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Macaulay2 website
Macaulay2Doc
::
Vector
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.
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
"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)
"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)
"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
"isHomogeneous(Vector)"
-- see
isHomogeneous
-- whether something is homogeneous (graded)
"leadComponent(Vector)"
-- see
leadComponent
-- the leading component(s) of a vector or matrix
"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
.