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<div><h1>Boolean -- the class of Boolean values</h1>
<div class="single"><h2>Description</h2>
<div>Predicate functions return these as values, and the logical connectives expect to receive them as arguments.<p/>
Special operators dealing with truth values.<ul><li><span><a href="_not.html" title="negation">not</a> -- negation</span></li>
<li><span><a href="_and.html" title="conjunction">and</a> -- conjunction</span></li>
<li><span><a href="_or.html" title="disjunction">or</a> -- disjunction</span></li>
<li><span><a href="_if.html" title="condition testing">if</a> -- condition testing</span></li>
</ul>
</div>
</div>
<div class="waystouse"><h2>Functions and methods returning a Boolean value :</h2>
<ul><li><span>Thing =!= Thing, see <span><a href="__eq!_eq.html" title="strict inequality">=!=</a> -- strict inequality</span></span></li>
<li><span>Boolean == Boolean, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>CC == CC, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>CC == QQ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>CC == RR, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>CC == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Net == Net, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Nothing == Nothing, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>QQ == CC, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>QQ == QQ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>QQ == RR, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>QQ == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RR == CC, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RR == QQ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RR == RR, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>RR == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Sequence == Sequence, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>String == String, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>Symbol == Symbol, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == CC, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == QQ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == RR, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span>ZZ == ZZ, see <span><a href="__eq_eq.html" title="equality">==</a> -- equality</span></span></li>
<li><span><a href="__qu.html" title="comparison operator">?</a> -- comparison operator</span></li>
<li><span><a href="_all.html" title="whether all elements satisfy a specified condition">all</a> -- whether all elements satisfy a specified condition</span></li>
<li><span><a href="_ancestor_lp__Type_cm__Type_rp.html" title="whether one type is an ancestor of another">ancestor(Type,Type)</a> -- whether one type is an ancestor of another</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="_at__End__Of__File_lp__File_rp.html" title="test for end of file">atEndOfFile(File)</a> -- test for end of file</span></li>
<li><span><a href="___Basic__List_sp_sh_qu_sp__Z__Z.html" title="check for element in list">BasicList #? ZZ</a> -- check for element in list</span></li>
<li><span><a href="___Database_sp_sh_qu_sp__String.html" title="check for value in database">Database #? String</a> -- check for value in database</span></li>
<li><span><a href="___Hash__Table_sp_sh_qu_sp__Thing.html" title="check for value in hash table">HashTable #? Thing</a> -- check for value in hash table</span></li>
<li><span><a href="_induces__Well__Defined__Map.html" title="whether a map is well defined">inducesWellDefinedMap</a> -- whether a map is well defined</span></li>
<li><span>instance(Thing,Type), see <span><a href="_instance.html" title="whether something has a certain type">instance</a> -- whether something has a certain type</span></span></li>
<li><span><a href="_is__Affine__Ring.html" title="whether something is an affine ring">isAffineRing</a> -- whether something is an affine ring</span></li>
<li><span><a href="_is__Borel.html" title="whether an ideal is fixed by upper triangular changes of coordinates">isBorel</a> -- whether an ideal is fixed by upper triangular changes of coordinates</span></li>
<li><span>isBorel(MonomialIdeal), see <span><a href="_is__Borel.html" title="whether an ideal is fixed by upper triangular changes of coordinates">isBorel</a> -- whether an ideal is fixed by upper triangular changes of coordinates</span></span></li>
<li><span><a href="_is__Commutative.html" title="whether a ring is commutative">isCommutative</a> -- whether a ring is commutative</span></li>
<li><span><a href="_is__Constant.html" title="whether a ring element is constant">isConstant</a> -- whether a ring element is constant</span></li>
<li><span><a href="_is__Field.html" title="whether something is a field">isField</a> -- whether something is a field</span></li>
<li><span><a href="_is__Free__Module.html" title="whether something is a free module">isFreeModule</a> -- whether something is a free module</span></li>
<li><span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></li>
<li><span>isHomogeneous(Module), see <span><a href="_is__Homogeneous.html" title="whether something is homogeneous (graded)">isHomogeneous</a> -- whether something is homogeneous (graded)</span></span></li>
<li><span><a href="_is__Ideal.html" title="whether something is an ideal">isIdeal</a> -- whether something is an ideal</span></li>
<li><span><a href="_is__Injective.html" title="whether a map is injective">isInjective</a> -- whether a map is injective</span></li>
<li><span><a href="_is__Input__File_lp__File_rp.html" title="whether a file is open for input">isInputFile(File)</a> -- whether a file is open for input</span></li>
<li><span><a href="_is__Isomorphism.html" title="whether a map is an isomorphism">isIsomorphism</a> -- whether a map is an isomorphism</span></li>
<li><span><a href="../../ReesAlgebra/html/_is__Linear__Type.html" title="is a module of linear type">isLinearType</a> -- is a module of linear type</span></li>
<li><span><a href="_is__Listener_lp__File_rp.html" title="whether a file is open for listening">isListener(File)</a> -- whether a file is open for listening</span></li>
<li><span><a href="_is__Module.html" title="whether something is a module">isModule</a> -- whether something is a module</span></li>
<li><span><a href="_is__Monomial__Ideal.html" title="whether something is a monomial ideal">isMonomialIdeal</a> -- whether something is a monomial ideal</span></li>
<li><span>isNormal(Ring), see <span><a href="../../IntegralClosure/html/_is__Normal.html" title="determine if a reduced ring is normal">isNormal</a> -- determine if a reduced ring is normal</span></span></li>
<li><span>isOpen(Database), see <span><a href="_is__Open.html" title="whether a file or database is open">isOpen</a> -- whether a file or database is open</span></span></li>
<li><span>isOpen(File), see <span><a href="_is__Open.html" title="whether a file or database is open">isOpen</a> -- whether a file or database is open</span></span></li>
<li><span><a href="_is__Output__File_lp__File_rp.html" title="whether a file is open for output">isOutputFile(File)</a> -- whether a file is open for output</span></li>
<li><span><a href="_is__Polynomial__Ring.html" title="whether someting is a polynomial ring">isPolynomialRing</a> -- whether someting is a polynomial ring</span></li>
<li><span><a href="_is__Prime.html" title="whether a integer, polynomial, or ideal is prime">isPrime</a> -- whether a integer, polynomial, or ideal is prime</span></li>
<li><span>isPrime(ZZ), see <span><a href="_is__Prime.html" title="whether a integer, polynomial, or ideal is prime">isPrime</a> -- whether a integer, polynomial, or ideal is prime</span></span></li>
<li><span>isPseudoprime, see <span><a href="_is__Pseudoprime_lp__Z__Z_rp.html" title="whether an integer is a pseudoprime">isPseudoprime(ZZ)</a> -- whether an integer is a pseudoprime</span></span></li>
<li><span><a href="_is__Pseudoprime_lp__Z__Z_rp.html" title="whether an integer is a pseudoprime">isPseudoprime(ZZ)</a> -- whether an integer is a pseudoprime</span></li>
<li><span><a href="_is__Quotient__Module.html" title="whether something is evidently a quotient of a free module">isQuotientModule</a> -- whether something is evidently a quotient of a free module</span></li>
<li><span><a href="_is__Quotient__Of.html" title="whether one thing is a quotient of another">isQuotientOf</a> -- whether one thing is a quotient of another</span></li>
<li><span><a href="_is__Quotient__Ring.html" title="whether something is a quotient ring">isQuotientRing</a> -- whether something is a quotient ring</span></li>
<li><span><a href="_is__Ready_lp__File_rp.html" title="whether a file has data available for reading">isReady(File)</a> -- whether a file has data available for reading</span></li>
<li><span><tt>isReduction</tt> (missing documentation<!-- tag: isReduction -->)</span></li>
<li><span><a href="_is__Ring.html" title="whether something is a ring">isRing</a> -- whether something is a ring</span></li>
<li><span><a href="_is__Skew__Commutative.html" title="whether a ring has skew commuting variables">isSkewCommutative</a> -- whether a ring has skew commuting variables</span></li>
<li><span><a href="_is__Square__Free.html" title="whether something is square free monomial ideal">isSquareFree</a> -- whether something is square free monomial ideal</span></li>
<li><span><a href="_is__Submodule.html" title="whether a module is evidently a submodule of a free module">isSubmodule</a> -- whether a module is evidently a submodule of a free module</span></li>
<li><span><a href="_is__Subset.html" title="whether one object is a subset of another">isSubset</a> -- whether one object is a subset of another</span></li>
<li><span><a href="_is__Subset_lp__Set_cm__Set_rp.html" title="whether one object is a subset of another">isSubset(Set,Set)</a> -- whether one object is a subset of another</span></li>
<li><span>isSubset(Set,VisibleList), see <span><a href="_is__Subset_lp__Set_cm__Set_rp.html" title="whether one object is a subset of another">isSubset(Set,Set)</a> -- whether one object is a subset of another</span></span></li>
<li><span>isSubset(VisibleList,Set), see <span><a href="_is__Subset_lp__Set_cm__Set_rp.html" title="whether one object is a subset of another">isSubset(Set,Set)</a> -- whether one object is a subset of another</span></span></li>
<li><span>isSubset(VisibleList,VisibleList), see <span><a href="_is__Subset_lp__Set_cm__Set_rp.html" title="whether one object is a subset of another">isSubset(Set,Set)</a> -- whether one object is a subset of another</span></span></li>
<li><span><a href="_is__Surjective.html" title="whether a map is surjective">isSurjective</a> -- whether a map is surjective</span></li>
<li><span><a href="_is__Unit.html" title="whether a ring element is a unit">isUnit</a> -- whether a ring element is a unit</span></li>
<li><span><a href="_is__Well__Defined.html" title="whether a map is well defined">isWellDefined</a> -- whether a map is well defined</span></li>
<li><span><a href="_liftable.html" title="whether lifting to another ring is possible">liftable</a> -- whether lifting to another ring is possible</span></li>
<li><span>match, see <span><a href="_match_lp__String_cm__String_rp.html" title="regular expression matching">match(String,String)</a> -- regular expression matching</span></span></li>
<li><span>member(Thing,Set), see <span><a href="_member.html" title="test membership in a list or set">member</a> -- test membership in a list or set</span></span></li>
<li><span>member(Thing,VisibleList), see <span><a href="_member.html" title="test membership in a list or set">member</a> -- test membership in a list or set</span></span></li>
<li><span>mutable(Thing), see <span><a href="_mutable.html" title="whether something may be modified">mutable</a> -- whether something may be modified</span></span></li>
<li><span><a href="___Set_sp_sh_qu_sp__Thing.html" title="test set membership">Set #? Thing</a> -- test set membership</span></li>
<li><span><a href="___String_sp_sh_qu_sp__Z__Z.html" title="check for character in string">String #? ZZ</a> -- check for character in string</span></li>
<li><span><a href="___Thing_sp_eq_eq_eq_sp__Thing.html" title="strict equality">Thing === Thing</a> -- strict equality</span></li>
</ul>
<h2>Methods that use a Boolean value :</h2>
<ul><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>
</ul>
<h2>Fixed objects of class Boolean :</h2>
<ul><li><span><a href="_false.html" title="">false</a></span></li>
<li><span><a href="_true.html" title="">true</a></span></li>
</ul>
</div>
<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Boolean.html" title="the class of Boolean values">Boolean</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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