MathAction Computing with Vectors

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How to multiply two vectors??

Multiplication element by element:

Vanuxem Gregory replies:

Try

fricas

(1) -> a:= vector [1,2,3,5,6]

$\label{eq1}\left[ 1, \: 2, \: 3, \: 5, \: 6 \right]$

(1)

Type: Vector(PositiveInteger?)

fricas

map(*,a,a)

$\label{eq2}\left[ 1, \: 4, \: 9, \:{25}, \:{36}\right]$

(2)

Type: Vector(PositiveInteger?)

otherwise use Matrix:

fricas

a:= matrix [[1,2,3,4,5,6]]

$\label{eq3}\left[ \begin{array}{cccccc} 1 & 2 & 3 & 4 & 5 & 6$

(3)

Type: Matrix(Integer)

fricas

a * transpose a

$\label{eq4}\left[ \begin{array}{c} {91}$

(4)

Type: Matrix(Integer)

Tim Daly replies:

make three vectors

fricas

)clear all

   All user variables and function definitions have been cleared.
u : VECTOR INT := new(5,12)

$\label{eq5}\left[{12}, \:{12}, \:{12}, \:{12}, \:{12}\right]$

(5)

Type: Vector(Integer)

fricas

v : VECTOR INT := vector([1,2,3])

$\label{eq6}\left[ 1, \: 2, \: 3 \right]$

(6)

Type: Vector(Integer)

fricas

w : VECTOR INT := vector([2,3,4])

$\label{eq7}\left[ 2, \: 3, \: 4 \right]$

(7)

Type: Vector(Integer)

multiply them

fricas

cross(v,w)

$\label{eq8}\left[ - 1, \: 2, \: - 1 \right]$

(8)

Type: Vector(Integer)

dot product

fricas

dot(v,w)

$\label{eq9}20$

(9)

Type: PositiveInteger?

ask for the length

fricas

#(v)

$\label{eq10}3$

(10)

Type: PositiveInteger?

access an element

fricas

v(2)

$\label{eq11}2$

(11)

Type: PositiveInteger?

set an element

fricas

v(3) := 99

$\label{eq12}99$

(12)

Type: PositiveInteger?

show the vector

fricas

$\label{eq13}\left[ 1, \: 2, \:{99}\right]$

(13)

Type: Vector(Integer)

multiply by a constant on either side

fricas

5 * v

$\label{eq14}\left[ 5, \:{10}, \:{495}\right]$

(14)

Type: Vector(Integer)

fricas

v * 7

$\label{eq15}\left[ 7, \:{14}, \:{693}\right]$

(15)

Type: Vector(Integer)

add them

fricas

v + w

$\label{eq16}\left[ 3, \: 5, \:{103}\right]$

(16)

Type: Vector(Integer)

substract them

fricas

v - w

$\label{eq17}\left[ - 1, \: - 1, \:{95}\right]$

(17)

Type: Vector(Integer)

display all possible functions

fricas

)show Vector(Integer)

 Vector(Integer) is a domain constructor.
 Abbreviation for Vector is VECTOR 
 This constructor is exposed in this frame.
 74 Names for 99 Operations in this Domain.
------------------------------- Operations --------------------------------

 #? : % -> NonNegativeInteger          ?*? : (Integer, %) -> %
 ?*? : (%, Integer) -> %               ?+? : (%, %) -> %
 ?-? : (%, %) -> %                     -? : % -> %
 ?<? : (%, %) -> Boolean               ?<=? : (%, %) -> Boolean
 ?=? : (%, %) -> Boolean               ?>? : (%, %) -> Boolean
 ?>=? : (%, %) -> Boolean              coerce : % -> OutputForm
 concat : (Integer, %) -> %            concat : List(%) -> %
 concat : (%, Integer) -> %            concat : (%, %) -> %
 construct : List(Integer) -> %        convert : % -> InputForm
 copy : % -> %                         cross : (%, %) -> %
 delete : (%, Integer) -> %            dot : (%, %) -> Integer
 elt : (%, Integer) -> Integer         empty : () -> %
 empty? : % -> Boolean                 entries : % -> List(Integer)
 entry? : (Integer, %) -> Boolean      eq? : (%, %) -> Boolean
 fill! : (%, Integer) -> %             first : % -> Integer
 hash : % -> SingleInteger             index? : (Integer, %) -> Boolean
 indices : % -> List(Integer)          insert : (%, %, Integer) -> %
 latex : % -> String                   leftTrim : (%, Integer) -> %
 max : % -> Integer                    max : (%, %) -> %
 maxIndex : % -> Integer               member? : (Integer, %) -> Boolean
 members : % -> List(Integer)          merge : (%, %) -> %
 min : % -> Integer                    min : (%, %) -> %
 minIndex : % -> Integer               parts : % -> List(Integer)
 qelt : (%, Integer) -> Integer        remove : (Integer, %) -> %
 removeDuplicates : % -> %             reverse : % -> %
 reverse! : % -> %                     rightTrim : (%, Integer) -> %
 sample : () -> %                      smaller? : (%, %) -> Boolean
 sort : % -> %                         sort! : % -> %
 sorted? : % -> Boolean                trim : (%, Integer) -> %
 vector : List(Integer) -> %           zero : NonNegativeInteger -> %
 zero? : % -> Boolean                  ?~=? : (%, %) -> Boolean
 any? : ((Integer -> Boolean), %) -> Boolean
 copyInto! : (%, %, Integer) -> %
 count : (Integer, %) -> NonNegativeInteger
 count : ((Integer -> Boolean), %) -> NonNegativeInteger
 delete : (%, UniversalSegment(Integer)) -> %
 elt : (%, Integer, Integer) -> Integer
 elt : (%, UniversalSegment(Integer)) -> %
 every? : ((Integer -> Boolean), %) -> Boolean
 find : ((Integer -> Boolean), %) -> Union(Integer,"failed")
 first : (%, NonNegativeInteger) -> %
 hashUpdate! : (HashState, %) -> HashState
 insert : (Integer, %, Integer) -> %
 less? : (%, NonNegativeInteger) -> Boolean
 map : (((Integer, Integer) -> Integer), %, %) -> %
 map : ((Integer -> Integer), %) -> %
 map! : ((Integer -> Integer), %) -> %
 max : (((Integer, Integer) -> Boolean), %) -> Integer
 merge : (((Integer, Integer) -> Boolean), %, %) -> %
 more? : (%, NonNegativeInteger) -> Boolean
 new : (NonNegativeInteger, Integer) -> %
 outerProduct : (%, %) -> Matrix(Integer)
 position : (Integer, %, Integer) -> Integer
 position : (Integer, %) -> Integer
 position : ((Integer -> Boolean), %) -> Integer
 qsetelt! : (%, Integer, Integer) -> Integer
 reduce : (((Integer, Integer) -> Integer), %, Integer, Integer) -> Integer
 reduce : (((Integer, Integer) -> Integer), %, Integer) -> Integer
 reduce : (((Integer, Integer) -> Integer), %) -> Integer
 remove : ((Integer -> Boolean), %) -> %
 select : ((Integer -> Boolean), %) -> %
 setelt! : (%, Integer, Integer) -> Integer
 setelt! : (%, UniversalSegment(Integer), Integer) -> Integer
 size? : (%, NonNegativeInteger) -> Boolean
 sort : (((Integer, Integer) -> Boolean), %) -> %
 sort! : (((Integer, Integer) -> Boolean), %) -> %
 sorted? : (((Integer, Integer) -> Boolean), %) -> Boolean
 swap! : (%, Integer, Integer) -> Void

Subject: Be Bold !!

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