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

## Description

If R is a ring handled by the engine, and M is a 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
• Number * Vector -- see * -- a binary operator, usually used for multiplication
• RingElement * Vector -- see * -- a binary operator, usually used for multiplication
• Vector * Number -- see * -- a binary operator, usually used for multiplication
• Vector * RingElement -- see * -- a binary operator, usually used for multiplication
• + Vector -- see + -- a unary or binary operator, usually used for addition
• 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
• lift(Vector,type of InexactNumber') (missing documentation)
• lift(Vector,type of InexactNumber) (missing documentation)
• lift(Vector,type of Number) (missing documentation)
• lift(Vector,type of RingElement) (missing documentation)
• Matrix Vector (missing documentation)
• random(Module) -- get a random vector in the module
• 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) -- see super -- get the ambient module
• 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)
• describe(Vector) -- see describe -- real description
• 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
• homomorphism(Vector) -- see homomorphism -- get the homomorphism from element of Hom
• isHomogeneous(Vector) -- see isHomogeneous -- whether something is homogeneous (graded)
• leadTerm(Vector) -- see leadTerm(Matrix) -- get the greatest term of each column
• matrix(Vector) -- make a matrix
• Module / Vector -- see Module / Module -- quotient module
• module(Vector) -- the module of a vector
• norm(Vector) -- see norm
• numeric(Vector) -- see numeric -- convert to floating point
• numeric(ZZ,Vector) -- see numeric -- convert to floating point
• ring(Vector) -- see ring -- get the associated ring of an object
• saturate(Vector) -- see saturate -- saturation of ideal or submodule
• saturate(Vector,Ideal) -- see saturate -- saturation of ideal or submodule
• saturate(Vector,RingElement) -- see saturate -- saturation of ideal or submodule
• solve(Matrix,Vector) (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.