition">position</a> -- find first element of a list satisfying a condition</span></span></li>
<li><span><a href="_position_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="find first element of a list satisfying a condition">position(VisibleList,VisibleList,Function)</a> -- find first element of a list satisfying a condition</span></li>
<li><span><a href="_positions_lp__Visible__List_cm__Function_rp.html" title="which elements of a list satisfy a condition">positions(VisibleList,Function)</a> -- which elements of a list satisfy a condition</span></li>
<li><span><a href="_product_lp__Visible__List_cm__Function_rp.html" title="product of values of a function">product(VisibleList,Function)</a> -- product of values of a function</span></li>
<li><span><a href="_product_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="product of results of applying a function pairwise">product(VisibleList,VisibleList,Function)</a> -- product of results of applying a function pairwise</span></li>
<li><span><a href="_product_lp__Z__Z_cm__Function_rp.html" title="product of consecutive values of a function">product(ZZ,Function)</a> -- product of consecutive values of a function</span></li>
<li><span>profile(String,Function), see <span><a href="_profile.html" title="profile a function">profile</a> -- profile a function</span></span></li>
<li><span><a href="_remove__Hook_lp__Hash__Table_cm__Thing_cm__Function_rp.html" title="remove a hook function from an object">removeHook(HashTable,Thing,Function)</a> -- remove a hook function from an object</span></li>
<li><span><a href="_remove__Hook_lp__Symbol_cm__Function_rp.html" title="remove a hook function from an object">removeHook(Symbol,Function)</a> -- remove a hook function from an object</span></li>
<li><span><a href="_scan_lp__Basic__List_cm__Function_rp.html" title="apply a function to each element of a list">scan(BasicList,Function)</a> -- apply a function to each element of a list</span></li>
<li><span><a href="_scan_lp__Z__Z_cm__Function_rp.html" title="apply a function to 0 .. n-1">scan(ZZ,Function)</a> -- apply a function to 0 .. n-1</span></li>
<li><span>scanKeys(Database,Function), see <span><a href="_scan__Keys.html" title="apply a function to each key in a hash table or database">scanKeys</a> -- apply a function to each key in a hash table or database</span></span></li>
<li><span>scanKeys(HashTable,Function), see <span><a href="_scan__Keys.html" title="apply a function to each key in a hash table or database">scanKeys</a> -- apply a function to each key in a hash table or database</span></span></li>
<li><span>scanLines(Function,List), see <span><a href="_scan__Lines.html" title="apply a function to each line of a file">scanLines</a> -- apply a function to each line of a file</span></span></li>
<li><span>scanLines(Function,String), see <span><a href="_scan__Lines.html" title="apply a function to each line of a file">scanLines</a> -- apply a function to each line of a file</span></span></li>
<li><span><a href="_scan__Pairs_lp__Hash__Table_cm__Function_rp.html" title="apply a function to pairs in a hash table">scanPairs(HashTable,Function)</a> -- apply a function to pairs in a hash table</span></li>
<li><span>scanValues(HashTable,Function), see <span><a href="_scan__Values.html" title="apply a function to each value in a hash table">scanValues</a> -- apply a function to each value in a hash table</span></span></li>
<li><span><a href="_select_lp__Basic__List_cm__Function_rp.html" title="select elements from a list">select(BasicList,Function)</a> -- select elements from a list</span></li>
<li><span><a href="_select_lp__Hash__Table_cm__Function_rp.html" title="select part of a hash table">select(HashTable,Function)</a> -- select part of a hash table</span></li>
<li><span><a href="_select_lp__Z__Z_cm__Basic__List_cm__Function_rp.html" title="select a limited number of elements from a list">select(ZZ,BasicList,Function)</a> -- select a limited number of elements from a list</span></li>
<li><span><a href="_select_lp__Z__Z_cm__Hash__Table_cm__Function_rp.html" title="select a limited number of pairs from a hash table">select(ZZ,HashTable,Function)</a> -- select a limited number of pairs from a hash table</span></li>
<li><span>sublists(VisibleList,Function), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Function), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Function,Function), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Function,Nothing), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Nothing), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Nothing,Function), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span>sublists(VisibleList,Function,Nothing,Nothing), see <span><a href="_sublists.html" title="process interspersed sublists of a list">sublists</a> -- process interspersed sublists of a list</span></span></li>
<li><span><a href="_sum_lp__Visible__List_cm__Function_rp.html" title="sum results of applying a function">sum(VisibleList,Function)</a> -- sum results of applying a function</span></li>
<li><span><a href="_sum_lp__Visible__List_cm__Visible__List_cm__Function_rp.html" title="sum results of applying a function pairwise">sum(VisibleList,VisibleList,Function)</a> -- sum results of applying a function pairwise</span></li>
<li><span><a href="_sum_lp__Z__Z_cm__Function_rp.html" title="sum consecutive values of a function">sum(ZZ,Function)</a> -- sum consecutive values of a function</span></li>
<li><span>Function \\ Thing, see <span><a href="___Thing_sp_sl_sl_sp__Function.html" title="apply a function">Thing // Function</a> -- apply a function</span></span></li>
<li><span><a href="___Thing_sp_sl_sl_sp__Function.html" title="apply a function">Thing // Function</a> -- apply a function</span></li>
<li><span>ultimate(Function,Thing), see <span><a href="_ultimate.html" title="ultimate value for an iteration">ultimate</a> -- ultimate value for an iteration</span></span></li>
<li><span>Function \ Tally, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>Function \ VisibleList, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>List / Function, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span>Tally / Function, see <span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></span></li>
<li><span><a href="___Visible__List_sp_sl_sp__Function.html" title="apply a function to elements of a list">VisibleList / Function</a> -- apply a function to elements of a list</span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Function.html" title="the class of all functions">Function</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor class <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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