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
• Dictionary #? 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
• List #? ZZ -- see #? -- check existence of value in a list, hash table, database, or string
• Net #? ZZ -- see #? -- check existence of value in a list, hash table, database, or string
• Nothing #? Thing -- see #? -- check existence of value in a list, hash table, database, or string
• Sequence #? ZZ -- 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
• 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
• Boolean and Boolean -- see and -- conjunction
• 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
• fileExecutable(String) -- see fileExecutable
• fileReadable(String) -- see fileReadable
• fileWritable(String) -- see fileWritable
• 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
• 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
• isConstant -- whether a ring element is constant
• isEmpty -- whether an object is empty
• isEmpty(RRi) -- empty test for an interval
• isExact
• isField -- whether something is a field
• isField(Ring) -- see isField -- whether something is a field
• isFinitePrimeField -- whether a ring is a finite prime 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) -- whether a file is open for input
• isIsomorphism -- whether a map is an isomorphism
• 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)
• 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
• isPolynomialRing -- whether something is a polynomial ring
• isPrime -- whether a integer or polynomial is prime
• isPrime(ZZ) -- see isPrime -- whether a integer or polynomial is prime
• isPrime(Ideal)
• isPseudoprime -- see isPseudoprime(ZZ) -- whether an integer is probably prime
• isPseudoprime(ZZ) -- whether an integer is probably 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
• isReady(Task) -- whether a task is finished
• isRing -- whether something is a ring
• 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
• match -- regular expression matching
• not Boolean (missing documentation)
• Boolean or Boolean -- see or -- disjunction
• Set #? Thing -- test set membership
• isWeylAlgebra -- see Weyl algebras

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.

The source of this document is in Macaulay2Doc/operators.m2:206:0.