# Vector -- the class of all elements of free modules that are handled by the engine

## Description

If R is a ring handled by the engine, and M is a free module over R, then M is a subclass of Vector.

## Functions and methods returning a vector :

• Matrix * Vector, see * -- a binary operator, usually used for multiplication
• RingElement * Vector, see * -- a binary operator, usually used for multiplication
• Vector + Vector, see + -- a unary or binary operator, usually used for addition
• Vector - Vector, see - -- a unary or binary operator, usually used for negation or subtraction
• - Vector -- negation of a Vector
• Matrix _ ZZ, see generators of ideals and modules
• Module _ ZZ, see generators of ideals and modules
• homogenize(Vector,RingElement), see homogenize -- homogenize with respect to a variable
• homogenize(Vector,RingElement,List), see homogenize -- homogenize with respect to a variable
• Matrix Vector (missing documentation)
• promote(Vector,type of InexactNumber') (missing documentation)
• promote(Vector,type of InexactNumber) (missing documentation)
• promote(Vector,type of Number) (missing documentation)
• promote(Vector,type of RingElement) (missing documentation)
• RingMap Vector, see RingMap RingElement -- apply a ring map
• substitute(Vector,List), see substitute -- substituting values for variables
• substitute(Vector,Matrix), see substitute -- substituting values for variables
• substitute(Vector,Ring), see substitute -- substituting values for variables
• substitute(Vector,RingFamily), see substitute -- substituting values for variables
• super(Vector) (missing documentation)
• Vector ** Vector -- tensor product
• Vector || Vector -- join Vectors
• ZZ _ Module -- integers or zero element

## Methods that use a vector :

• Ideal * Vector, see * -- a binary operator, usually used for multiplication
• Ring * Vector, see * -- a binary operator, usually used for multiplication
• Vector == Vector, see == -- equality
• contract(Matrix,Vector), 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,Vector), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,Matrix), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,Number), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,RingElement), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• contract(Vector,Vector), see contract(Matrix,Matrix) -- contract a matrix by a matrix
• degree(Vector), see degree(RingElement)
• diff(Matrix,Vector), see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(RingElement,Vector), see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Vector,Matrix), see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Vector,RingElement), see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• diff(Vector,Vector), see diff(Matrix,Matrix) -- differentiate a matrix by a matrix
• entries(Vector) -- lists the entries of a vector
• html(Vector) (missing documentation)
• isHomogeneous(Vector), see isHomogeneous -- whether something is homogeneous (graded)
• leadTerm(Vector), see leadTerm(Matrix) -- get the greatest term of each column
• matrix(Vector)
• Module / Vector, see Module / Module -- quotient module
• module(Vector) -- the module of a vector
• norm(Vector), see norm
• numeric(Vector) (missing documentation)
• numeric(ZZ,Vector) (missing documentation)
• ring(Vector), see ring -- get the associated ring of an object
• saturate(Vector,Ideal) (missing documentation)
• saturate(Vector,RingElement) (missing documentation)
• substitute(Vector,Option), see substitute -- substituting values for variables
• Vector % Ideal (missing documentation)
• Vector ^ List (missing documentation)

## For the programmer

The object Vector is a type, with ancestor classes BasicList < Thing.