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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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3
Task/Vector/00-META.yaml Normal file
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---
from: http://rosettacode.org/wiki/Vector
note: Physics

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Task/Vector/00-TASK.txt Normal file
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;Task
Implement a Vector class (or a set of functions) that models a Physical Vector. The four basic operations and a ''pretty print'' function should be implemented.
The Vector may be initialized in any reasonable way.
* Start and end points, and direction
* Angular coefficient and value (length)
The four operations to be implemented are:
* Vector <big><b> + </b></big> Vector addition
* Vector <big><b> - </b></big> Vector subtraction
* Vector <big><b> * </b></big> scalar multiplication
* Vector <big><b> / </b></big> scalar division
<br><br>

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T Vector
Float x, y
F (x, y)
.x = x
.y = y
F +(vector)
R Vector(.x + vector.x, .y + vector.y)
F -(vector)
R Vector(.x - vector.x, .y - vector.y)
F *(mult)
R Vector(.x * mult, .y * mult)
F /(denom)
R Vector(.x / denom, .y / denom)
F String()
R ‘(#., #.)’.format(.x, .y)
print(Vector(5, 7) + Vector(2, 3))
print(Vector(5, 7) - Vector(2, 3))
print(Vector(5, 7) * 11)
print(Vector(5, 7) / 2)

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Task/Vector/ALGOL-68/vector.alg Normal file
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# the standard mode COMPLEX is a two element vector #
MODE VECTOR = COMPLEX;
# the operations required for the task plus many others are provided as standard for COMPLEX and REAL items #
# the two components are fields called "re" and "im" #
# we can define a "pretty-print" operator: #
# returns a formatted representation of the vector #
OP TOSTRING = ( VECTOR a )STRING: "[" + TOSTRING re OF a + ", " + TOSTRING im OF a + "]";
# returns a formatted representation of the scaler #
OP TOSTRING = ( REAL a )STRING: fixed( a, 0, 4 );
# test the operations #
VECTOR a = 5 I 7, b = 2 I 3; # note the use of the I operator to construct a COMPLEX from two scalers #
print( ( "a+b : ", TOSTRING ( a + b ), newline ) );
print( ( "a-b : ", TOSTRING ( a - b ), newline ) );
print( ( "a*11: ", TOSTRING ( a * 11 ), newline ) );
print( ( "a/2 : ", TOSTRING ( a / 2 ), newline ) )

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INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
DEFINE X_="+0"
DEFINE Y_="+6"
TYPE Vector=[CARD x1,x2,x3,y1,y2,y3]
PROC PrintVec(Vector POINTER v)
Print("[") PrintR(v X_)
Print(",") PrintR(v Y_) Print("]")
RETURN
PROC VecIntInit(Vector POINTER v INT ix,iy)
IntToReal(ix,v X_)
IntToReal(iy,v Y_)
RETURN
PROC VecRealInit(Vector POINTER v REAL POINTER rx,ry)
RealAssign(rx,v X_)
RealAssign(ry,v Y_)
RETURN
PROC VecStringInit(Vector POINTER v CHAR ARRAY sx,sy)
ValR(sx,v X_)
ValR(sy,v Y_)
RETURN
PROC VecAdd(Vector POINTER v1,v2,res)
RealAdd(v1 X_,v2 X_,res X_) ;res.x=v1.x+v2.x
RealAdd(v1 Y_,v2 Y_,res Y_) ;res.y=v1.y+v2.y
RETURN
PROC VecSub(Vector POINTER v1,v2,res)
RealSub(v1 X_,v2 X_,res X_) ;res.x=v1.x-v2.x
RealSub(v1 Y_,v2 Y_,res Y_) ;res.y=v1.y-v2.y
RETURN
PROC VecMult(Vector POINTER v REAL POINTER a Vector POINTER res)
RealMult(v X_,a,res X_) ;res.x=v.x*a
RealMult(v Y_,a,res Y_) ;res.y=v.y*a
RETURN
PROC VecDiv(Vector POINTER v REAL POINTER a Vector POINTER res)
RealDiv(v X_,a,res X_) ;res.x=v.x/a
RealDiv(v Y_,a,res Y_) ;res.y=v.y/a
RETURN
PROC Main()
Vector v1,v2,res
REAL s
Put(125) PutE() ;clear the screen
VecStringInit(v1,"12.3","-4.56")
VecStringInit(v2,"9.87","654.3")
ValR("0.1",s)
VecAdd(v1,v2,res)
PrintVec(v1) Print(" + ") PrintVec(v2)
Print(" =") PutE() PrintVec(res) PutE() PutE()
VecSub(v1,v2,res)
PrintVec(v1) Print(" - ") PrintVec(v2)
Print(" =") PutE() PrintVec(res) PutE() PutE()
VecMult(v1,s,res)
PrintVec(v1) Print(" * ") PrintR(s)
Print(" = ") PrintVec(res) PutE() PutE()
VecDiv(v1,s,res)
PrintVec(v1) Print(" / ") PrintR(s)
Print(" = ") PrintVec(res)
RETURN

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define :vector [
x y
][
print: -> render "(|this\x|, |this\y|)" ; prettyprint function
]
ensureVector: function [block][
ensure -> every? @block => [is? :vector &]
]
vadd: function [a b][
ensureVector [a b]
to :vector @[a\x + b\x, a\y + b\y]
]
vsub: function [a b][
ensureVector [a b]
to :vector @[a\x - b\x, a\y - b\y]
]
vmul: function [a n][
ensureVector [a]
to :vector @[a\x * n, a\y * n]
]
vdiv: function [a n][
ensureVector [a]
to :vector @[a\x // n, a\y // n]
]
; test our vector object
a: to :vector [5 7]
b: to :vector [2 3]
print [a '+ b '= vadd a b]
print [a '- b '= vsub a b]
print [a '* 11 '= vmul a 11]
print [a '/ 11 '= vdiv a 2]

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arraybase 1
dim vect1(2)
vect1[1] = 5 : vect1[2] = 7
dim vect2(2)
vect2[1] = 2 : vect2[2] = 3
dim vect3(vect1[?])
subroutine showarray(vect3)
print "[";
svect$ = ""
for n = 1 to vect3[?]
svect$ &= vect3[n] & ", "
next n
svect$ = left(svect$, length(svect$) - 2)
print svect$;
print "]"
end subroutine
for n = 1 to vect1[?]
vect3[n] = vect1[n] + vect2[n]
next n
print "[" & vect1[1] & ", " & vect1[2] & "] + [" & vect2[1] & ", " & vect2[2] & "] = ";
call showarray(vect3)
for n = 1 to vect1[?]
vect3[n] = vect1[n] - vect2[n]
next n
print "[" & vect1[1] & ", " & vect1[2] & "] - [" & vect2[1] & ", " & vect2[2] & "] = ";
call showarray(vect3)
for n = 1 to vect1[?]
vect3[n] = vect1[n] * 11
next n
print "[" & vect1[1] & ", " & vect1[2] & "] * " & 11 & " = ";
call showarray(vect3)
for n = 1 to vect1[?]
vect3[n] = vect1[n] / 2
next n
print "[" & vect1[1] & ", " & vect1[2] & "] / " & 2 & " = ";
call showarray(vect3)
end

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5‿7 + 2‿3
⟨7 10⟩
5‿7 - 2‿3
⟨3 4⟩
5‿7 × 11
⟨55 77⟩
5‿7 ÷ 2
⟨2.5 3.5⟩

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#include <iostream>
#include <cmath>
#include <cassert>
using namespace std;
#define PI 3.14159265359
class Vector
{
public:
Vector(double ix, double iy, char mode)
{
if(mode=='a')
{
x=ix*cos(iy);
y=ix*sin(iy);
}
else
{
x=ix;
y=iy;
}
}
Vector(double ix,double iy)
{
x=ix;
y=iy;
}
Vector operator+(const Vector& first)
{
return Vector(x+first.x,y+first.y);
}
Vector operator-(Vector first)
{
return Vector(x-first.x,y-first.y);
}
Vector operator*(double scalar)
{
return Vector(x*scalar,y*scalar);
}
Vector operator/(double scalar)
{
return Vector(x/scalar,y/scalar);
}
bool operator==(Vector first)
{
return (x==first.x&&y==first.y);
}
void v_print()
{
cout << "X: " << x << " Y: " << y;
}
double x,y;
};
int main()
{
Vector vec1(0,1);
Vector vec2(2,2);
Vector vec3(sqrt(2),45*PI/180,'a');
vec3.v_print();
assert(vec1+vec2==Vector(2,3));
assert(vec1-vec2==Vector(-2,-1));
assert(vec1*5==Vector(0,5));
assert(vec2/2==Vector(1,1));
return 0;
}

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using System;
using System.Collections.Generic;
using System.Linq;
namespace RosettaVectors
{
public class Vector
{
public double[] store;
public Vector(IEnumerable<double> init)
{
store = init.ToArray();
}
public Vector(double x, double y)
{
store = new double[] { x, y };
}
static public Vector operator+(Vector v1, Vector v2)
{
return new Vector(v1.store.Zip(v2.store, (a, b) => a + b));
}
static public Vector operator -(Vector v1, Vector v2)
{
return new Vector(v1.store.Zip(v2.store, (a, b) => a - b));
}
static public Vector operator *(Vector v1, double scalar)
{
return new Vector(v1.store.Select(x => x * scalar));
}
static public Vector operator /(Vector v1, double scalar)
{
return new Vector(v1.store.Select(x => x / scalar));
}
public override string ToString()
{
return string.Format("[{0}]", string.Join(",", store));
}
}
class Program
{
static void Main(string[] args)
{
var v1 = new Vector(5, 7);
var v2 = new Vector(2, 3);
Console.WriteLine(v1 + v2);
Console.WriteLine(v1 - v2);
Console.WriteLine(v1 * 11);
Console.WriteLine(v1 / 2);
// Works with arbitrary size vectors, too.
var lostVector = new Vector(new double[] { 4, 8, 15, 16, 23, 42 });
Console.WriteLine(lostVector * 7);
Console.ReadLine();
}
}
}

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#include<stdio.h>
#include<math.h>
#define pi M_PI
typedef struct{
double x,y;
}vector;
vector initVector(double r,double theta){
vector c;
c.x = r*cos(theta);
c.y = r*sin(theta);
return c;
}
vector addVector(vector a,vector b){
vector c;
c.x = a.x + b.x;
c.y = a.y + b.y;
return c;
}
vector subtractVector(vector a,vector b){
vector c;
c.x = a.x - b.x;
c.y = a.y - b.y;
return c;
}
vector multiplyVector(vector a,double b){
vector c;
c.x = b*a.x;
c.y = b*a.y;
return c;
}
vector divideVector(vector a,double b){
vector c;
c.x = a.x/b;
c.y = a.y/b;
return c;
}
void printVector(vector a){
printf("%lf %c %c %lf %c",a.x,140,(a.y>=0)?'+':'-',(a.y>=0)?a.y:fabs(a.y),150);
}
int main()
{
vector a = initVector(3,pi/6);
vector b = initVector(5,2*pi/3);
printf("\nVector a : ");
printVector(a);
printf("\n\nVector b : ");
printVector(b);
printf("\n\nSum of vectors a and b : ");
printVector(addVector(a,b));
printf("\n\nDifference of vectors a and b : ");
printVector(subtractVector(a,b));
printf("\n\nMultiplying vector a by 3 : ");
printVector(multiplyVector(a,3));
printf("\n\nDividing vector b by 2.5 : ");
printVector(divideVector(b,2.5));
return 0;
}

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% Parameterized vector class
vector = cluster [T: type] is make, add, sub, mul, div,
get_x, get_y, to_string
% The inner type must support basic math
where T has add: proctype (T,T) returns (T)
signals (overflow, underflow),
sub: proctype (T,T) returns (T)
signals (overflow, underflow),
mul: proctype (T,T) returns (T)
signals (overflow, underflow),
div: proctype (T,T) returns (T)
signals (zero_divide, overflow, underflow)
rep = struct [x,y: T]
% instantiate
make = proc (x,y: T) returns (cvt)
return(rep${x:x, y:y})
end make
% vector addition and subtraction
add = proc (a,b: cvt) returns (cvt)
signals (overflow, underflow)
return(rep${x: up(a).x + up(b).x,
y: up(a).y + up(b).y})
resignal overflow, underflow
end add
sub = proc (a,b: cvt) returns (cvt)
signals (overflow, underflow)
return(rep${x: up(a).x - up(b).x,
y: up(a).y - up(b).y})
resignal overflow, underflow
end sub
% scalar multiplication and division
mul = proc (a: cvt, b: T) returns (cvt)
signals (overflow, underflow)
return(rep${x: up(a).x*b, y: up(a).y*b})
resignal overflow, underflow
end mul
div = proc (a: cvt, b: T) returns (cvt)
signals (zero_divide, overflow, underflow)
return(rep${x: up(a).x/b, y: up(a).y/b})
resignal zero_divide, overflow, underflow
end div
% accessors
get_x = proc (v: cvt) returns (T) return(v.x) end get_x
get_y = proc (v: cvt) returns (T) return(v.y) end get_y
% we can't just use T$unparse for pretty-printing, since
% for floats it always prints the exponential form, and
% that's not very pretty.
% passing in a conversion function at the moment of
% generating the string form is the least bad way.
to_string = proc (v: cvt, f: proctype (T) returns (string))
returns (string)
return("(" || f(v.x) || ", " || f(v.y) || ")")
end to_string
end vector
% this function formats a real somewhat neatly without needing
% extra parameters
format_real = proc (r: real) returns (string)
return(f_form(r, 2, 4))
end format_real
start_up = proc ()
vr = vector[real] % use real numbers
po: stream := stream$primary_output()
% vectors
a: vr := vr$make(5.0, 7.0)
b: vr := vr$make(2.0, 3.0)
% do some math
a_plus_b: vr := a + b
a_minus_b: vr := a - b
a_times_11: vr := a * 11.0
a_div_2: vr := a / 2.0
% show the results
stream$putl(po, " a = " || vr$to_string(a, format_real))
stream$putl(po, " b = " || vr$to_string(b, format_real))
stream$putl(po, " a + b = " || vr$to_string(a_plus_b, format_real))
stream$putl(po, " a - b = " || vr$to_string(a_minus_b, format_real))
stream$putl(po, "a * 11 = " || vr$to_string(a_times_11, format_real))
stream$putl(po, " a / 2 = " || vr$to_string(a_div_2, format_real))
end start_up

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import std.stdio;
void main() {
writeln(VectorReal(5, 7) + VectorReal(2, 3));
writeln(VectorReal(5, 7) - VectorReal(2, 3));
writeln(VectorReal(5, 7) * 11);
writeln(VectorReal(5, 7) / 2);
}
alias VectorReal = Vector!real;
struct Vector(T) {
private T x, y;
this(T x, T y) {
this.x = x;
this.y = y;
}
auto opBinary(string op : "+")(Vector rhs) const {
return Vector(x + rhs.x, y + rhs.y);
}
auto opBinary(string op : "-")(Vector rhs) const {
return Vector(x - rhs.x, y - rhs.y);
}
auto opBinary(string op : "/")(T denom) const {
return Vector(x / denom, y / denom);
}
auto opBinary(string op : "*")(T mult) const {
return Vector(x * mult, y * mult);
}
void toString(scope void delegate(const(char)[]) sink) const {
import std.format;
sink.formattedWrite!"(%s, %s)"(x, y);
}
}

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program Vector;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.Math.Vectors,
SysUtils;
procedure VectorToString(v: TVector);
begin
WriteLn(Format('(%.1f + i%.1f)', [v.X, v.Y]));
end;
var
a, b: TVector;
begin
a := TVector.Create(5, 7);
b := TVector.Create(2, 3);
VectorToString(a + b);
VectorToString(a - b);
VectorToString(a * 11);
VectorToString(a / 2);
ReadLn;
end
.

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open System
let add (ax, ay) (bx, by) =
(ax+bx, ay+by)
let sub (ax, ay) (bx, by) =
(ax-bx, ay-by)
let mul (ax, ay) c =
(ax*c, ay*c)
let div (ax, ay) c =
(ax/c, ay/c)
[<EntryPoint>]
let main _ =
let a = (5.0, 7.0)
let b = (2.0, 3.0)
printfn "%A" (add a b)
printfn "%A" (sub a b)
printfn "%A" (mul a 11.0)
printfn "%A" (div a 2.0)
0 // return an integer exit code

5
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(scratchpad) USE: math.vectors
(scratchpad) { 1 2 } { 3 4 } v+
--- Data stack:
{ 4 6 }

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USING: accessors arrays kernel math parser prettyprint
prettyprint.custom sequences ;
IN: rosetta-code.vector
TUPLE: vec { x real read-only } { y real read-only } ;
C: <vec> vec
<PRIVATE
: parts ( vec -- x y ) [ x>> ] [ y>> ] bi ;
: devec ( vec1 vec2 -- x1 y1 x2 y2 ) [ parts ] bi@ rot swap ;
: binary-op ( vec1 vec2 quot -- vec3 )
[ devec ] dip 2bi@ <vec> ; inline
: scalar-op ( vec1 scalar quot -- vec2 )
[ parts ] 2dip curry bi@ <vec> ; inline
PRIVATE>
SYNTAX: VEC{ \ } [ first2 <vec> ] parse-literal ;
: v+ ( vec1 vec2 -- vec3 ) [ + ] binary-op ;
: v- ( vec1 vec2 -- vec3 ) [ - ] binary-op ;
: v* ( vec1 scalar -- vec2 ) [ * ] scalar-op ;
: v/ ( vec1 scalar -- vec2 ) [ / ] scalar-op ;
M: vec pprint-delims drop \ VEC{ \ } ;
M: vec >pprint-sequence parts 2array ;
M: vec pprint* pprint-object ;

17
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USING: kernel formatting prettyprint rosetta-code.vector
sequences ;
IN: rosetta-code.vector
: demo ( a b quot -- )
3dup [ unparse ] tri@ rest but-last
"%16s %16s%3s= " printf call . ; inline
VEC{ -8.4 1.35 } VEC{ 10 11/123 } [ v+ ] demo
VEC{ 5 3 } VEC{ 4 2 } [ v- ] demo
VEC{ 4 -8 } 2 [ v* ] demo
VEC{ 5 7 } 2 [ v/ ] demo
! You can still make a vector without the literal syntax of
! course.
5 2 <vec> 1.3 [ v* ] demo

5
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: v. swap . . ;
: v* swap over * >r * r> ;
: v/ swap over / >r / r> ;
: v+ >r swap >r + r> r> + ;
: v- >r swap >r - r> r> - ;

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MODULE ROSETTA_VECTOR
IMPLICIT NONE
TYPE VECTOR
REAL :: X, Y
END TYPE VECTOR
INTERFACE OPERATOR(+)
MODULE PROCEDURE VECTOR_ADD
END INTERFACE
INTERFACE OPERATOR(-)
MODULE PROCEDURE VECTOR_SUB
END INTERFACE
INTERFACE OPERATOR(/)
MODULE PROCEDURE VECTOR_DIV
END INTERFACE
INTERFACE OPERATOR(*)
MODULE PROCEDURE VECTOR_MULT
END INTERFACE
CONTAINS
FUNCTION VECTOR_ADD(VECTOR_1, VECTOR_2)
TYPE(VECTOR), INTENT(IN) :: VECTOR_1, VECTOR_2
TYPE(VECTOR) :: VECTOR_ADD
VECTOR_ADD%X = VECTOR_1%X+VECTOR_2%X
VECTOR_ADD%Y = VECTOR_1%Y+VECTOR_2%Y
END FUNCTION VECTOR_ADD
FUNCTION VECTOR_SUB(VECTOR_1, VECTOR_2)
TYPE(VECTOR), INTENT(IN) :: VECTOR_1, VECTOR_2
TYPE(VECTOR) :: VECTOR_SUB
VECTOR_SUB%X = VECTOR_1%X-VECTOR_2%X
VECTOR_SUB%Y = VECTOR_1%Y-VECTOR_2%Y
END FUNCTION VECTOR_SUB
FUNCTION VECTOR_DIV(VEC, SCALAR)
TYPE(VECTOR), INTENT(IN) :: VEC
REAL, INTENT(IN) :: SCALAR
TYPE(VECTOR) :: VECTOR_DIV
VECTOR_DIV%X = VEC%X/SCALAR
VECTOR_DIV%Y = VEC%Y/SCALAR
END FUNCTION VECTOR_DIV
FUNCTION VECTOR_MULT(VEC, SCALAR)
TYPE(VECTOR), INTENT(IN) :: VEC
REAL, INTENT(IN) :: SCALAR
TYPE(VECTOR) :: VECTOR_MULT
VECTOR_MULT%X = VEC%X*SCALAR
VECTOR_MULT%Y = VEC%Y*SCALAR
END FUNCTION VECTOR_MULT
FUNCTION FROM_RTHETA(R, THETA)
REAL :: R, THETA
TYPE(VECTOR) :: FROM_RTHETA
FROM_RTHETA%X = R*SIN(THETA)
FROM_RTHETA%Y = R*COS(THETA)
END FUNCTION FROM_RTHETA
FUNCTION FROM_XY(X, Y)
REAL :: X, Y
TYPE(VECTOR) :: FROM_XY
FROM_XY%X = X
FROM_XY%Y = Y
END FUNCTION FROM_XY
FUNCTION PRETTY_PRINT(VEC)
TYPE(VECTOR), INTENT(IN) :: VEC
CHARACTER(LEN=100) PRETTY_PRINT
WRITE(PRETTY_PRINT,"(A, F0.5, A, F0.5, A)") "[", VEC%X, ", ", VEC%Y, "]"
END FUNCTION PRETTY_PRINT
END MODULE ROSETTA_VECTOR
PROGRAM VECTOR_DEMO
USE ROSETTA_VECTOR
IMPLICIT NONE
TYPE(VECTOR) :: VECTOR_1, VECTOR_2
REAL, PARAMETER :: PI = 4*ATAN(1.0)
REAL :: SCALAR
SCALAR = 2.0
VECTOR_1 = FROM_XY(2.0, 3.0)
VECTOR_2 = FROM_RTHETA(2.0, PI/6.0)
WRITE(*,*) "VECTOR_1 (X: 2.0, Y: 3.0) : ", PRETTY_PRINT(VECTOR_1)
WRITE(*,*) "VECTOR_2 (R: 2.0, THETA: PI/6) : ", PRETTY_PRINT(VECTOR_2)
WRITE(*,*) NEW_LINE('A')
WRITE(*,*) "VECTOR_1 + VECTOR_2 = ", PRETTY_PRINT(VECTOR_1+VECTOR_2)
WRITE(*,*) "VECTOR_1 - VECTOR_2 = ", PRETTY_PRINT(VECTOR_1-VECTOR_2)
WRITE(*,*) "VECTOR_1 / 2.0 = ", PRETTY_PRINT(VECTOR_1/SCALAR)
WRITE(*,*) "VECTOR_1 * 2.0 = ", PRETTY_PRINT(VECTOR_1*SCALAR)
END PROGRAM VECTOR_DEMO

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' FB 1.05.0 Win64
Type Vector
As Double x, y
Declare Operator Cast() As String
End Type
Operator Vector.Cast() As String
Return "[" + Str(x) + ", " + Str(y) + "]"
End Operator
Operator + (vec1 As Vector, vec2 As Vector) As Vector
Return Type<Vector>(vec1.x + vec2.x, vec1.y + vec2.y)
End Operator
Operator - (vec1 As Vector, vec2 As Vector) As Vector
Return Type<Vector>(vec1.x - vec2.x, vec1.y - vec2.y)
End Operator
Operator * (vec As Vector, scalar As Double) As Vector
Return Type<Vector>(vec.x * scalar, vec.y * scalar)
End Operator
Operator / (vec As Vector, scalar As Double) As Vector
' No need to check for division by zero as we're using Doubles
Return Type<Vector>(vec.x / scalar, vec.y / scalar)
End Operator
Dim v1 As Vector = (5, 7)
Dim v2 As Vector = (2, 3)
Print v1; " + "; v2; " = "; v1 + v2
Print v1; " - "; v2; " = "; v1 - v2
Print v1; " * "; 11; " = "; v1 * 11.0
Print v1; " / "; 2; " = "; v1 / 2.0
Print
Print "Press any key to quit"
Sleep

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package main
import "fmt"
type vector []float64
func (v vector) add(v2 vector) vector {
r := make([]float64, len(v))
for i, vi := range v {
r[i] = vi + v2[i]
}
return r
}
func (v vector) sub(v2 vector) vector {
r := make([]float64, len(v))
for i, vi := range v {
r[i] = vi - v2[i]
}
return r
}
func (v vector) scalarMul(s float64) vector {
r := make([]float64, len(v))
for i, vi := range v {
r[i] = vi * s
}
return r
}
func (v vector) scalarDiv(s float64) vector {
r := make([]float64, len(v))
for i, vi := range v {
r[i] = vi / s
}
return r
}
func main() {
v1 := vector{5, 7}
v2 := vector{2, 3}
fmt.Println(v1.add(v2))
fmt.Println(v1.sub(v2))
fmt.Println(v1.scalarMul(11))
fmt.Println(v1.scalarDiv(2))
}

32
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import groovy.transform.EqualsAndHashCode
@EqualsAndHashCode
class Vector {
private List<Number> elements
Vector(List<Number> e ) {
if (!e) throw new IllegalArgumentException("A Vector must have at least one element.")
if (!e.every { it instanceof Number }) throw new IllegalArgumentException("Every element must be a number.")
elements = [] + e
}
Vector(Number... e) { this(e as List) }
def order() { elements.size() }
def norm2() { elements.sum { it ** 2 } ** 0.5 }
def plus(Vector that) {
if (this.order() != that.order()) throw new IllegalArgumentException("Vectors must be conformable for addition.")
[this.elements,that.elements].transpose()*.sum() as Vector
}
def minus(Vector that) { this + (-that) }
def multiply(Number that) { this.elements.collect { it * that } as Vector }
def div(Number that) { this * (1/that) }
def negative() { this * -1 }
String toString() { "(${elements.join(',')})" }
}
class VectorCategory {
static Vector plus (Number a, Vector b) { b + a }
static Vector minus (Number a, Vector b) { -b + a }
static Vector multiply (Number a, Vector b) { b * a }
}

16
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Number.metaClass.mixin VectorCategory
def a = [1, 5] as Vector
def b = [6, -2] as Vector
def x = 8
println "a = $a b = $b x = $x"
assert a + b == [7, 3] as Vector
println "a + b == $a + $b == ${a+b}"
assert a - b == [-5, 7] as Vector
println "a - b == $a - $b == ${a-b}"
assert a * x == [8, 40] as Vector
println "a * x == $a * $x == ${a*x}"
assert x * a == [8, 40] as Vector
println "x * a == $x * $a == ${x*a}"
assert b / x == [3/4, -1/4] as Vector
println "b / x == $b / $x == ${b/x}"

15
Task/Vector/Haskell/vector.hs Normal file
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add (u,v) (x,y) = (u+x,v+y)
minus (u,v) (x,y) = (u-x,v-y)
multByScalar k (x,y) = (k*x,k*y)
divByScalar (x,y) k = (x/k,y/k)
main = do
let vecA = (3.0,8.0) -- cartersian coordinates
let (r,theta) = (3,pi/12) :: (Double,Double)
let vecB = (r*(cos theta),r*(sin theta)) -- from polar coordinates to cartesian coordinates
putStrLn $ "vecA = " ++ (show vecA)
putStrLn $ "vecB = " ++ (show vecB)
putStrLn $ "vecA + vecB = " ++ (show.add vecA $ vecB)
putStrLn $ "vecA - vecB = " ++ (show.minus vecA $ vecB)
putStrLn $ "2 * vecB = " ++ (show.multByScalar 2 $ vecB)
putStrLn $ "vecA / 3 = " ++ (show.divByScalar vecA $ 3)

8
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5 7+2 3
7 10
5 7-2 3
3 4
5 7*11
55 77
5 7%2
2.5 3.5

8
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2ad45
1.41421j1.41421
+. 2ad45
1.41421 1.41421
2ar0.785398
1.41421j1.41421
+. 2ar0.785398
1.41421 1.41421

41
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import java.util.Locale;
public class Test {
public static void main(String[] args) {
System.out.println(new Vec2(5, 7).add(new Vec2(2, 3)));
System.out.println(new Vec2(5, 7).sub(new Vec2(2, 3)));
System.out.println(new Vec2(5, 7).mult(11));
System.out.println(new Vec2(5, 7).div(2));
}
}
class Vec2 {
final double x, y;
Vec2(double x, double y) {
this.x = x;
this.y = y;
}
Vec2 add(Vec2 v) {
return new Vec2(x + v.x, y + v.y);
}
Vec2 sub(Vec2 v) {
return new Vec2(x - v.x, y - v.y);
}
Vec2 div(double val) {
return new Vec2(x / val, y / val);
}
Vec2 mult(double val) {
return new Vec2(x * val, y * val);
}
@Override
public String toString() {
return String.format(Locale.US, "[%s, %s]", x, y);
}
}

44
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def polar(r; angle):
[ r*(angle|cos), r*(angle|sin) ];
# If your jq allows multi-arity functions, you may wish to uncomment the following line:
# def polar(r): [r, 0];
def polar2vector: polar(.[0]; .[1]);
def vector(x; y):
if (x|type) == "number" and (y|type) == "number" then [x,y]
else error("TypeError")
end;
# Input: an array of same-dimensional vectors of any dimension to be added
def sum:
def sum2: .[0] as $a | .[1] as $b | reduce range(0;$a|length) as $i ($a; .[$i] += $b[$i]);
if length <= 1 then .
else reduce .[1:][] as $v (.[0] ; [., $v]|sum2)
end;
def multiply(scalar): [ .[] * scalar ];
def negate: multiply(-1);
def minus(v): [., (v|negate)] | sum;
def divide(scalar):
if scalar == 0 then error("division of a vector by 0 is not supported")
else [ .[] / scalar ]
end;
def r: (.[0] | .*.) + (.[1] | .*.) | sqrt;
def atan2:
def pi: 1 | atan * 4;
def sign: if . < 0 then -1 elif . > 0 then 1 else 0 end;
.[0] as $x | .[1] as $y
| if $x == 0 then $y | sign * pi / 2
else ($y / $x) | if $x > 0 then atan elif . > 0 then atan - pi else atan + pi end
end;
def angle: atan2;
def topolar: [r, angle];

23
Task/Vector/Jq/vector-2.jq Normal file
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def examples:
def pi: 1 | atan * 4;
[1,1] as $v
| [3,4] as $w
| polar(1; pi/2) as $z
| polar(-2; pi/4) as $z2
| "v is \($v)",
" w is \($w)",
"v + w is \([$v, $w] | sum)",
"v - w is \( $v |minus($w))",
" - v is \( $v|negate )",
"w * 5 is \($w | multiply(5))",
"w / 2 is \($w | divide(2))",
"v|topolar is \($v|topolar)",
"w|topolar is \($w|topolar)",
"z = polar(1; pi/2) is \($z)",
"z|topolar is \($z|topolar)",
"z2 = polar(-2; pi/4) is \($z2)",
"z2|topolar is \($z2|topolar)",
"z2|topolar|polar is \($z2|topolar|polar2vector)" ;
examples

15
Task/Vector/Jq/vector-3.jq Normal file
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$ jq -r -n -f vector.jq
v is [1,1]
w is [3,4]
v + w is [4,5]
v - w is [-2,-3]
- v is [-1,-1]
w * 5 is [15,20]
w / 2 is [1.5,2]
v|topolar is [1.4142135623730951,0.7853981633974483]
w|topolar is [5,0.9272952180016122]
z = polar(1; pi/2) is [6.123233995736766e-17,1]
z|topolar is [1,1.5707963267948966]
z2 = polar(-2; pi/4) is [-1.4142135623730951,-1.414213562373095]
z2|topolar is [2,-2.356194490192345]
z2|topolar|polar is [-1.414213562373095,-1.4142135623730951]

48
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module SpatialVectors
export SpatialVector
struct SpatialVector{N, T}
coord::NTuple{N, T}
end
SpatialVector(s::NTuple{N,T}, e::NTuple{N,T}) where {N,T} =
SpatialVector{N, T}(e .- s)
function SpatialVector(∠::T, val::T) where T
θ = atan(∠)
x = val * cos(θ)
y = val * sin(θ)
return SpatialVector((x, y))
end
angularcoef(v::SpatialVector{2, T}) where T = v.coord[2] / v.coord[1]
Base.norm(v::SpatialVector) = sqrt(sum(x -> x^2, v.coord))
function Base.show(io::IO, v::SpatialVector{2, T}) where T
∠ = angularcoef(v)
val = norm(v)
println(io, """2-dim spatial vector
- Angular coef ∠: $(∠) (θ = $(rad2deg(atan(∠)))°)
- Magnitude: $(val)
- X coord: $(v.coord[1])
- Y coord: $(v.coord[2])""")
end
Base.:-(v::SpatialVector) = SpatialVector(.- v.coord)
for op in (:+, :-)
@eval begin
Base.$op(a::SpatialVector{N, T}, b::SpatialVector{N, U}) where {N, T, U} =
SpatialVector{N, promote_type(T, U)}(broadcast($op, a.coord, b.coord))
end
end
for op in (:*, :/)
@eval begin
Base.$op(n::T, v::SpatialVector{N, U}) where {N, T, U} =
SpatialVector{N, promote_type(T, U)}(broadcast($op, n, v.coord))
Base.$op(v::SpatialVector, n::Number) = $op(n, v)
end
end
end # module Vectors

28
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// version 1.1.2
class Vector2D(val x: Double, val y: Double) {
operator fun plus(v: Vector2D) = Vector2D(x + v.x, y + v.y)
operator fun minus(v: Vector2D) = Vector2D(x - v.x, y - v.y)
operator fun times(s: Double) = Vector2D(s * x, s * y)
operator fun div(s: Double) = Vector2D(x / s, y / s)
override fun toString() = "($x, $y)"
}
operator fun Double.times(v: Vector2D) = v * this
fun main(args: Array<String>) {
val v1 = Vector2D(5.0, 7.0)
val v2 = Vector2D(2.0, 3.0)
println("v1 = $v1")
println("v2 = $v2")
println()
println("v1 + v2 = ${v1 + v2}")
println("v1 - v2 = ${v1 - v2}")
println("v1 * 11 = ${v1 * 11.0}")
println("11 * v2 = ${11.0 * v2}")
println("v1 / 2 = ${v1 / 2.0}")
}

40
Task/Vector/Lang/vector.lang Normal file
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&Vector = {
$x
$y
}
fp.initVector = ($x, $y) -> {
return &Vector(fn.double($x), fn.double($y))
}
fp.addVector = ($a, $b) -> {
return parser.op(&Vector($a::$x + $b::$x, $a::$y + $b::$y))
}
fp.subVector = ($a, $b) -> {
return parser.op(&Vector($a::$x - $b::$x, $a::$y - $b::$y))
}
fp.mulVector = ($vec, $scalar) -> {
return parser.op(&Vector($vec::$x * $scalar, $vec::$y * $scalar))
}
fp.divVector = ($vec, $scalar) -> {
return parser.op(&Vector($vec::$x / $scalar, $vec::$y / $scalar))
}
fp.printVector = ($vec) -> {
fn.println([parser.op($vec::$x), parser.op($vec::$y)])
}
$vec1 = fp.initVector(5, 7)
$vec2 = fp.initVector(2, 3)
fp.printVector($vec1)
fp.printVector($vec2)
fn.println()
fp.printVector(fp.addVector($vec1, $vec2))
fp.printVector(fp.subVector($vec1, $vec2))
fp.printVector(fp.mulVector($vec1, 11))
fp.printVector(fp.divVector($vec1, 2))

33
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vector = {mt = {}}
function vector.new (x, y)
local new = {x = x or 0, y = y or 0}
setmetatable(new, vector.mt)
return new
end
function vector.mt.__add (v1, v2)
return vector.new(v1.x + v2.x, v1.y + v2.y)
end
function vector.mt.__sub (v1, v2)
return vector.new(v1.x - v2.x, v1.y - v2.y)
end
function vector.mt.__mul (v, s)
return vector.new(v.x * s, v.y * s)
end
function vector.mt.__div (v, s)
return vector.new(v.x / s, v.y / s)
end
function vector.print (vec)
print("(" .. vec.x .. ", " .. vec.y .. ")")
end
local a, b = vector.new(5, 7), vector.new(2, 3)
vector.print(a + b)
vector.print(a - b)
vector.print(a * 11)
vector.print(a / 2)

67
Task/Vector/M2000-Interpreter/vector.m2000 Normal file
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class vector {
private:
double x, y
public:
class literal {
double v
class:
module Literal(.v) {
}
}
operator "+" (b as vector){
.x+=b.x
.y+=b.y
}
operator "-" (b as vector){
.x-=b.x
.y-=b.y
}
operator "*" (b as literal){
.x*=b.v
.y*=b.v
}
operator "/" (b as literal){
.x/=b.v
.y/=b.v
}
property printVector {
value {
link parent x, y to x, y
value=format$(.fm$, str$(round(x,.r), .Lcid),if$(y>=0->"+", "-"),str$(abs(round(y,.r)),.lcid))
}
}="" // make type string
// added members to printVector (is a group type)
group printVector {
integer Lcid=1033
fm$="{0} î {1}{2} û"
r=6
}
class:
module vector(r as double, theta as double, Lcid=1033) {
def deg(rad)=rad*180@/pi
.printVector.Lcid<=Lcid
.x<=r*cos(deg(theta))
.y<=r*sin(deg(theta))
}
}
document s$
a=vector(3,pi/6)
s$="Vector a : "+a.printVector+{
}
b=vector(5,2*pi/3)
s$="Vector b : "+b.printVector+{
}
sum_a_b=a+b
s$="Sum of vectors a and b : "+sum_a_b.printVector+{
}
diff_a_b=a-b
s$="Difference of vectors a and b : "+diff_a_b.printVector+{
}
mul_a_3=a*a.literal(3)
s$="Multiplying vector a by 3 : "+mul_a_3.printVector+{
}
div_b_2.5=b/b.literal(2.5)
s$="Dividing vector b by 2.5 : "+div_b_2.5.printVector+{
}
report s$
clipboard s$

28
Task/Vector/Maple/vector-1.maple Normal file
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module MyVector()
option object;
local value := Vector();
export ModuleApply::static := proc( )
Object( MyVector, _passed );
end proc;
export ModuleCopy::static := proc( mv::MyVector, proto::MyVector, v::Vector, $ )
mv:-value := v;
end proc;
export ModulePrint::static := proc(mv::MyVector, $ )
mv:-value;
end proc;
# operations:
export `+`::static := proc( v1::MyVector, v2::MyVector )
MyVector( v1:-value + v2:-value );
end proc;
export `*`::static := proc( v::MyVector, scalar_val::numeric)
MyVector( v:-value * scalar_val);
end proc;
end module:

7
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a := MyVector(<3|4>):
b := MyVector(<5|4>):
a + b;
a - b;
a * 5;
a / 5;

12
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ClearAll[vector,PrintVector]
vector[{r_,\[Theta]_}]:=vector@@AngleVector[{r,\[Theta]}]
vector[x_,y_]+vector[w_,z_]^:=vector[x+w,y+z]
a_ vector[x_,y_]^:=vector[a x,a y]
vector[x_,y_]-vector[w_,z_]^:=vector[x-w,y-z]
PrintVector[vector[x_,y_]]:=Print["vector has first component: ",x," And second component: ",y]
vector[1,2]+vector[3,4]
vector[1,2]-vector[3,4]
12vector[1,2]
vector[1,2]/3
PrintVector@vector[{Sqrt[2],45Degree}]

23
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vplus = function(v1, v2)
return [v1[0]+v2[0],v1[1]+v2[1]]
end function
vminus = function (v1, v2)
return [v1[0]-v2[0],v1[1]-v2[1]]
end function
vmult = function(v1, scalar)
return [v1[0]*scalar, v1[1]*scalar]
end function
vdiv = function(v1, scalar)
return [v1[0]/scalar, v1[1]/scalar]
end function
vector1 = [2,3]
vector2 = [4,5]
print vplus(vector1,vector2)
print vminus(vector2, vector1)
print vmult(vector1, 3)
print vdiv(vector2, 2)

60
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MODULE Vector;
FROM FormatString IMPORT FormatString;
FROM RealStr IMPORT RealToStr;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
TYPE Vector =
RECORD
x,y : REAL;
END;
PROCEDURE Add(a,b : Vector) : Vector;
BEGIN
RETURN Vector{a.x+b.x, a.y+b.y}
END Add;
PROCEDURE Sub(a,b : Vector) : Vector;
BEGIN
RETURN Vector{a.x-b.x, a.y-b.y}
END Sub;
PROCEDURE Mul(v : Vector; r : REAL) : Vector;
BEGIN
RETURN Vector{a.x*r, a.y*r}
END Mul;
PROCEDURE Div(v : Vector; r : REAL) : Vector;
BEGIN
RETURN Vector{a.x/r, a.y/r}
END Div;
PROCEDURE Print(v : Vector);
VAR buf : ARRAY[0..64] OF CHAR;
BEGIN
WriteString("<");
RealToStr(v.x, buf);
WriteString(buf);
WriteString(", ");
RealToStr(v.y, buf);
WriteString(buf);
WriteString(">")
END Print;
VAR a,b : Vector;
BEGIN
a := Vector{5.0, 7.0};
b := Vector{2.0, 3.0};
Print(Add(a, b));
WriteLn;
Print(Sub(a, b));
WriteLn;
Print(Mul(a, 11.0));
WriteLn;
Print(Div(a, 2.0));
WriteLn;
ReadChar
END Vector.

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class Vector
declare x
declare y
def Vector(x, y)
this.x = float(x)
this.y = float(y)
end
def operator+(other)
return new(Vector, this.x + other.x, this.y + other.y)
end
def operator-(other)
return new(Vector, this.x - other.x, this.y - other.y)
end
def operator/(val)
return new(Vector, this.x / val, this.y / val)
end
def operator*(val)
return new(Vector, this.x * val, this.y * val)
end
def toString()
return format("[%s, %s]", this.x, this.y)
end
end
println new(Vector, 5, 7) + new(Vector, 2, 3)
println new(Vector, 5, 7) - new(Vector, 2, 3)
println new(Vector, 5, 7) * 11
println new(Vector, 5, 7) / 2

38
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import strformat
type Vec2[T: SomeNumber] = tuple[x, y: T]
proc initVec2[T](x, y: T): Vec2[T] = (x, y)
func`+`[T](a, b: Vec2[T]): Vec2[T] = (a.x + b.x, a.y + b.y)
func `-`[T](a, b: Vec2[T]): Vec2[T] = (a.x - b.x, a.y - b.y)
func `*`[T](a: Vec2[T]; m: T): Vec2[T] = (a.x * m, a.y * m)
func `/`[T](a: Vec2[T]; d: T): Vec2[T] =
if d == 0:
raise newException(DivByZeroDefect, "division of vector by 0")
when T is SomeInteger:
(a.x div d, a.y div d)
else:
(a.x / d, a.y / d)
func `$`[T](a: Vec2[T]): string =
&"({a.x}, {a.y})"
# Three ways to initialize a vector.
let v1 = initVec2(2, 3)
let v2: Vec2[int] = (-1, 2)
let v3 = (x: 4, y: -2)
echo &"{v1} + {v2} = {v1 + v2}"
echo &"{v3} - {v2} = {v3 - v2}"
# Float vectors.
let v4 = initVec2(2.0, 3.0)
let v5 = (x: 3.0, y: 2.0)
echo &"{v4} * 2 = {v4 * 2}"
echo &"{v3} / 2 = {v3 / 2}" # Int division.
echo &"{v5} / 2 = {v5 / 2}" # Float division.

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module Vector =
struct
type t = { x : float; y : float }
let make x y = { x; y }
let add a b = { x = a.x +. b.x; y = a.y +. b.y }
let sub a b = { x = a.x -. b.x; y = a.y -. b.y }
let mul a n = { x = a.x *. n; y = a.y *. n }
let div a n = { x = a.x /. n; y = a.y /. n }
let to_string {x; y} = Printf.sprintf "(%F, %F)" x y
let ( + ) = add
let ( - ) = sub
let ( * ) = mul
let ( / ) = div
end
open Printf
let test () =
let a, b = Vector.make 5. 7., Vector.make 2. 3. in
printf "a: %s\n" (Vector.to_string a);
printf "b: %s\n" (Vector.to_string b);
printf "a+b: %s\n" Vector.(a + b |> to_string);
printf "a-b: %s\n" Vector.(a - b |> to_string);
printf "a*11: %s\n" Vector.(a * 11. |> to_string);
printf "a/2: %s\n" Vector.(a / 2. |> to_string)

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MODULE Vector;
IMPORT Out;
TYPE
Vector = POINTER TO VectorDesc;
VectorDesc = RECORD
x,y:REAL;
END;
VAR
a,b:Vector;
PROCEDURE Add*(a,b:Vector):Vector;
VAR res:Vector;
BEGIN
NEW(res);
res.x := a.x+b.x;
res.y := a.y+b.y;
RETURN res;
END Add;
PROCEDURE Sub*(a,b:Vector):Vector;
VAR res:Vector;
BEGIN
NEW(res);
res.x := a.x-b.x;
res.y := a.y-b.y;
RETURN res;
END Sub;
PROCEDURE Mul*(v:Vector;r:REAL):Vector;
VAR res:Vector;
BEGIN
NEW(res);
res.x := v.x*r;
res.y := v.y*r;
RETURN res;
END Mul;
PROCEDURE Div*(v:Vector;r:REAL):Vector;
VAR res:Vector;
BEGIN
NEW(res);
res.x := v.x/r;
res.y := v.y/r;
RETURN res;
END Div;
PROCEDURE Print*(op:ARRAY OF CHAR;v:Vector);
BEGIN
Out.String(op);
Out.String("(");
Out.Real(v.x,0);
Out.String(", ");
Out.Real(v.y,0);
Out.String(")");
END Print;
BEGIN
NEW(a); NEW(b);
a.x := 5.0; a.y := 7.0;
b.x := 2.0; b.y := 3.0;
Print("Add: ",Add(a,b));
Out.Ln;
Print("Sub: ",Sub(a,b));
Out.Ln;
Print("Mul: ",Mul(a,11.0));
Out.Ln;
Print("Div: ",Div(a,2.0));
Out.Ln
END Vector.

46
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class Test {
function : Main(args : String[]) ~ Nil {
Vec2->New(5, 7)->Add(Vec2->New(2, 3))->ToString()->PrintLine();
Vec2->New(5, 7)->Sub(Vec2->New(2, 3))->ToString()->PrintLine();
Vec2->New(5, 7)->Mult(11)->ToString()->PrintLine();
Vec2->New(5, 7)->Div(2)->ToString()->PrintLine();
}
}
class Vec2 {
@x : Float;
@y : Float;
New(x : Float, y : Float) {
@x := x;
@y := y;
}
method : GetX() ~ Float {
return @x;
}
method : GetY() ~ Float {
return @y;
}
method : public : Add(v : Vec2) ~ Vec2 {
return Vec2->New(@x + v->GetX(), @y + v->GetY());
}
method : public : Sub(v : Vec2) ~ Vec2 {
return Vec2->New(@x - v->GetX(), @y - v->GetY());
}
method : public : Div(val : Float) ~ Vec2 {
return Vec2->New(@x / val, @y / val);
}
method : public : Mult(val : Float) ~ Vec2 {
return Vec2->New(@x * val, @y * val);
}
method : public : ToString() ~ String {
return "[{$@x}, {$@y}]";
}
}

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(define :+ +)
(define (+ a b)
(if (vector? a)
(if (vector? b)
(vector-map :+ a b)
(error "error:" "not applicable (+ vector non-vector)"))
(if (vector? b)
(error "error:" "not applicable (+ non-vector vector)")
(:+ a b))))
(define :- -)
(define (- a b)
(if (vector? a)
(if (vector? b)
(vector-map :- a b)
(error "error:" "not applicable (+ vector non-vector)"))
(if (vector? b)
(error "error:" "not applicable (+ non-vector vector)")
(:- a b))))
(define :* *)
(define (* a b)
(if (vector? a)
(if (not (vector? b))
(vector-map (lambda (x) (:* x b)) a)
(error "error:" "not applicable (* vector vector)"))
(if (vector? b)
(error "error:" "not applicable (* scalar vector)")
(:* a b))))
(define :/ /)
(define (/ a b)
(if (vector? a)
(if (not (vector? b))
(vector-map (lambda (x) (:/ x b)) a)
(error "error:" "not applicable (/ vector vector)"))
(if (vector? b)
(error "error:" "not applicable (/ scalar vector)")
(:/ a b))))
(define x [1 2 3 4 5])
(define y [7 8 5 4 2])
(print x " + " y " = " (+ x y))
(print x " - " y " = " (- x y))
(print x " * " 7 " = " (* x 7))
(print x " / " 7 " = " (/ x 7))

58
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v=.vector~new(12,-3); Say "v=.vector~new(12,-3) =>" v~print
v~ab(1,1,6,4); Say "v~ab(1,1,6,4) =>" v~print
v~al(45,2); Say "v~al(45,2) =>" v~print
w=v~'+'(v); Say "w=v~'+'(v) =>" w~print
x=v~'-'(w); Say "x=v~'-'(w) =>" x~print
y=x~'*'(3); Say "y=x~'*'(3) =>" y~print
z=x~'/'(0.1); Say "z=x~'/'(0.1) =>" z~print
::class vector
::attribute x
::attribute y
::method init
Use Arg a,b
self~x=a
self~y=b
::method ab /* set vector from point (a,b) to point (c,d) */
Use Arg a,b,c,d
self~x=c-a
self~y=d-b
::method al /* set vector given angle a and length l */
Use Arg a,l
self~x=l*rxCalccos(a)
self~y=l*rxCalcsin(a)
::method '+' /* add: Return sum of self and argument */
Use Arg v
x=self~x+v~x
y=self~y+v~y
res=.vector~new(x,y)
Return res
::method '-' /* subtract: Return difference of self and argument */
Use Arg v
x=self~x-v~x
y=self~y-v~y
res=.vector~new(x,y)
Return res
::method '*' /* multiply: Return self multiplied by t */
Use Arg t
x=self~x*t
y=self~y*t
res=.vector~new(x,y)
Return res
::method '/' /* divide: Return self divided by t */
Use Arg t
x=self~x/t
y=self~y/t
res=.vector~new(x,y)
Return res
::method print /* prettyprint a vector */
return '['self~x','self~y']'
::requires rxMath Library

21
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*process source attributes xref or(!);
vectors: Proc Options(main);
Dcl (v,w,x,y,z) Dec Float(9) Complex;
real(v)=12; imag(v)=-3; Put Edit(pp(v))(Skip,a);
real(v)=6-1; imag(v)=4-1; Put Edit(pp(v))(Skip,a);
real(v)=2*cosd(45);
imag(v)=2*sind(45); Put Edit(pp(v))(Skip,a);
w=v+v; Put Edit(pp(w))(Skip,a);
x=v-w; Put Edit(pp(x))(Skip,a);
y=x*3; Put Edit(pp(y))(Skip,a);
z=x/.1; Put Edit(pp(z))(Skip,a);
pp: Proc(c) Returns(Char(50) Var);
Dcl c Dec Float(9) Complex;
Dcl res Char(50) Var;
Put String(res) Edit('[',real(c),',',imag(c),']')
(3(a,f(9,5)));
Return(res);
End;
End;

29
Task/Vector/Perl/vector.pl Normal file
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use v5.36;
package Vector;
use Moose;
use overload '+' => \&add,
'-' => \&sub,
'*' => \&mul,
'/' => \&div,
'""' => \&stringify;
has 'x' => (is =>'rw', isa => 'Num', required => 1);
has 'y' => (is =>'rw', isa => 'Num', required => 1);
sub add ($a, $b, $) { Vector->new( x => $a->x + $b->x, y => $a->y + $b->y) }
sub sub ($a, $b, $) { Vector->new( x => $a->x - $b->x, y => $a->y - $b->y) }
sub mul ($a, $b, $) { Vector->new( x => $a->x * $b, y => $a->y * $b) }
sub div ($a, $b, $) { Vector->new( x => $a->x / $b, y => $a->y / $b) }
sub stringify ($self, $, $) { '(' . $self->x . ',' . $self->y . ')' }
package main;
my $a = Vector->new(x => 5, y => 7);
my $b = Vector->new(x => 2, y => 3);
say "a: $a";
say "b: $b";
say "a+b: ",$a+$b;
say "a-b: ",$a-$b;
say "a*11: ",$a*11;
say "a/2: ",$a/2;

7
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-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">}</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<!--

30
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include ..\Utilitys.pmt
def add + enddef
def sub - enddef
def mul * enddef
def div / enddef
def opVect /# a b op -- a b c #/
var op
list? not if swap len rot swap repeat endif
len var lon
( lon 1 -1 ) for var i
i get rot i get rot op exec >ps swap
endfor
lon for drop
ps>
endfor
lon tolist
enddef
( 5 7 ) ( 2 3 )
getid add opVect ?
getid sub opVect ?
drop 2
getid mul opVect ?
getid div opVect ?

13
Task/Vector/PicoLisp/vector.l Normal file
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(de add (A B)
(mapcar + A B) )
(de sub (A B)
(mapcar - A B) )
(de mul (A B)
(mapcar '((X) (* X B)) A) )
(de div (A B)
(mapcar '((X) (*/ X B)) A) )
(let (X (5 7) Y (2 3))
(println (add X Y))
(println (sub X Y))
(println (mul X 11))
(println (div X 2)) )

8
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$V1 = New-Object System.Windows.Vector ( 2.5, 3.4 )
$V2 = New-Object System.Windows.Vector ( -6, 2 )
$V1
$V2
$V1 + $V2
$V1 - $V2
$V1 * 3
$V1 / 8

17
Task/Vector/Processing-Python-mode/vector.processing-py Normal file
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v1 = PVector(5, 7)
v2 = PVector(2, 3)
println('{} {} {} {}\n'.format( v1.x, v1.y, v1.mag(), v1.heading()))
# math overloaded operators (static methods in the comments)
println(v1 + v2) # PVector.add(v1, v2)
println(v1 - v2) # PVector.sub(v1, v2)
println(v1 * 11) # PVector.mult(v1, 11)
println(v1 / 2) # PVector.div(v1, 2)
println('')
# object methods (related augmented assigment in the comments)
println(v1.sub(v1)) # v1 -= v1; println(v1)
println(v1.add(v2)) # v1 += v2; println(v2)
println(v1.mult(10)) # v1 *= 10; println(v1)
println(v1.div(10)) # v1 /= 10; println(v1)

16
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PVector v1 = new PVector(5, 7);
PVector v2 = new PVector(2, 3);
println(v1.x, v1.y, v1.mag(), v1.heading(),'\n');
// static methods
println(PVector.add(v1, v2));
println(PVector.sub(v1, v2));
println(PVector.mult(v1, 11));
println(PVector.div(v1, 2), '\n');
// object methods
println(v1.sub(v1));
println(v1.add(v2));
println(v1.mult(10));
println(v1.div(10));

69
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class Vector:
def __init__(self,m,value):
self.m = m
self.value = value
self.angle = math.degrees(math.atan(self.m))
self.x = self.value * math.sin(math.radians(self.angle))
self.y = self.value * math.cos(math.radians(self.angle))
def __add__(self,vector):
"""
>>> Vector(1,10) + Vector(1,2)
Vector:
- Angular coefficient: 1.0
- Angle: 45.0 degrees
- Value: 12.0
- X component: 8.49
- Y component: 8.49
"""
final_x = self.x + vector.x
final_y = self.y + vector.y
final_value = pytagoras(final_x,final_y)
final_m = final_y / final_x
return Vector(final_m,final_value)
def __neg__(self):
return Vector(self.m,-self.value)
def __sub__(self,vector):
return self + (- vector)
def __mul__(self,scalar):
"""
>>> Vector(4,5) * 2
Vector:
- Angular coefficient: 4
- Angle: 75.96 degrees
- Value: 10
- X component: 9.7
- Y component: 2.43
"""
return Vector(self.m,self.value*scalar)
def __div__(self,scalar):
return self * (1 / scalar)
def __repr__(self):
"""
Returns a nicely formatted list of the properties of the Vector.
>>> Vector(1,10)
Vector:
- Angular coefficient: 1
- Angle: 45.0 degrees
- Value: 10
- X component: 7.07
- Y component: 7.07
"""
return """Vector:
- Angular coefficient: {}
- Angle: {} degrees
- Value: {}
- X component: {}
- Y component: {}""".format(self.m.__round__(2),
self.angle.__round__(2),
self.value.__round__(2),
self.x.__round__(2),
self.y.__round__(2))

76
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from __future__ import annotations
import math
from functools import lru_cache
from typing import NamedTuple
CACHE_SIZE = None
def hypotenuse(leg: float,
other_leg: float) -> float:
"""Returns hypotenuse for given legs"""
return math.sqrt(leg ** 2 + other_leg ** 2)
class Vector(NamedTuple):
slope: float
length: float
@property
@lru_cache(CACHE_SIZE)
def angle(self) -> float:
return math.atan(self.slope)
@property
@lru_cache(CACHE_SIZE)
def x(self) -> float:
return self.length * math.sin(self.angle)
@property
@lru_cache(CACHE_SIZE)
def y(self) -> float:
return self.length * math.cos(self.angle)
def __add__(self, other: Vector) -> Vector:
"""Returns self + other"""
new_x = self.x + other.x
new_y = self.y + other.y
new_length = hypotenuse(new_x, new_y)
new_slope = new_y / new_x
return Vector(new_slope, new_length)
def __neg__(self) -> Vector:
"""Returns -self"""
return Vector(self.slope, -self.length)
def __sub__(self, other: Vector) -> Vector:
"""Returns self - other"""
return self + (-other)
def __mul__(self, scalar: float) -> Vector:
"""Returns self * scalar"""
return Vector(self.slope, self.length * scalar)
def __truediv__(self, scalar: float) -> Vector:
"""Returns self / scalar"""
return self * (1 / scalar)
if __name__ == '__main__':
v1 = Vector(1, 1)
print("Pretty print:")
print(v1, end='\n' * 2)
print("Addition:")
v2 = v1 + v1
print(v1 + v1, end='\n' * 2)
print("Subtraction:")
print(v2 - v1, end='\n' * 2)
print("Multiplication:")
print(v1 * 2, end='\n' * 2)
print("Division:")
print(v2 / 2)

41
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/*REXX program shows how to support mathematical functions for vectors using functions. */
s1 = 11 /*define the s1 scalar: eleven */
s2 = 2 /*define the s2 scalar: two */
x = '(5, 7)' /*define the X vector: five and seven*/
y = '(2, 3)' /*define the Y vector: two and three*/
z = '(2, 45)' /*define vector of length 2 at 45º */
call show 'define a vector (length,ºangle):', z , Vdef(z)
call show 'addition (vector+vector):', x " + " y , Vadd(x, y)
call show 'subtraction (vector-vector):', x " - " y , vsub(x, y)
call show 'multiplication (Vector*scalar):', x " * " s1, Vmul(x, s1)
call show 'division (vector/scalar):', x " ÷ " s2, Vdiv(x, s2)
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
$fuzz: return min( arg(1), max(1, digits() - arg(2) ) )
cosD: return cos( d2r( arg(1) ) )
d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle. */
d2r: return r2r( d2d(arg(1)) * pi() / 180) /*convert degrees ──► radians. */
pi: pi=3.14159265358979323846264338327950288419716939937510582; return pi
r2d: return d2d( (arg(1)*180 / pi())) /*convert radians ──► degrees. */
r2r: return arg(1) // (pi() * 2) /*normalize radians ──► a unit circle. */
show: say right( arg(1), 33) right( arg(2), 20) ' ──► ' arg(3); return
sinD: return sin( d2r( d2d( arg(1) ) ) )
V: return word( translate( arg(1), , '{[(JI)]}') 0, 1) /*get the number or zero*/
V$: parse arg r,c; _='['r; if c\=0 then _=_"," c; return _']'
V#: a=V(a); b=V(b); c=V(c); d=V(d); ac=a*c; ad=a*d; bc=b*c; bd=b*d; s=c*c+d*d; return
Vadd: procedure; arg a ',' b,c "," d; call V#; return V$(a+c, b+d)
Vsub: procedure; arg a ',' b,c "," d; call V#; return V$(a-c, b-d)
Vmul: procedure; arg a ',' b,c "," d; call V#; return V$(ac-bd, bc+ad)
Vdiv: procedure; arg a ',' b,c "," d; call V#; return V$((ac+bd)/s, (bc-ad)/s)
Vdef: procedure; arg a ',' b,c "," d; call V#; return V$(a*sinD(b), a*cosD(b))
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x=r2r(x); a=abs(x); numeric fuzz $fuzz(9, 9)
if a=pi then return -1;
if a=pi*.5 | a=pi*2 then return 0; return .sinCos(1,-1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
if x=pi*.5 then return 1; if x=pi*1.5 then return -1
if abs(x)=pi | x=0 then return 0; return .sinCos(x,+1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: parse arg z 1 _,i; q=x*x
do k=2 by 2 until p=z; p=z; _= -_*q / (k*(k+i)); z=z+_; end; return z

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Task/Vector/Racket/vector-1.rkt Normal file
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#lang racket
(require racket/flonum)
(define (rad->deg x) (fl* 180. (fl/ (exact->inexact x) pi)))
;Custom printer
;no shared internal structures
(define (vec-print v port mode)
(write-string "Vec:\n" port)
(write-string (format " -Slope: ~a\n" (vec-slope v)) port)
(write-string (format " -Angle(deg): ~a\n" (rad->deg (vec-angle v))) port)
(write-string (format " -Norm: ~a\n" (vec-norm v)) port)
(write-string (format " -X: ~a\n" (vec-x v)) port)
(write-string (format " -Y: ~a\n" (vec-y v)) port))
(struct vec (x y)
#:methods gen:custom-write
[(define write-proc vec-print)])
;Alternative constructor
(define (vec/slope-norm s n)
(vec (* n (/ 1 (sqrt (+ 1 (sqr s)))))
(* n (/ s (sqrt (+ 1 (sqr s)))))))
;Properties
(define (vec-norm v)
(sqrt (+ (sqr (vec-x v)) (sqr (vec-y v)))))
(define (vec-slope v)
(fl/ (exact->inexact (vec-y v)) (exact->inexact (vec-x v))))
(define (vec-angle v)
(atan (vec-y v) (vec-x v)))
;Operations
(define (vec+ v w)
(vec (+ (vec-x v) (vec-x w))
(+ (vec-y v) (vec-y w))))
(define (vec- v w)
(vec (- (vec-x v) (vec-x w))
(- (vec-y v) (vec-y w))))
(define (vec*e v l)
(vec (* (vec-x v) l)
(* (vec-y v) l)))
(define (vec/e v l)
(vec (/ (vec-x v) l)
(/ (vec-y v) l)))

13
Task/Vector/Racket/vector-2.rkt Normal file
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(vec/slope-norm 1 10)
(vec/slope-norm 0 10)
(vec 3 4)
(vec 0 10)
(vec 10 0)
(vec+ (vec/slope-norm 1 10) (vec/slope-norm 1 2))
(vec*e (vec/slope-norm 4 5) 2)

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class Vector {
has Real $.x;
has Real $.y;
multi submethod BUILD (:$!x!, :$!y!) {
*
}
multi submethod BUILD (:$length!, :$angle!) {
$!x = $length * cos $angle;
$!y = $length * sin $angle;
}
multi submethod BUILD (:from([$x1, $y1])!, :to([$x2, $y2])!) {
$!x = $x2 - $x1;
$!y = $y2 - $y1;
}
method length { sqrt $.x ** 2 + $.y ** 2 }
method angle { atan2 $.y, $.x }
method add ($v) { Vector.new(x => $.x + $v.x, y => $.y + $v.y) }
method subtract ($v) { Vector.new(x => $.x - $v.x, y => $.y - $v.y) }
method multiply ($n) { Vector.new(x => $.x * $n, y => $.y * $n ) }
method divide ($n) { Vector.new(x => $.x / $n, y => $.y / $n ) }
method gist { "vec[$.x, $.y]" }
}
multi infix:<+> (Vector $v, Vector $w) is export { $v.add: $w }
multi infix:<-> (Vector $v, Vector $w) is export { $v.subtract: $w }
multi prefix:<-> (Vector $v) is export { $v.multiply: -1 }
multi infix:<*> (Vector $v, $n) is export { $v.multiply: $n }
multi infix:</> (Vector $v, $n) is export { $v.divide: $n }
#####[ Usage example: ]#####
say my $u = Vector.new(x => 3, y => 4); #: vec[3, 4]
say my $v = Vector.new(from => [1, 0], to => [2, 3]); #: vec[1, 3]
say my $w = Vector.new(length => 1, angle => pi/4); #: vec[0.707106781186548, 0.707106781186547]
say $u.length; #: 5
say $u.angle * 180/pi; #: 53.130102354156
say $u + $v; #: vec[4, 7]
say $u - $v; #: vec[2, 1]
say -$u; #: vec[-3, -4]
say $u * 10; #: vec[30, 40]
say $u / 2; #: vec[1.5, 2]

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Red [
Source: https://github.com/vazub/rosetta-red
Tabs: 4
]
comment {
Vector type is one of base datatypes in Red, with all arithmetic already implemented.
Caveats to keep in mind:
- Arithmetic on a single vector will modify the vector in place, so we use copy to avoid that
- Division result on integer vectors will get truncated, use floats for decimal precision
}
v1: make vector! [5.0 7.0]
v2: make vector! [2.0 3.0]
prin pad "v1: " 10 print v1
prin pad "v2: " 10 print v2
prin pad "v1 + v2: " 10 print v1 + v2
prin pad "v1 - v2: " 10 print v1 - v2
prin pad "v1 * 11" 10 print (copy v1) * 11
prin pad "v1 / 2" 10 print (copy v1) / 2

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# Project : Vector
decimals(1)
vect1 = [5, 7]
vect2 = [2, 3]
vect3 = list(len(vect1))
for n = 1 to len(vect1)
vect3[n] = vect1[n] + vect2[n]
next
showarray(vect3)
for n = 1 to len(vect1)
vect3[n] = vect1[n] - vect2[n]
next
showarray(vect3)
for n = 1 to len(vect1)
vect3[n] = vect1[n] * vect2[n]
next
showarray(vect3)
for n = 1 to len(vect1)
vect3[n] = vect1[n] / 2
next
showarray(vect3)
func showarray(vect3)
see "["
svect = ""
for n = 1 to len(vect3)
svect = svect + vect3[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl

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class Vector
def self.polar(r, angle=0)
new(r*Math.cos(angle), r*Math.sin(angle))
end
attr_reader :x, :y
def initialize(x, y)
raise TypeError unless x.is_a?(Numeric) and y.is_a?(Numeric)
@x, @y = x, y
end
def +(other)
raise TypeError if self.class != other.class
self.class.new(@x + other.x, @y + other.y)
end
def -@; self.class.new(-@x, -@y) end
def -(other) self + (-other) end
def *(scalar)
raise TypeError unless scalar.is_a?(Numeric)
self.class.new(@x * scalar, @y * scalar)
end
def /(scalar)
raise TypeError unless scalar.is_a?(Numeric) and scalar.nonzero?
self.class.new(@x / scalar, @y / scalar)
end
def r; @r ||= Math.hypot(@x, @y) end
def angle; @angle ||= Math.atan2(@y, @x) end
def polar; [r, angle] end
def rect; [@x, @y] end
def to_s; "#{self.class}#{[@x, @y]}" end
alias inspect to_s
end
p v = Vector.new(1,1) #=> Vector[1, 1]
p w = Vector.new(3,4) #=> Vector[3, 4]
p v + w #=> Vector[4, 5]
p v - w #=> Vector[-2, -3]
p -v #=> Vector[-1, -1]
p w * 5 #=> Vector[15, 20]
p w / 2.0 #=> Vector[1.5, 2.0]
p w.x #=> 3
p w.y #=> 4
p v.polar #=> [1.4142135623730951, 0.7853981633974483]
p w.polar #=> [5.0, 0.9272952180016122]
p z = Vector.polar(1, Math::PI/2) #=> Vector[6.123031769111886e-17, 1.0]
p z.rect #=> [6.123031769111886e-17, 1.0]
p z.polar #=> [1.0, 1.5707963267948966]
p z = Vector.polar(-2, Math::PI/4) #=> Vector[-1.4142135623730951, -1.414213562373095]
p z.polar #=> [2.0, -2.356194490192345]

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use std::fmt;
use std::ops::{Add, Div, Mul, Sub};
#[derive(Copy, Clone, Debug)]
pub struct Vector<T> {
pub x: T,
pub y: T,
}
impl<T> fmt::Display for Vector<T>
where
T: fmt::Display,
{
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if let Some(prec) = f.precision() {
write!(f, "[{:.*}, {:.*}]", prec, self.x, prec, self.y)
} else {
write!(f, "[{}, {}]", self.x, self.y)
}
}
}
impl<T> Vector<T> {
pub fn new(x: T, y: T) -> Self {
Vector { x, y }
}
}
impl Vector<f64> {
pub fn from_polar(r: f64, theta: f64) -> Self {
Vector {
x: r * theta.cos(),
y: r * theta.sin(),
}
}
}
impl<T> Add for Vector<T>
where
T: Add<Output = T>,
{
type Output = Self;
fn add(self, other: Self) -> Self::Output {
Vector {
x: self.x + other.x,
y: self.y + other.y,
}
}
}
impl<T> Sub for Vector<T>
where
T: Sub<Output = T>,
{
type Output = Self;
fn sub(self, other: Self) -> Self::Output {
Vector {
x: self.x - other.x,
y: self.y - other.y,
}
}
}
impl<T> Mul<T> for Vector<T>
where
T: Mul<Output = T> + Copy,
{
type Output = Self;
fn mul(self, scalar: T) -> Self::Output {
Vector {
x: self.x * scalar,
y: self.y * scalar,
}
}
}
impl<T> Div<T> for Vector<T>
where
T: Div<Output = T> + Copy,
{
type Output = Self;
fn div(self, scalar: T) -> Self::Output {
Vector {
x: self.x / scalar,
y: self.y / scalar,
}
}
}
fn main() {
use std::f64::consts::FRAC_PI_3;
println!("{:?}", Vector::new(4, 5));
println!("{:.4}", Vector::from_polar(3.0, FRAC_PI_3));
println!("{}", Vector::new(2, 3) + Vector::new(4, 6));
println!("{:.4}", Vector::new(5.6, 1.3) - Vector::new(4.2, 6.1));
println!("{:.4}", Vector::new(3.0, 4.2) * 2.3);
println!("{:.4}", Vector::new(3.0, 4.2) / 2.3);
println!("{}", Vector::new(3, 4) / 2);
}

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object Vector extends App {
case class Vector2D(x: Double, y: Double) {
def +(v: Vector2D) = Vector2D(x + v.x, y + v.y)
def -(v: Vector2D) = Vector2D(x - v.x, y - v.y)
def *(s: Double) = Vector2D(s * x, s * y)
def /(s: Double) = Vector2D(x / s, y / s)
override def toString() = s"Vector($x, $y)"
}
val v1 = Vector2D(5.0, 7.0)
val v2 = Vector2D(2.0, 3.0)
println(s"v1 = $v1")
println(s"v2 = $v2\n")
println(s"v1 + v2 = ${v1 + v2}")
println(s"v1 - v2 = ${v1 - v2}")
println(s"v1 * 11 = ${v1 * 11.0}")
println(s"11 * v2 = ${v2 * 11.0}")
println(s"v1 / 2 = ${v1 / 2.0}")
println(s"\nSuccessfully completed without errors. [total ${scala.compat.Platform.currentTime - executionStart} ms]")
}

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class MyVector(:args) {
has Number x
has Number y
method init {
if ([:x, :y] ~~ args) {
x = args{:x}
y = args{:y}
}
elsif ([:length, :angle] ~~ args) {
x = args{:length}*args{:angle}.cos
y = args{:length}*args{:angle}.sin
}
elsif ([:from, :to] ~~ args) {
x = args{:to}[0]-args{:from}[0]
y = args{:to}[1]-args{:from}[1]
}
else {
die "Invalid arguments: #{args}"
}
}
method length { hypot(x, y) }
method angle { atan2(y, x) }
method +(MyVector v) { MyVector(x => x + v.x, y => y + v.y) }
method -(MyVector v) { MyVector(x => x - v.x, y => y - v.y) }
method *(Number n) { MyVector(x => x * n, y => y * n) }
method /(Number n) { MyVector(x => x / n, y => y / n) }
 
method neg { self * -1 }
method to_s { "vec[#{x}, #{y}]" }
}
var u = MyVector(x => 3, y => 4)
var v = MyVector(from => [1, 0], to => [2, 3])
var w = MyVector(length => 1, angle => 45.deg2rad)
say u #: vec[3, 4]
say v #: vec[1, 3]
say w #: vec[0.70710678118654752440084436210485, 0.70710678118654752440084436210485]
say u.length #: 5
say u.angle.rad2deg #: 53.13010235415597870314438744090659
say u+v #: vec[4, 7]
say u-v #: vec[2, 1]
say -u #: vec[-3, -4]
say u*10 #: vec[30, 40]
say u/2 #: vec[1.5, 2]

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import Foundation
#if canImport(Numerics)
import Numerics
#endif
struct Vector<T: Numeric> {
var x: T
var y: T
func prettyPrinted(precision: Int = 4) -> String where T: CVarArg & FloatingPoint {
return String(format: "[%.\(precision)f, %.\(precision)f]", x, y)
}
static func +(lhs: Vector, rhs: Vector) -> Vector {
return Vector(x: lhs.x + rhs.x, y: lhs.y + rhs.y)
}
static func -(lhs: Vector, rhs: Vector) -> Vector {
return Vector(x: lhs.x - rhs.x, y: lhs.y - rhs.y)
}
static func *(lhs: Vector, scalar: T) -> Vector {
return Vector(x: lhs.x * scalar, y: lhs.y * scalar)
}
static func /(lhs: Vector, scalar: T) -> Vector where T: FloatingPoint {
return Vector(x: lhs.x / scalar, y: lhs.y / scalar)
}
static func /(lhs: Vector, scalar: T) -> Vector where T: BinaryInteger {
return Vector(x: lhs.x / scalar, y: lhs.y / scalar)
}
}
#if canImport(Numerics)
extension Vector where T: ElementaryFunctions {
static func fromPolar(radians: T, theta: T) -> Vector {
return Vector(x: radians * T.cos(theta), y: radians * T.sin(theta))
}
}
#else
extension Vector where T == Double {
static func fromPolar(radians: Double, theta: Double) -> Vector {
return Vector(x: radians * cos(theta), y: radians * sin(theta))
}
}
#endif
print(Vector(x: 4, y: 5))
print(Vector.fromPolar(radians: 3.0, theta: .pi / 3).prettyPrinted())
print((Vector(x: 2, y: 3) + Vector(x: 4, y: 6)))
print((Vector(x: 5.6, y: 1.3) - Vector(x: 4.2, y: 6.1)).prettyPrinted())
print((Vector(x: 3.0, y: 4.2) * 2.3).prettyPrinted())
print((Vector(x: 3.0, y: 4.2) / 2.3).prettyPrinted())
print(Vector(x: 3, y: 4) / 2)

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namespace path ::tcl::mathop
proc vec {op a b} {
if {[llength $a] == 1 && [llength $b] == 1} {
$op $a $b
} elseif {[llength $a]==1} {
lmap i $b {vec $op $a $i}
} elseif {[llength $b]==1} {
lmap i $a {vec $op $i $b}
} elseif {[llength $a] == [llength $b]} {
lmap i $a j $b {vec $op $i $j}
} else {error "length mismatch [llength $a] != [llength $b]"}
}
proc polar {r t} {
list [expr {$r * cos($t)}] [expr {$r * sin($t)}]
}
proc check {cmd res} {
set r [uplevel 1 $cmd]
if {$r eq $res} {
puts "Ok! $cmd \t = $res"
} else {
puts "ERROR: $cmd = $r \t expected $res"
}
}
check {vec + {5 7} {2 3}} {7 10}
check {vec - {5 7} {2 3}} {3 4}
check {vec * {5 7} 11} {55 77}
check {vec / {5 7} 2.0} {2.5 3.5}
check {polar 2 0.785398} {1.41421 1.41421}

47
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Type vector
x As Double
y As Double
End Type
Type vector2
phi As Double
r As Double
End Type
Private Function vector_addition(u As vector, v As vector) As vector
vector_addition.x = u.x + v.x
vector_addition.y = u.y + v.y
End Function
Private Function vector_subtraction(u As vector, v As vector) As vector
vector_subtraction.x = u.x - v.x
vector_subtraction.y = u.y - v.y
End Function
Private Function scalar_multiplication(u As vector, v As Double) As vector
scalar_multiplication.x = u.x * v
scalar_multiplication.y = u.y * v
End Function
Private Function scalar_division(u As vector, v As Double) As vector
scalar_division.x = u.x / v
scalar_division.y = u.y / v
End Function
Private Function to_cart(v2 As vector2) As vector
to_cart.x = v2.r * Cos(v2.phi)
to_cart.y = v2.r * Sin(v2.phi)
End Function
Private Sub display(u As vector)
Debug.Print "( " & Format(u.x, "0.000") & "; " & Format(u.y, "0.000") & ")";
End Sub
Public Sub main()
Dim a As vector, b As vector, c As vector2, d As Double
c.phi = WorksheetFunction.Pi() / 3
c.r = 5
d = 10
a = to_cart(c)
b.x = 1: b.y = -2
Debug.Print "addition : ";: display a: Debug.Print "+";: display b
Debug.Print "=";: display vector_addition(a, b): Debug.Print
Debug.Print "subtraction : ";: display a: Debug.Print "-";: display b
Debug.Print "=";: display vector_subtraction(a, b): Debug.Print
Debug.Print "scalar multiplication: ";: display a: Debug.Print " *";: Debug.Print d;
Debug.Print "=";: display scalar_multiplication(a, d): Debug.Print
Debug.Print "scalar division : ";: display a: Debug.Print " /";: Debug.Print d;
Debug.Print "=";: display scalar_division(a, d)
End Sub

47
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Module Module1
Class Vector
Public store As Double()
Public Sub New(init As IEnumerable(Of Double))
store = init.ToArray()
End Sub
Public Sub New(x As Double, y As Double)
store = {x, y}
End Sub
Public Overloads Shared Operator +(v1 As Vector, v2 As Vector)
Return New Vector(v1.store.Zip(v2.store, Function(a, b) a + b))
End Operator
Public Overloads Shared Operator -(v1 As Vector, v2 As Vector)
Return New Vector(v1.store.Zip(v2.store, Function(a, b) a - b))
End Operator
Public Overloads Shared Operator *(v1 As Vector, scalar As Double)
Return New Vector(v1.store.Select(Function(x) x * scalar))
End Operator
Public Overloads Shared Operator /(v1 As Vector, scalar As Double)
Return New Vector(v1.store.Select(Function(x) x / scalar))
End Operator
Public Overrides Function ToString() As String
Return String.Format("[{0}]", String.Join(",", store))
End Function
End Class
Sub Main()
Dim v1 As New Vector(5, 7)
Dim v2 As New Vector(2, 3)
Console.WriteLine(v1 + v2)
Console.WriteLine(v1 - v2)
Console.WriteLine(v1 * 11)
Console.WriteLine(v1 / 2)
' Works with arbitrary size vectors, too.
Dim lostVector As New Vector({4, 8, 15, 16, 23, 42})
Console.WriteLine(lostVector * 7)
End Sub
End Module

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let a => import 'arrays';
let s => import 'stream';
let vmath f v1 v2 =>
s.zip (a.stream v1) (a.stream v2)
-> s.map (@ m v =>
let [v1 v2] => v;
f (v1 { == s.end => 0 }) (v2 { == s.end => 0 });
)
-> s.collect
;
let smath f scalar vector => a.stream vector -> s.map (f scalar) -> s.collect;
let v+ => vmath +;
let v- => vmath -;
let s* => smath *;
let s/ => smath /;

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v+ [1; 2; 3] [2; 5; 2] -- io.writeln io.stdout;
s* 3 [1; 5; 10] -- io.writeln io.stdout;

33
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class Vector2D {
construct new(x, y) {
_x = x
_y = y
}
static fromPolar(r, theta) { new(r * theta.cos, r * theta.sin) }
x { _x }
y { _y }
+(v) { Vector2D.new(_x + v.x, _y + v.y) }
-(v) { Vector2D.new(_x - v.x, _y - v.y) }
*(s) { Vector2D.new(_x * s, _y * s) }
/(s) { Vector2D.new(_x / s, _y / s) }
toString { "(%(_x), %(_y))" }
}
var times = Fn.new { |d, v| v * d }
var v1 = Vector2D.new(5, 7)
var v2 = Vector2D.new(2, 3)
var v3 = Vector2D.fromPolar(2.sqrt, Num.pi / 4)
System.print("v1 = %(v1)")
System.print("v2 = %(v2)")
System.print("v3 = %(v3)")
System.print()
System.print("v1 + v2 = %(v1 + v2)")
System.print("v1 - v2 = %(v1 - v2)")
System.print("v1 * 11 = %(v1 * 11)")
System.print("11 * v2 = %(times.call(11, v2))")
System.print("v1 / 2 = %(v1 / 2)")

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import "./vector" for Vector2
var v1 = Vector2.new(5, 7)
var v2 = Vector2.new(2, 3)
var v3 = Vector2.fromPolar(2.sqrt, Num.pi / 4)
System.print("v1 = %(v1)")
System.print("v2 = %(v2)")
System.print("v3 = %(v3)")
System.print()
System.print("v1 + v2 = %(v1 + v2)")
System.print("v1 - v2 = %(v1 - v2)")
System.print("v1 * 11 = %(v1 * 11)")
System.print("11 * v2 = %(Vector2.scale(11, v2))")
System.print("v1 / 2 = %(v1 / 2)")

59
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func real VAdd(A, B, C); \Add two 2D vectors
real A, B, C; \A:= B + C
[A(0):= B(0) + C(0); \VAdd(A, A, C) => A:= A + C
A(1):= B(1) + C(1);
return A;
];
func real VSub(A, B, C); \Subtract two 2D vectors
real A, B, C; \A:= B - C
[A(0):= B(0) - C(0); \VSub(A, A, C) => A:= A - C
A(1):= B(1) - C(1);
return A;
];
func real VMul(A, B, S); \Multiply 2D vector by a scalar
real A, B, S; \A:= B * S
[A(0):= B(0) * S; \VMul(A, A, S) => A:= A * S
A(1):= B(1) * S;
return A;
];
func real VDiv(A, B, S); \Divide 2D vector by a scalar
real A, B, S; \A:= B / S
[A(0):= B(0) / S; \VDiv(A, A, S) => A:= A / S
A(1):= B(1) / S;
return A;
];
proc VOut(Dev, A); \Output a 2D vector number to specified device
int Dev; real A; \e.g: Format(1,1); (-1.5, 0.3)
[ChOut(Dev, ^();
RlOut(Dev, A(0));
Text(Dev, ", ");
RlOut(Dev, A(1));
ChOut(Dev, ^));
];
proc Polar2Rect(@X, @Y, Ang, Dist); \Return rectangular coordinates
real X, Y, Ang, Dist;
[X(0):= Dist*Cos(Ang);
Y(0):= Dist*Sin(Ang);
]; \Polar2Rect
real V0(2), V1, V2, V3(2);
def Pi = 3.14159265358979323846;
[Format(1, 1);
V1:= [5., 7.];
V2:= [2., 3.];
Polar2Rect(@V3(0), @V3(1), Pi/4., sqrt(2.));
Text(0, "V1 = "); VOut(0, V1); CrLf(0);
Text(0, "V2 = "); VOut(0, V2); CrLf(0);
Text(0, "V3 = "); VOut(0, V3); CrLf(0);
CrLf(0);
Text(0, "V1 + V2 = "); VOut(0, VAdd(V0, V1, V2 )); CrLf(0);
Text(0, "V1 - V2 = "); VOut(0, VSub(V0, V1, V2 )); CrLf(0);
Text(0, "V1 * 11 = "); VOut(0, VMul(V0, V1, 11.)); CrLf(0);
Text(0, "11 * V2 = "); VOut(0, VMul(V0, V2, 11.)); CrLf(0);
Text(0, "V1 / 2 = "); VOut(0, VDiv(V0, V1, 2. )); CrLf(0);
]

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dim vect1(2)
vect1(1) = 5 : vect1(2) = 7
dim vect2(2)
vect2(1) = 2 : vect2(2) = 3
dim vect3(arraysize(vect1(),1))
for n = 1 to arraysize(vect1(),1)
vect3(n) = vect1(n) + vect2(n)
next n
print "[", vect1(1), ", ", vect1(2), "] + [", vect2(1), ", ", vect2(2), "] = ";
showarray(vect3)
for n = 1 to arraysize(vect1(),1)
vect3(n) = vect1(n) - vect2(n)
next n
print "[", vect1(1), ", ", vect1(2), "] - [", vect2(1), ", ", vect2(2), "] = ";
showarray(vect3)
for n = 1 to arraysize(vect1(),1)
vect3(n) = vect1(n) * 11
next n
print "[", vect1(1), ", ", vect1(2), "] * ", 11, " = ";
showarray(vect3)
for n = 1 to arraysize(vect1(),1)
vect3(n) = vect1(n) / 2
next n
print "[", vect1(1), ", ", vect1(2), "] / ", 2, " = ";
showarray(vect3)
end
sub showarray(vect3)
print "[";
svect$ = ""
for n = 1 to arraysize(vect3(),1)
svect$ = svect$ + str$(vect3(n)) + ", "
next n
svect$ = left$(svect$, len(svect$) - 2)
print svect$;
print "]"
end sub

33
Task/Vector/Zkl/vector-1.zkl Normal file
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class Vector{
var length,angle; // polar coordinates, radians
fcn init(length,angle){ // angle in degrees
self.length,self.angle = vm.arglist.apply("toFloat");
self.angle=self.angle.toRad();
}
fcn toXY{ length.toRectangular(angle) }
// math is done in place
fcn __opAdd(vector){
x1,y1:=toXY(); x2,y2:=vector.toXY();
length,angle=(x1+x2).toPolar(y1+y2);
self
}
fcn __opSub(vector){
x1,y1:=toXY(); x2,y2:=vector.toXY();
length,angle=(x1-x2).toPolar(y1-y2);
self
}
fcn __opMul(len){ length*=len; self }
fcn __opDiv(len){ length/=len; self }
fcn print(msg=""){
#<<<
"Vector%s:
Length: %f
Angle: %f\Ub0;
X: %f
Y: %f"
#<<<
.fmt(msg,length,angle.toDeg(),length.toRectangular(angle).xplode())
.println();
}
fcn toString{ "Vector(%f,%f\Ub0;)".fmt(length,angle.toDeg()) }
}

6
Task/Vector/Zkl/vector-2.zkl Normal file
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Vector(2,45).println();
Vector(2,45).print(" create");
(Vector(2,45) * 2).print(" *");
(Vector(4,90) / 2).print(" /");
(Vector(2,45) + Vector(2,45)).print(" +");
(Vector(4,45) - Vector(2,45)).print(" -");