Boolean -- the class of Boolean values

Functions and methods returning a Boolean value :

• Thing =!= Thing, see =!= -- strict inequality
• Thing === Thing, see === -- strict equality
• ? -- 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(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• atEndOfFile(File) -- test for end of file
• BasicList #? ZZ -- check for element in list
• Database #? String -- check for value in database
• HashTable #? Thing -- check for value in hash table
• inducesWellDefinedMap -- whether a map is well defined
• instance(Thing,Type), see instance -- whether something has a certain type
• isAffineRing -- whether something is an affine ring
• 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
• isCommutative -- whether a ring is commutative
• isConstant -- whether a ring element is constant
• isField -- whether something is a field
• isFreeModule -- whether something is a free module
• 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), see isInputFile -- whether a file is open for input
• isIsomorphism -- whether a map is an isomorphism
• isListener(File), see isListener -- whether a file is open for listening
• isModule -- whether something is a module
• isMonomialIdeal -- whether something is a monomial ideal
• isNormal(Ring) -- determine whether 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), see isOpen -- whether a file or database is open
• isPolynomialRing -- whether someting is a polynomial ring
• isPrime -- whether a integer, polynomial, or ideal is prime
• isPrime(ZZ), see isPrime -- whether a integer, polynomial, or ideal is prime
• 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
• isRing -- whether something is a ring
• isSkewCommutative -- whether a ring has skew commuting variables
• 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
• isWellDefined -- whether a map is well defined
• liftable -- whether a ring element can be lifted to another ring
• match -- regular expression matching
• member(Thing,Set), see member -- test membership in a list or set
• member(Thing,VisibleList), see member -- test membership in a list or set
• mutable(Thing), see mutable -- whether something may be modified
• Set #? Thing -- test set membership
• String #? ZZ -- check for character in string

Fixed objects of class Boolean :

• false
• true

For the programmer

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