Boolean -- the class of Boolean values

Functions and methods returning a Boolean value:

• BasicList #? ZZ -- see #? -- check existence of value in a list, hash table, database, or string
• Database #? String -- see #? -- check existence of value in a list, hash table, database, or string
• HashTable #? Thing -- see #? -- check existence of value in a list, hash table, database, or string
• String #? ZZ -- see #? -- check existence of value in a list, hash table, database, or string
• Thing =!= Thing -- see =!= -- strict inequality
• ? -- comparison operator
• all -- whether all elements satisfy a specified condition
• ancestor(Type,Type) -- whether one type is an ancestor of another
• any(BasicList,BasicList,Function) -- whether any corresponding elements of a pair of lists satisfy a condition
• any(BasicList,Function) -- whether any elements of a list satisfy a specified condition
• any(ZZ,Function) -- see any(BasicList,Function) -- whether any elements of a list satisfy a specified condition
• any(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• atEndOfFile(File) -- test for end of file
• BettiTally == BettiTally (missing documentation)
• Boolean == Boolean (missing documentation)
• CC == CC (missing documentation)
• CC == QQ (missing documentation)
• CC == RR (missing documentation)
• CC == ZZ (missing documentation)
• CoherentSheaf == CoherentSheaf (missing documentation)
• CoherentSheaf == ZZ (missing documentation)
• commonFace -- checks if the intersection is a face of both Cones or Polyhedra, or of cones with fans
• contains -- checks if the first argument contains the second argument
• Dictionary #? String (missing documentation)
• fileExecutable(String) -- see fileExecutable
• fileReadable(String) -- see fileReadable
• fileWritable(String) -- see fileWritable
• inducesWellDefinedMap -- whether a map is well defined
• inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron
• instance(Thing,Type) -- see instance -- whether something has a certain type
• isAffineRing -- whether something is an affine ring
• isANumber(Number) -- see isANumber -- whether a number is not not-a-number
• isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isBorel(MonomialIdeal) -- see isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isCanceled(Task) -- whether a task has been canceled
• isCommutative -- whether a ring is commutative
• isCommutative(ChainComplexMap) (missing documentation)
• isCompact -- checks compactness of a Polyhedron
• isComplete -- checks completeness of a Fan or PolyhedralComplex
• isConstant -- whether a ring element is constant
• isEmpty
• isEmpty(RRi) -- empty test for an interval
• isFace -- tests if the first argument is a face of the second
• isField -- whether something is a field
• isField(Ring) -- see isField -- whether something is a field
• isFreeModule -- whether something is a free module
• isFullDimensional -- Determine whether a polyhedral object is full-dimensional
• isHomogeneous -- whether something is homogeneous (graded)
• isHomogeneous(Module) -- see isHomogeneous -- whether something is homogeneous (graded)
• isIdeal -- whether something is an ideal
• isInjective -- whether a map is injective
• isInputFile(File) -- whether a file is open for input
• isIsomorphism -- whether a map is an isomorphism
• isIsomorphism(SheafMap) (missing documentation)
• isLatticePolytope(Polyhedron) -- see isLatticePolytope -- checks if a polyhedron is a lattice polytope
• isLinearType -- Determine whether module has linear type
• isListener(File) -- whether a file is open for listening
• isMember(Thing,Set) -- see isMember -- test membership in a list or set
• isMember(Thing,VisibleList) -- see isMember -- test membership in a list or set
• isModule -- whether something is a module
• isMonomialIdeal -- whether something is a monomial ideal
• isMutable(Thing) -- see isMutable -- whether something may be modified
• isNormal(Ring) -- determine if a reduced ring is normal
• isOpen(Database) -- see isOpen -- whether a file or database is open
• isOpen(File) -- see isOpen -- whether a file or database is open
• isOutputFile(File) -- whether a file is open for output
• isPointed -- checks if a Cone or Fan is pointed
• isPolynomialRing -- whether something is a polynomial ring
• isPolytopal -- checks if a Fan is polytopal
• isPrime -- whether a integer or polynomial is prime
• isPrime(ZZ) -- see isPrime -- whether a integer or polynomial is prime
• isPrime(Ideal) -- whether an ideal is prime
• isProjective (missing documentation)
• isPseudoprime -- see isPseudoprime(ZZ) -- whether an integer is probably prime
• isPseudoprime(ZZ) -- whether an integer is probably prime
• isPure -- checks if a Fan or PolyhedralComplex is of pure dimension
• isQuotientModule -- whether something is evidently a quotient of a free module
• isQuotientOf -- whether one thing is a quotient of another
• isQuotientRing -- whether something is a quotient ring
• isReady(File) -- whether a file has data available for reading
• isReady(Task) -- whether a task is finished
• isReduction -- Determine whether an ideal is a reduction
• isReflexive -- checks if a Polytope is reflexive
• isRing -- whether something is a ring
• isSimplicial -- checks if a polyhedral object is simplicial
• isSkewCommutative -- whether a ring has skew commuting variables
• isSmooth
• isSquareFree -- whether something is square free monomial ideal
• isSubmodule -- whether a module is evidently a submodule of a free module
• isSubset -- whether one object is a subset of another
• isSubset(Set,Set) -- whether one object is a subset of another
• isSubset(Set,VisibleList) -- see isSubset(Set,Set) -- whether one object is a subset of another
• isSubset(VisibleList,Set) -- see isSubset(Set,Set) -- whether one object is a subset of another
• isSubset(VisibleList,VisibleList) -- see isSubset(Set,Set) -- whether one object is a subset of another
• isSurjective -- whether a map is surjective
• isUnit -- whether a ring element is a unit
• isVeryAmple
• isWellDefined -- whether a map is well defined
• liftable -- whether lifting to another ring is possible
• List #? ZZ (missing documentation)
• match -- regular expression matching
• Net #? ZZ (missing documentation)
• Net == Net (missing documentation)
• Nothing #? Thing (missing documentation)
• Nothing == Nothing (missing documentation)
• ProjectiveHilbertPolynomial == ProjectiveHilbertPolynomial (missing documentation)
• ProjectiveHilbertPolynomial == ZZ (missing documentation)
• QQ == CC (missing documentation)
• QQ == QQ (missing documentation)
• QQ == RR (missing documentation)
• QQ == RRi (missing documentation)
• QQ == ZZ (missing documentation)
• radicalContainment -- whether an element is contained in the radical of an ideal
• radicalContainment(Ideal,Ideal) -- see radicalContainment -- whether an element is contained in the radical of an ideal
• radicalContainment(RingElement,Ideal) -- see radicalContainment -- whether an element is contained in the radical of an ideal
• RR == CC (missing documentation)
• RR == QQ (missing documentation)
• RR == RR (missing documentation)
• RR == RRi (missing documentation)
• RR == ZZ (missing documentation)
• RRi == QQ (missing documentation)
• RRi == RR (missing documentation)
• RRi == RRi (missing documentation)
• RRi == ZZ (missing documentation)
• Sequence #? ZZ (missing documentation)
• Sequence == Sequence (missing documentation)
• Set #? Thing -- test set membership
• SheafMap == ZZ (missing documentation)
• String == String (missing documentation)
• Symbol == Symbol (missing documentation)
• testHunekeQuestion(RingElement) -- see testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
• Thing === Thing -- strict equality
• isWeylAlgebra -- see Weyl algebras
• ZZ == CC (missing documentation)
• ZZ == CoherentSheaf (missing documentation)
• ZZ == ProjectiveHilbertPolynomial (missing documentation)
• ZZ == QQ (missing documentation)
• ZZ == RR (missing documentation)
• ZZ == RRi (missing documentation)
• ZZ == SheafMap (missing documentation)
• ZZ == ZZ (missing documentation)

Methods that use a Boolean value:

• Boolean >> Function -- see OptionTable >> Function -- attaching options to a function
• Boolean xor Boolean -- see xor -- exclusive disjunction

Protected objects of class Boolean:

• false
• true

For the programmer

The object Boolean is a type, with ancestor class Thing.