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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.
See also
engine
Module
-- the class of all modules
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)
Vector / Number
-- see
Matrix / Number
-- scalar division
Vector / RingElement
-- see
Matrix / Number
-- scalar division
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
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)
leadComponent(Vector)
-- see
leadComponent
-- the leading component(s) of a vector or matrix
leadMonomial(Vector)
(missing documentation)
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 == Vector
(missing documentation)
Vector ^ List
(missing documentation)
For the programmer
The object
Vector
is
a
type
, with ancestor classes
BasicList
<
Thing
.