# Number -- the class of all numbers

## Types of number :

• InexactNumber
• QQ -- the class of all rational numbers
• ZZ -- the class of all integers

## Methods that use a number :

• Number % GroebnerBasis, see % -- a binary operator, usually used for remainder and reduction
• Number % Ideal, see % -- a binary operator, usually used for remainder and reduction
• Number % RingElement, see % -- a binary operator, usually used for remainder and reduction
• RingElement % Number, see % -- a binary operator, usually used for remainder and reduction
• Constant * Number, see * -- a binary operator, usually used for multiplication
• Matrix * Number, see * -- a binary operator, usually used for multiplication
• Number * Constant, see * -- a binary operator, usually used for multiplication
• Number * Matrix, see * -- a binary operator, usually used for multiplication
• Constant + Number, see + -- a unary or binary operator, usually used for addition
• InfiniteNumber + Number, see + -- a unary or binary operator, usually used for addition
• Matrix + Number, see + -- a unary or binary operator, usually used for addition
• Number + Constant, see + -- a unary or binary operator, usually used for addition
• Number + InfiniteNumber, see + -- a unary or binary operator, usually used for addition
• Number + Matrix, see + -- a unary or binary operator, usually used for addition
• Constant - Number, see - -- a unary or binary operator, usually used for negation or subtraction
• InfiniteNumber - Number, see - -- a unary or binary operator, usually used for negation or subtraction
• Matrix - Number, see - -- a unary or binary operator, usually used for negation or subtraction
• Number - Constant, see - -- a unary or binary operator, usually used for negation or subtraction
• Number - InfiniteNumber, see - -- a unary or binary operator, usually used for negation or subtraction
• Number - Matrix, see - -- a unary or binary operator, usually used for negation or subtraction
• Matrix // Number, see // -- a binary operator, usually used for quotient
• Number // InfiniteNumber, see // -- a binary operator, usually used for quotient
• Number // Matrix, see // -- a binary operator, usually used for quotient
• Number // RingElement, see // -- a binary operator, usually used for quotient
• RingElement // Number, see // -- a binary operator, usually used for quotient
• InfiniteNumber == Number, see == -- equality
• Matrix == Number, see == -- equality
• Number == InfiniteNumber, see == -- equality
• Number == Matrix, see == -- equality
• Number == RingElement, see == -- equality
• RingElement == Number, see == -- equality
• acosh(Number), see acosh -- inverse hyperbolic cosine
• acot(Number), see acot -- compute the inverse cotangent
• asinh(Number), see asinh -- inverse hyperbolic sine
• ceiling(Number) -- ceiling function
• clean(RR,Number), see clean -- Set to zero elements that are approximately zero
• columnAdd(MutableMatrix,ZZ,Number,ZZ), see columnAdd -- add a multiple of one column to another
• columnMult(MutableMatrix,ZZ,Number), see columnMult -- multiply a column by a ring element
• conjugate(Number), see conjugate(CC) -- complex conjugate
• Constant / Number, see Constant
• Constant ^ Number, see Constant
• Number / Constant, see Constant
• Number ^ Constant, see Constant
• Constant Number (missing documentation)
• contract(Matrix,Number), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Number,Matrix), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Number,RingElement), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Number,Vector), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(RingElement,Number), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,Number), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• floor(Number) -- floor function
• Ideal + Number (missing documentation)
• ideal(Number), see ideal(RingElement) -- make an ideal
• imaginaryPart(Number) (missing documentation)
• isANumber(Number), see isANumber -- whether a number is not not-a-number
• isFinite(Number), see isFinite -- whether a number is finite
• isHomogeneous(Number) (missing documentation)
• isInfinite(Number), see isInfinite -- whether a number is infinite
• isUnit(Number), see isUnit -- whether a ring element is a unit
• lift(Matrix,type of Number), see lift -- lift to another ring
• Number ^ Ring, see lift -- lift to another ring
• Number ^ RingFamily, see lift -- lift to another ring
• lift(Module,type of Number) (missing documentation)
• lift(MutableMatrix,type of Number) (missing documentation)
• liftable(Matrix,type of Number) (missing documentation)
• List % Number (missing documentation)
• List // Number (missing documentation)
• map(Module,Module,Number), see map(Module,Module,RingElement) -- construct the map induced by multiplication by a ring element on the generators
• Matrix \\ Number (missing documentation)
• matrix(Number), see matrix(RingElement) -- make a matrix from a ring element
• nextPrime(Number), see nextPrime -- compute the smallest prime greater than or equal to a given number
• norm(InfiniteNumber,Number), see norm
• norm(Number), see norm
• norm(RR,Number), see norm
• Number * IndexedVariable (missing documentation)
• Number + Ideal (missing documentation)
• Number \\ Matrix (missing documentation)
• Number Constant (missing documentation)
• Number Number (missing documentation)
• numeric(Number), see numeric -- convert to floating point
• numeric(ZZ,Number), see numeric -- convert to floating point
• part(InfiniteNumber,InfiniteNumber,Number) (missing documentation)
• part(InfiniteNumber,ZZ,Number) (missing documentation)
• part(ZZ,InfiniteNumber,Number) (missing documentation)
• part(ZZ,Number) (missing documentation)
• part(ZZ,ZZ,Number) (missing documentation)
• precision(Number), see precision
• Number _ Ring, see promote -- promote to another ring
• promote(Module,type of Number) (missing documentation)
• promote(MutableMatrix,type of Number) (missing documentation)
• promote(Vector,type of Number) (missing documentation)
• quotientRemainder(Number,RingElement), see quotientRemainder(RingElement,RingElement) -- quotient and remainder
• quotientRemainder(RingElement,Number), see quotientRemainder(RingElement,RingElement) -- quotient and remainder
• realPart(Number) (missing documentation)
• ring(Number), see ring -- get the associated ring of an object
• rowAdd(MutableMatrix,ZZ,Number,ZZ), see rowAdd -- add a multiple of one row to another
• rowMult(MutableMatrix,ZZ,Number), see rowMult -- multiply a row by a ring element
• substitute(Number,Ring), see substitute -- substituting values for variables
• substitute(Number,RingFamily), see substitute -- substituting values for variables

## For the programmer

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