# Display a linear combination

Display a linear combination
You are encouraged to solve this task according to the task description, using any language you may know.

Display a finite linear combination in an infinite vector basis ${\displaystyle (e_{1},e_{2},\ldots )}$.

Write a function that, when given a finite list of scalars ${\displaystyle (\alpha ^{1},\alpha ^{2},\ldots )}$,
creates a string representing the linear combination ${\displaystyle \sum _{i}\alpha ^{i}e_{i}}$ in an explicit format often used in mathematics, that is:

${\displaystyle \alpha ^{i_{1}}e_{i_{1}}\pm |\alpha ^{i_{2}}|e_{i_{2}}\pm |\alpha ^{i_{3}}|e_{i_{3}}\pm \ldots }$

where ${\displaystyle \alpha ^{i_{k}}\neq 0}$

The output must comply to the following rules:

•   don't show null terms, unless the whole combination is null.
e(1)     is fine,     e(1) + 0*e(3)     or     e(1) + 0     is wrong.
•   don't show scalars when they are equal to one or minus one.
e(3)     is fine,     1*e(3)     is wrong.
•   don't prefix by a minus sign if it follows a preceding term.   Instead you use subtraction.
e(4) - e(5)     is fine,     e(4) + -e(5)     is wrong.

Show here output for the following lists of scalars:

 1)    1,  2,  3
2)    0,  1,  2,  3
3)    1,  0,  3,  4
4)    1,  2,  0
5)    0,  0,  0
6)    0
7)    1,  1,  1
8)   -1, -1, -1
9)   -1, -2,  0, -3
10)   -1


## 11l

Translation of: Python
F linear(x)
V a = enumerate(x).filter2((i, v) -> v != 0).map2((i, v) -> ‘#.e(#.)’.format(I v == -1 {‘-’} E I v == 1 {‘’} E String(v)‘*’, i + 1))
R (I !a.empty {a} E [String(‘0’)]).join(‘ + ’).replace(‘ + -’, ‘ - ’)

L(x) [[1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, 3], [-1]]
print(linear(x))
Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) + 3*e(4)
-e(1)


with Ada.Text_Io;

procedure Display_Linear is

subtype Position is Positive;
type Coefficient is new Integer;
type Combination is array (Position range <>) of Coefficient;

function Linear_Combination (Comb : Combination) return String is
Accu : Unbounded_String;
begin
for Pos in Comb'Range loop
case Comb (Pos) is
when Coefficient'First .. -1 =>
Append (Accu, (if Accu = "" then "-" else " - "));
when 0 => null;
when 1 .. Coefficient'Last =>
Append (Accu, (if Accu /= "" then " + " else ""));
end case;

if Comb (Pos) /= 0 then
declare
Abs_Coeff   : constant Coefficient := abs Comb (Pos);
Coeff_Image : constant String := Fixed.Trim (Coefficient'Image (Abs_Coeff), Left);
Exp_Image   : constant String := Fixed.Trim (Position'Image (Pos), Left);
begin
if Abs_Coeff /= 1 then
Append (Accu, Coeff_Image & "*");
end if;
Append (Accu, "e(" & Exp_Image & ")");
end;
end if;
end loop;

return (if Accu = "" then "0" else To_String (Accu));
end Linear_Combination;

begin
Put_Line (Linear_Combination ((1, 2, 3)));
Put_Line (Linear_Combination ((0, 1, 2, 3)));
Put_Line (Linear_Combination ((1, 0, 3, 4)));
Put_Line (Linear_Combination ((1, 2, 0)));
Put_Line (Linear_Combination ((0, 0, 0)));
Put_Line (Linear_Combination ((1 => 0)));
Put_Line (Linear_Combination ((1, 1, 1)));
Put_Line (Linear_Combination ((-1, -1, -1)));
Put_Line (Linear_Combination ((-1, -2, 0, -3)));
Put_Line (Linear_Combination ((1 => -1)));
end Display_Linear;

Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) - 3*e(4)
-e(1)

## ALGOL 68

Using implicit multiplication operators, as in the C and Mathematica samples.

BEGIN # display a string representation of some linear combinations              #
# returns a string representing the sum of the terms of a linear combination #
#         whose coefficients are the elements of coeffs                      #
PROC linear combination = ( []INT coeffs )STRING:
BEGIN
[]INT  cf          = coeffs[ AT 1 ]; # ensure the lower bound is 1   #
STRING result     := "";
BOOL   first term := TRUE;
FOR i FROM LWB cf TO UPB cf DO
IF INT c = cf[ i ];
c /= 0
THEN                                          # non-null element #
IF first term THEN
# first term - only add the operator if it is "-"        #
IF c < 0 THEN result +:= "-" FI;
first term := FALSE
ELSE
# second or subsequent term - separate from the previous #
#                            and always add the operator #
result +:= " " + IF c < 0 THEN "-" ELSE "+" FI + " "
FI;
# add the coefficient, unless it is one                      #
IF ABS c /= 1 THEN
result +:= whole( ABS c, 0 )
FI;
result +:= "e(" + whole( i, 0 ) + ")"
FI
OD;
IF result = "" THEN "0" ELSE result FI
END # linear combination # ;

# test cases #
[][]INT tests = ( (  1,  2,  3  )
, (  0,  1,  2,  3  )
, (  1,  0,  3,  4  )
, (  1,  2,  0  )
, (  0,  0,  0  )
, (  0  )
, (  1,  1,  1  )
, ( -1, -1, -1  )
, ( -1, -2,  0, -3  )
, ( -1  )
);
FOR i FROM LWB tests TO UPB tests DO
print( ( linear combination( tests[ i ] ), newline ) )
OD
END
Output:
e(1) + 2e(2) + 3e(3)
e(2) + 2e(3) + 3e(4)
e(1) + 3e(3) + 4e(4)
e(1) + 2e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2e(2) - 3e(4)
-e(1)


## APL

Works with: Dyalog APL
 lincomb←{
fmtco←{
mul←(⍵≠1)/(⍕|⍵),'*'
mul,'e(',(⍕⍺),')'
}

co←⊃¨fmtco/¨(⍵≠0)/(⍳⍴,⍵),¨|⍵
sgn←'-+'[1+(×⍵)/×⍵]
lc←(('+'=⊃)↓⊢)∊sgn,¨co
0=⍴lc:'0' ⋄ lc
}

Output:
      ↑lincomb¨(1 2 3)(0 1 2 3)(1 0 3 4)(1 2 0)(0 0 0)(0)(1 1 1)(¯1 1 1)(¯1 2 0 ¯3)(¯1)
e(1)+2*e(2)+3*e(3)
e(2)+2*e(3)+3*e(4)
e(1)+3*e(3)+4*e(4)
e(1)+2*e(2)
0
0
e(1)+e(2)+e(3)
-e(1)+e(2)+e(3)
-e(1)+2*e(2)-3*e(4)
-e(1)              

## Arturo

linearCombination: function [coeffs][
combo: new []
loop.with:'i coeffs 'x [
case [x]
when? [=0] []
when? [=1] -> 'combo ++ ~"e(|i+1|)"
when? [= neg 1] -> 'combo ++ ~"-e(|i+1|)"
else -> 'combo ++ ~"|x|*e(|i+1|)"
]
join.with: " + " 'combo
replace 'combo {/\+ -/} "- "
(empty? combo)? -> "0" -> combo
]

loop @[
[1 2 3]
[0 1 2 3]
[1 0 3 4]
[1 2 0]
[0 0 0]
[0]
[1 1 1]
@[neg 1 neg 1 neg 1]
@[neg 1 neg 2 0 neg 3]
@[neg 1]
] => [print linearCombination &]

Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) - 3*e(4)
-e(1)

## BASIC

### Applesoft BASIC

Translation of: Chipmunk Basic

The Spanish word "cadena" means "string" in English.

 100  READ UX,UY
110  DIM SCALARS(UX,UY)
120  FOR N = 1 TO UX
130  FOR M = 1 TO UY
150  NEXT M,N
160  DATA10,4
170  DATA1,2,3,0,0,1,2,3
180  DATA1,0,3,4,1,2,0,0
190  DATA0,0,0,0,0,0,0,0
200  DATA1,1,1,0,-1,-1,-1,0
210  DATA-1,-2,0,-3,-1,0,0,0
220  FOR N = 1 TO UX
230      CADENA$= "" 240 FOR M = 1 TO UY 250 SCALAR = SCALARS(N,M) 260 IF SCALAR THEN CADENA$ = CADENA$+ CHR$ (44 -  SGN (SCALAR)) +  MID$( STR$ ( ABS (SCALAR)) + "*",1,255 * ( ABS (SCALAR) <  > 1)) + "E" +  STR$(M) 270 NEXT M 280 IF CADENA$ = "" THEN CADENA$= "0" 290 IF LEFT$ (CADENA$,1) = "+" THEN CADENA$ =  RIGHT$(CADENA$, LEN (CADENA$) - 1) 300 PRINT CADENA$
310  NEXT N


### Chipmunk Basic

Translation of: FreeBASIC
Works with: Chipmunk Basic version 3.6.4
100 dim scalars(10,4)
110 scalars(1,1) = 1 : scalars(1,2) = 2 : scalars(1,3) = 3
120 scalars(2,1) = 0 : scalars(2,2) = 1 : scalars(2,3) = 2 : scalars(2,4) = 3
130 scalars(3,1) = 1 : scalars(3,2) = 0 : scalars(3,3) = 3 : scalars(3,4) = 4
140 scalars(4,1) = 1 : scalars(4,2) = 2 : scalars(4,3) = 0
150 scalars(5,1) = 0 : scalars(5,2) = 0 : scalars(5,3) = 0
160 scalars(6,1) = 0
170 scalars(7,1) = 1 : scalars(7,2) = 1 : scalars(7,3) = 1
180 scalars(8,1) = -1 : scalars(8,2) = -1 : scalars(8,3) = -1
190 scalars(9,1) = -1 : scalars(9,2) = -2 : scalars(9,3) = 0 : scalars(9,4) = -3
200 scalars(10,1) = -1
210 cls
220 for n = 1 to ubound(scalars)
230   cadena$= "" 240 scalar = 0 250 for m = 1 to ubound(scalars,2) 260 scalar = scalars(n,m) 270 if scalar <> 0 then 280 if scalar = 1 then 290 cadena$ = cadena$+"+e"+str$(m)
300       else
310       if scalar = -1 then
320        cadena$= cadena$+"-e"+str$(m) 330 else 340 if scalar > 0 then 350 cadena$ = cadena$+chr$(43)+str$(scalar)+"*e"+str$(m)
360         else
370           cadena$= cadena$+str$(scalar)+"*e"+str$(m)
380         endif
390        endif
400       endif
410     endif
420   next m
430   if cadena$= "" then cadena$ = "0"
440   if left$(cadena$,1) = "+" then cadena$= right$(cadena$,len(cadena$)-1)
450   print cadena$460 next n 470 end  ### FreeBASIC Translation of: Ring Dim scalars(1 To 10, 1 To 4) As Integer => {{1, 2, 3}, {0, 1, 2, 3}, _ {1, 0, 3, 4}, {1, 2, 0}, {0, 0, 0}, {0}, {1, 1, 1}, {-1, -1, -1}, _ {-1, -2, 0, -3}, {-1}} For n As Integer = 1 To Ubound(scalars) Dim As String cadena = "" Dim As Integer scalar For m As Integer = 1 To Ubound(scalars,2) scalar = scalars(n, m) If scalar <> 0 Then If scalar = 1 Then cadena &= "+e" & m Elseif scalar = -1 Then cadena &= "-e" & m Else If scalar > 0 Then cadena &= Chr(43) & scalar & "*e" & m Else cadena &= scalar & "*e" & m End If End If End If Next m If cadena = "" Then cadena = "0" If Left(cadena, 1) = "+" Then cadena = Right(cadena, Len(cadena)-1) Print cadena Next n Sleep Output: Same as Ring entry. ### GW-BASIC Works with: PC-BASIC version any Works with: BASICA Works with: Chipmunk Basic Works with: QBasic Works with: MSX BASIC 100 DIM SKLS(10, 4) 110 SKLS(1, 1) = 1: SKLS(1, 2) = 2: SKLS(1, 3) = 3 120 SKLS(2, 1) = 0: SKLS(2, 2) = 1: SKLS(2, 3) = 2: SKLS(2, 4) = 3 130 SKLS(3, 1) = 1: SKLS(3, 2) = 0: SKLS(3, 3) = 3: SKLS(3, 4) = 4 140 SKLS(4, 1) = 1: SKLS(4, 2) = 2: SKLS(4, 3) = 0 150 SKLS(5, 1) = 0: SKLS(5, 2) = 0: SKLS(5, 3) = 0 160 SKLS(6, 1) = 0 170 SKLS(7, 1) = 1: SKLS(7, 2) = 1: SKLS(7, 3) = 1 180 SKLS(8, 1) = -1: SKLS(8, 2) = -1: SKLS(8, 3) = -1 190 SKLS(9, 1) = -1: SKLS(9, 2) = -2: SKLS(9, 3) = 0: SKLS(9, 4) = -3 200 SKLS(10, 1) = -1 210 CLS 220 FOR N = 1 TO 10 230 CAD$ = ""
240  SCL = 0
250  FOR M = 1 TO 4
260   SCL = SKLS(N, M)
270   IF SCL <> 0 THEN IF SCL = 1 THEN CAD$= CAD$ + "+e" + STR$(M) ELSE IF SCL = -1 THEN CAD$ = CAD$+ "-e" + STR$(M) ELSE IF SCL > 0 THEN CAD$= CAD$ + CHR$(43) + STR$(SCL) + "*e" + STR$(M) ELSE CAD$ = CAD$+ STR$(SCL) + "*e" + STR$(M) 280 NEXT M 290 IF CAD$ = "" THEN CAD$= "0" 300 IF LEFT$(CAD$, 1) = "+" THEN CAD$ = RIGHT$(CAD$, LEN(CAD$) - 1) 310 PRINT CAD$
320 NEXT N
330 END


### MSX Basic

Works with: MSX BASIC version any

The GW-BASIC solution works without any changes.ht>

### QBasic

Translation of: FreeBASIC
Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
Works with: QB64
DIM scalars(1 TO 10, 1 TO 4)
scalars(1, 1) = 1: scalars(1, 2) = 2: scalars(1, 3) = 3
scalars(2, 1) = 0: scalars(2, 2) = 1: scalars(2, 3) = 2: scalars(2, 4) = 3
scalars(3, 1) = 1: scalars(3, 2) = 0: scalars(3, 3) = 3: scalars(3, 4) = 4
scalars(4, 1) = 1: scalars(4, 2) = 2: scalars(4, 3) = 0
scalars(5, 1) = 0: scalars(5, 2) = 0: scalars(5, 3) = 0
scalars(6, 1) = 0
scalars(7, 1) = 1: scalars(7, 2) = 1: scalars(7, 3) = 1
scalars(8, 1) = -1: scalars(8, 2) = -1: scalars(8, 3) = -1
scalars(9, 1) = -1: scalars(9, 2) = -2: scalars(9, 3) = 0: scalars(9, 4) = -3
scalars(10, 1) = -1

CLS
FOR n = 1 TO UBOUND(scalars)
cadena$= "" scalar = 0 FOR m = 1 TO UBOUND(scalars, 2) scalar = scalars(n, m) IF scalar <> 0 THEN IF scalar = 1 THEN cadena$ = cadena$+ "+e" + STR$(m)
ELSEIF scalar = -1 THEN
cadena$= cadena$ + "-e" + STR$(m) ELSE IF scalar > 0 THEN cadena$ = cadena$+ CHR$(43) + STR$(scalar) + "*e" + STR$(m)
ELSE
cadena$= cadena$ + STR$(scalar) + "*e" + STR$(m)
END IF
END IF
END IF
NEXT m
IF cadena$= "" THEN cadena$ = "0"
IF LEFT$(cadena$, 1) = "+" THEN cadena$= RIGHT$(cadena$, LEN(cadena$) - 1)
PRINT cadena$NEXT n END  ### Yabasic Translation of: FreeBASIC dim scalars(10,4) scalars(1,1) = 1: scalars(1,2) = 2: scalars(1,3) = 3 scalars(2,1) = 0: scalars(2,2) = 1: scalars(2,3) = 2: scalars(2,4) = 3 scalars(3,1) = 1: scalars(3,2) = 0: scalars(3,3) = 3: scalars(3,4) = 4 scalars(4,1) = 1: scalars(4,2) = 2: scalars(4,3) = 0 scalars(5,1) = 0: scalars(5,2) = 0: scalars(5,3) = 0 scalars(6,1) = 0 scalars(7,1) = 1: scalars(7,2) = 1: scalars(7,3) = 1 scalars(8,1) = -1: scalars(8,2) = -1: scalars(8,3) = -1 scalars(9,1) = -1: scalars(9,2) = -2: scalars(9,3) = 0: scalars(9,4) = -3 scalars(10,1) = -1 for n = 1 to arraysize(scalars(),1) cadena$ = ""

for m = 1 to arraysize(scalars(),2)
scalar = scalars(n, m)
if scalar <> 0 then
if scalar = 1 then
cadena$= cadena$ + "+e" + str$(m) else if scalar = -1 then cadena$ = cadena$+ "-e" + str$(m)
else
if scalar > 0 then
cadena$= cadena$ + chr$(43) + str$(scalar) + "*e" + str$(m) else cadena$ = cadena$+ str$(scalar) + "*e" + str$(m) fi fi fi fi next m if cadena$ = ""  cadena$= "0" if left$(cadena$, 1) = "+" cadena$ = right$(cadena$, len(cadena$)-1) print cadena$
next n
end

## C

Accepts vector coefficients from the command line, prints usage syntax if invoked with no arguments. This implementation can handle floating point values but displays integer values as integers. All test case results shown with invocation. A multiplication sign is not shown between a coefficient and the unit vector when a vector is written out by hand ( i.e. human readable) and is thus not shown here as well.

#include<stdlib.h>
#include<stdio.h>
#include<math.h> /*Optional, but better if included as fabs, labs and abs functions are being used. */

int main(int argC, char* argV[])
{

int i,zeroCount= 0,firstNonZero = -1;
double* vector;

if(argC == 1){
printf("Usage : %s <Vector component coefficients seperated by single space>",argV[0]);
}

else{

printf("Vector for [");
for(i=1;i<argC;i++){
printf("%s,",argV[i]);
}
printf("\b] -> ");

vector = (double*)malloc((argC-1)*sizeof(double));

for(i=1;i<=argC;i++){
vector[i-1] = atof(argV[i]);
if(vector[i-1]==0.0)
zeroCount++;
if(vector[i-1]!=0.0 && firstNonZero==-1)
firstNonZero = i-1;
}

if(zeroCount == argC){
printf("0");
}

else{
for(i=0;i<argC;i++){
if(i==firstNonZero && vector[i]==1)
printf("e%d ",i+1);
else if(i==firstNonZero && vector[i]==-1)
printf("- e%d ",i+1);
else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])>0.0)
printf("- %lf e%d ",fabs(vector[i]),i+1);
else if(i==firstNonZero && vector[i]<0 && fabs(vector[i])-abs(vector[i])==0.0)
printf("- %ld e%d ",labs(vector[i]),i+1);
else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])>0.0)
printf("%lf e%d ",vector[i],i+1);
else if(i==firstNonZero && vector[i]>0 && fabs(vector[i])-abs(vector[i])==0.0)
printf("%ld e%d ",vector[i],i+1);
else if(fabs(vector[i])==1.0 && i!=0)
printf("%c e%d ",(vector[i]==-1)?'-':'+',i+1);
else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])>0.0)
printf("%c %lf e%d ",(vector[i]<0)?'-':'+',fabs(vector[i]),i+1);
else if(i!=0 && vector[i]!=0 && fabs(vector[i])-abs(vector[i])==0.0)
printf("%c %ld e%d ",(vector[i]<0)?'-':'+',labs(vector[i]),i+1);
}
}
}

free(vector);

return 0;
}

Output:
C:\rossetaCode>vectorDisplay.exe 1 2 3
Vector for [1,2,3] -> e1 + 2 e2 + 3 e3
C:\rossetaCode>vectorDisplay.exe 0 0 0
Vector for [0,0,0] -> 0
C:\rossetaCode>vectorDisplay.exe 0 1 2 3
Vector for [0,1,2,3] -> e2 + 2 e3 + 3 e4
C:\rossetaCode>vectorDisplay.exe 1 0 3 4
Vector for [1,0,3,4] -> e1 + 3 e3 + 4 e4
C:\rossetaCode>vectorDisplay.exe 1 2 0
Vector for [1,2,0] -> e1 + 2 e2
C:\rossetaCode>vectorDisplay.exe 0 0 0
Vector for [0,0,0] -> 0
C:\rossetaCode>vectorDisplay.exe 0
Vector for [0] -> 0
C:\rossetaCode>vectorDisplay.exe 1 1 1
Vector for [1,1,1] -> e1 + e2 + e3
C:\rossetaCode>vectorDisplay.exe -1 -1 -1
Vector for [-1,-1,-1] -> - e1 - e2 - e3
C:\rossetaCode>vectorDisplay.exe -1 -2 0 -3
Vector for [-1,-2,0,-3] -> - e1 - 2 e2 - 3 e4
C:\rossetaCode>vectorDisplay.exe -1
Vector for [-1] -> - e1


## C#

Translation of: D
using System;
using System.Collections.Generic;
using System.Text;

namespace DisplayLinearCombination {
class Program {
static string LinearCombo(List<int> c) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < c.Count; i++) {
int n = c[i];
if (n < 0) {
if (sb.Length == 0) {
sb.Append('-');
} else {
sb.Append(" - ");
}
} else if (n > 0) {
if (sb.Length != 0) {
sb.Append(" + ");
}
} else {
continue;
}

int av = Math.Abs(n);
if (av != 1) {
sb.AppendFormat("{0}*", av);
}
sb.AppendFormat("e({0})", i + 1);
}
if (sb.Length == 0) {
sb.Append('0');
}
return sb.ToString();
}

static void Main(string[] args) {
List<List<int>> combos = new List<List<int>>{
new List<int> { 1, 2, 3},
new List<int> { 0, 1, 2, 3},
new List<int> { 1, 0, 3, 4},
new List<int> { 1, 2, 0},
new List<int> { 0, 0, 0},
new List<int> { 0},
new List<int> { 1, 1, 1},
new List<int> { -1, -1, -1},
new List<int> { -1, -2, 0, -3},
new List<int> { -1},
};

foreach (List<int> c in combos) {
var arr = "[" + string.Join(", ", c) + "]";
Console.WriteLine("{0,15} -> {1}", arr, LinearCombo(c));
}
}
}
}

Output:
      [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)

## C++

Translation of: D
#include <iomanip>
#include <iostream>
#include <sstream>
#include <vector>

template<typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
auto it = v.cbegin();
auto end = v.cend();

os << '[';
if (it != end) {
os << *it;
it = std::next(it);
}
while (it != end) {
os << ", " << *it;
it = std::next(it);
}
return os << ']';
}

std::ostream& operator<<(std::ostream& os, const std::string& s) {
return os << s.c_str();
}

std::string linearCombo(const std::vector<int>& c) {
std::stringstream ss;
for (size_t i = 0; i < c.size(); i++) {
int n = c[i];
if (n < 0) {
if (ss.tellp() == 0) {
ss << '-';
} else {
ss << " - ";
}
} else if (n > 0) {
if (ss.tellp() != 0) {
ss << " + ";
}
} else {
continue;
}

int av = abs(n);
if (av != 1) {
ss << av << '*';
}
ss << "e(" << i + 1 << ')';
}
if (ss.tellp() == 0) {
return "0";
}
return ss.str();
}

int main() {
using namespace std;

vector<vector<int>> combos{
{1, 2, 3},
{0, 1, 2, 3},
{1, 0, 3, 4},
{1, 2, 0},
{0, 0, 0},
{0},
{1, 1, 1},
{-1, -1, -1},
{-1, -2, 0, -3},
{-1},
};

for (auto& c : combos) {
stringstream ss;
ss << c;
cout << setw(15) << ss.str() << " -> ";
cout << linearCombo(c) << '\n';
}

return 0;
}

Output:
      [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)

## Cowgol

include "cowgol.coh";

sub abs(n: int32): (r: uint32) is
if n < 0
then r := (-n) as uint32;
else r := n as uint32;
end if;
end sub;

sub lincomb(scalar: [int32], size: intptr) is
var first: uint8 := 1;
var item: uint8 := 1;

sub print_sign() is
if first == 1 then
if [scalar] < 0 then print("-"); end if;
else
if [scalar] < 0
then print(" - ");
else print(" + ");
end if;
end if;
end sub;

sub print_term() is
if [scalar] == 0 then return; end if;
print_sign();
if abs([scalar]) > 1 then
print_i32(abs([scalar]));
print("*");
end if;
print("e(");
print_i8(item);
print(")");
first := 0;
end sub;

while size > 0 loop
print_term();
scalar := @next scalar;
size := size - 1;
item := item + 1;
end loop;

if first == 1 then
print("0");
end if;
print_nl();
end sub;

var a1: int32[] := {1, 2, 3}; lincomb(&a1[0], @sizeof a1);
var a2: int32[] := {0, 1, 2, 3}; lincomb(&a2[0], @sizeof a2);
var a3: int32[] := {1, 0, 3, 4}; lincomb(&a3[0], @sizeof a3);
var a4: int32[] := {1, 2, 0}; lincomb(&a4[0], @sizeof a4);
var a5: int32[] := {0, 0, 0}; lincomb(&a5[0], @sizeof a5);
var a6: int32[] := {0}; lincomb(&a6[0], @sizeof a6);
var a7: int32[] := {1, 1, 1}; lincomb(&a7[0], @sizeof a7);
var a8: int32[] := {-1, -1, -1}; lincomb(&a8[0], @sizeof a8);
var a9: int32[] := {-1, -2, 0, 3}; lincomb(&a9[0], @sizeof a9);
var a10: int32[] := {-1}; lincomb(&a10[0], @sizeof a10);
Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) + 3*e(4)
-e(1)

## D

Translation of: Kotlin
import std.array;
import std.conv;
import std.format;
import std.math;
import std.stdio;

string linearCombo(int[] c) {
auto sb = appender!string;
foreach (i, n; c) {
if (n==0) continue;
string op;
if (n < 0) {
if (sb.data.empty) {
op = "-";
} else {
op = " - ";
}
} else if (n > 0) {
if (!sb.data.empty) {
op = " + ";
}
}
auto av = abs(n);
string coeff;
if (av != 1) {
coeff = to!string(av) ~ "*";
}
sb.formattedWrite("%s%se(%d)", op, coeff, i+1);
}
if (sb.data.empty) {
return "0";
}
return sb.data;
}

void main() {
auto combos = [
[1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1],
];
foreach (c; combos) {
auto arr = c.format!"%s";
writefln("%-15s  ->  %s", arr, linearCombo(c));
}
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)

## Draco

proc abs(int n) int: if n<0 then -n else n fi corp

proc write_term(word index; int scalar; bool first) void:
if first then
if scalar<0 then write("-") fi
else
write(if scalar<0 then " - " else " + " fi)
fi;
if abs(scalar)>1 then
write(abs(scalar), '*')
fi;
write("e(",index,")")
corp

proc lincomb([*]int terms) void:
bool first;
word index;
first := true;

for index from 0 upto dim(terms,1)-1 do
if terms[index] /= 0 then
write_term(index+1, terms[index], first);
first := false
fi
od;

writeln(if first then "0" else "" fi)
corp

proc main() void:
[3]int a1 = (1,2,3);
[4]int a2 = (0,1,2,3);
[4]int a3 = (1,0,3,4);
[3]int a4 = (1,2,0);
[3]int a5 = (0,0,0);
[1]int a6 = (0);
[3]int a7 = (1,1,1);
[3]int a8 = (-1,-1,-1);
[4]int a9 = (-1,-2,0,3);
[1]int a10 = (-1);
lincomb(a1); lincomb(a2); lincomb(a3); lincomb(a4);
lincomb(a5); lincomb(a6); lincomb(a7); lincomb(a8);
lincomb(a9); lincomb(a10)
corp
Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) + 3*e(4)
-e(1)

## EasyLang

Translation of: Ring
scalars[][] = [ [ 1 2 3 ] [ 0 1 2 3 ] [ 1 0 3 4 ] [ 1 2 0 ] [ 0 0 0 ] [ 0 ] [ 1 1 1 ] [ -1 -1 -1 ] [ -1 -2 0 -3 ] [ -1 ] ]
for n = 1 to len scalars[][]
str$= "" for m = 1 to len scalars[n][] scalar = scalars[n][m] if scalar <> 0 if scalar = 1 str$ &= "+e" & m
elif scalar = -1
str$&= "-e" & m else if scalar > 0 str$ &= strchar 43 & scalar & "*e" & m
else
str$= scalar & "*e" & m . . . . if str$ = ""
str$= 0 . if substr str$ 1 1 = "+"
str$= substr str$ 2 (len str$- 1) . print str$
.
Output:
e1+2*e2+3*e3
e2+2*e3+3*e4
e1+3*e3+4*e4
e1+2*e2
0
0
e1+e2+e3
-e1-e2-e3
-3*e4
-e1


## EchoLisp

;; build an html string from list of coeffs

(define (linear->html coeffs)
(define plus #f)
(or*
(for/fold (html "") ((a coeffs) (i (in-naturals 1)))
(unless (zero? a)
(set! plus (if plus "+" "")))
(string-append html
(cond
((= a 1)  (format "%a e<sub>%d</sub> " plus i))
((= a -1) (format "- e<sub>%d</sub> " i))
((> a 0)  (format "%a %d*e<sub>%d</sub> " plus a i))
((< a 0)  (format "- %d*e<sub>%d</sub> " (abs a) i))
(else ""))))
"0"))

(define linears '((1 2 3)
(0 1 2 3)
(1 0 3 4)
(1 2 0)
(0 0 0)
(0)
(1 1 1)
(-1 -1 -1)
(-1 -2 0 -3)
(-1)))

(html-print ;; send string to stdout
(for/string ((linear linears))
(format "%a -> <span style='color:blue'>%a</span> <br>" linear (linear->html linear)))))

Output:

(1 2 3) -> e1 + 2*e2 + 3*e3
(0 1 2 3) -> e2 + 2*e3 + 3*e4
(1 0 3 4) -> e1 + 3*e3 + 4*e4
(1 2 0) -> e1 + 2*e2
(0 0 0) -> 0
(0) -> 0
(1 1 1) -> e1 + e2 + e3
(-1 -1 -1) -> - e1 - e2 - e3
(-1 -2 0 -3) -> - e1 - 2*e2 - 3*e4
(-1) -> - e1

## Elixir

Works with: Elixir version 1.3
defmodule Linear_combination do
def display(coeff) do
Enum.with_index(coeff)
|> Enum.map_join(fn {n,i} ->
{m,s} = if n<0, do: {-n,"-"}, else: {n,"+"}
case {m,i} do
{0,_} -> ""
{1,i} -> "#{s}e(#{i+1})"
{n,i} -> "#{s}#{n}*e(#{i+1})"
end
end)
|> case do
""  -> IO.puts "0"
str -> IO.puts str
end
end
end

coeffs =
[ [1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1]
]
Enum.each(coeffs, &Linear_combination.display(&1))

Output:
e(1)+2*e(2)+3*e(3)
e(2)+2*e(3)+3*e(4)
e(1)+3*e(3)+4*e(4)
e(1)+2*e(2)
0
0
e(1)+e(2)+e(3)
-e(1)-e(2)-e(3)
-e(1)-2*e(2)-3*e(4)
-e(1)


## F#

### The function

// Display a linear combination. Nigel Galloway: March 28th., 2018
let fN g =
let rec fG n g=match g with
|0::g    ->                        fG (n+1) g
|1::g    -> printf "+e(%d)" n;     fG (n+1) g
|(-1)::g -> printf "-e(%d)" n;     fG (n+1) g
|i::g    -> printf "%+de(%d)" i n; fG (n+1) g
|_       -> printfn ""
let rec fN n g=match g with
|0::g    ->                        fN (n+1) g
|1::g    -> printf "e(%d)" n;      fG (n+1) g
|(-1)::g -> printf "-e(%d)" n;     fG (n+1) g
|i::g    -> printf "%de(%d)" i n;  fG (n+1) g
|_       -> printfn "0"
fN 1 g


fN [1;2;3]

Output:
e(1)+2e(2)+3e(3)

fN [0;1;2;3]

Output:
e(2)+2e(3)+3e(4)

fN[1;0;3;4]

Output:
e(1)+3e(3)+4e(4)

fN[1;2;0]

Output:
e(1)+2e(2)

fN[0;0;0]

Output:
0

fN[0]

Output:
0

fN[1;1;1]

Output:
e(1)+e(2)+e(3)

fN[-1;-1;-1]

Output:
-e(1)-e(2)-e(3)

fN[-1;-2;0;-3]

Output:
-e(1)-2e(2)-3e(4)

fN[1]

Output:
e(1)


## Factor

USING: formatting kernel match math pair-rocket regexp sequences ;

MATCH-VARS: ?a ?b ;

: choose-term ( coeff i -- str )
1 + { } 2sequence {
{  0  _ } => [       ""                 ]
{  1 ?a } => [ ?a    "e(%d)"    sprintf ]
{ -1 ?a } => [ ?a    "-e(%d)"   sprintf ]
{ ?a ?b } => [ ?a ?b "%d*e(%d)" sprintf ]
} match-cond ;

: linear-combo ( seq -- str )
[ choose-term ] map-index harvest " + " join
R/ \+ -/ "- " re-replace [ "0" ] when-empty ;

{ { 1 2 3 } { 0 1 2 3 } { 1 0 3 4 } { 1 2 0 } { 0 0 0 } { 0 }
{ 1 1 1 } { -1 -1 -1 } { -1 -2 0 -3 } { -1 } }
[ dup linear-combo "%-14u  ->  %s\n" printf ] each

Output:
{ 1 2 3 }       ->  e(1) + 2*e(2) + 3*e(3)
{ 0 1 2 3 }     ->  e(2) + 2*e(3) + 3*e(4)
{ 1 0 3 4 }     ->  e(1) + 3*e(3) + 4*e(4)
{ 1 2 0 }       ->  e(1) + 2*e(2)
{ 0 0 0 }       ->  0
{ 0 }           ->  0
{ 1 1 1 }       ->  e(1) + e(2) + e(3)
{ -1 -1 -1 }    ->  -e(1) - e(2) - e(3)
{ -1 -2 0 -3 }  ->  -e(1) - 2*e(2) - 3*e(4)
{ -1 }          ->  -e(1)

## Go

Translation of: Kotlin
package main

import (
"fmt"
"strings"
)

func linearCombo(c []int) string {
var sb strings.Builder
for i, n := range c {
if n == 0 {
continue
}
var op string
switch {
case n < 0 && sb.Len() == 0:
op = "-"
case n < 0:
op = " - "
case n > 0 && sb.Len() == 0:
op = ""
default:
op = " + "
}
av := n
if av < 0 {
av = -av
}
coeff := fmt.Sprintf("%d*", av)
if av == 1 {
coeff = ""
}
sb.WriteString(fmt.Sprintf("%s%se(%d)", op, coeff, i+1))
}
if sb.Len() == 0 {
return "0"
} else {
return sb.String()
}
}

func main() {
combos := [][]int{
{1, 2, 3},
{0, 1, 2, 3},
{1, 0, 3, 4},
{1, 2, 0},
{0, 0, 0},
{0},
{1, 1, 1},
{-1, -1, -1},
{-1, -2, 0, -3},
{-1},
}
for _, c := range combos {
t := strings.Replace(fmt.Sprint(c), " ", ", ", -1)
fmt.Printf("%-15s  ->  %s\n", t, linearCombo(c))
}
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)


## Groovy

Translation of: Java
class LinearCombination {
private static String linearCombo(int[] c) {
StringBuilder sb = new StringBuilder()
for (int i = 0; i < c.length; ++i) {
if (c[i] == 0) continue
String op
if (c[i] < 0 && sb.length() == 0) {
op = "-"
} else if (c[i] < 0) {
op = " - "
} else if (c[i] > 0 && sb.length() == 0) {
op = ""
} else {
op = " + "
}
int av = Math.abs(c[i])
String coeff = av == 1 ? "" : "" + av + "*"
sb.append(op).append(coeff).append("e(").append(i + 1).append(')')
}
if (sb.length() == 0) {
return "0"
}
return sb.toString()
}

static void main(String[] args) {
int[][] combos = [
[1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1]
]

for (int[] c : combos) {
printf("%-15s  ->  %s\n", Arrays.toString(c), linearCombo(c))
}
}
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)

import Text.Printf (printf)

linearForm :: [Int] -> String
linearForm = strip . concat . zipWith term [1..]
where
term :: Int -> Int -> String
term i c = case c of
0  -> mempty
1  -> printf "+e(%d)" i
-1 -> printf "-e(%d)" i
c  -> printf "%+d*e(%d)" c i

strip str = case str of
'+':s -> s
""    -> "0"
s     -> s


Testing

coeffs :: [[Int]]
coeffs = [ [1, 2, 3]
, [0, 1, 2, 3]
, [1, 0, 3, 4]
, [1, 2, 0]
, [0, 0, 0]
, [0]
, [1, 1, 1]
, [-1, -1, -1]
, [-1, -2, 0, -3]
, [-1] ]

λ> mapM_ (print . linearForm) coeffs
"e(1)+2*e(2)+3*e(3)"
"e(2)+2*e(3)+3*e(4)"
"e(1)+3*e(3)+4*e(4)"
"e(1)+2*e(2)"
"0"
"0"
"e(1)+e(2)+e(3)"
"-e(1)-e(2)-e(3)"
"-e(1)-2*e(2)-3*e(4)"
"-e(1)"

## J

Implementation:

fourbanger=:3 :0
e=. ('e(',')',~])@":&.> 1+i.#y
firstpos=. 0< {.y-.0
if. */0=y do. '0' else. firstpos}.;y gluedto e end.
)

gluedto=:4 :0 each
pfx=. '+-' {~ x<0
select. |x
case. 0 do. ''
case. 1 do. pfx,y
case.   do. pfx,(":|x),'*',y
end.
)


Example use:

   fourbanger 1 2 3
e(1)+2*e(2)+3*e(3)
fourbanger 0 1 2 3
e(2)+2*e(3)+3*e(4)
fourbanger 1 0 3 4
e(1)+3*e(3)+4*e(4)
fourbanger 0 0 0
0
fourbanger 0
0
fourbanger 1 1 1
e(1)+e(2)+e(3)
fourbanger _1 _1 _1
-e(1)-e(2)-e(3)
fourbanger _1 _2 0 _3
-e(1)-2*e(2)-3*e(4)
fourbanger _1
-e(1)


## Java

Translation of: Kotlin
import java.util.Arrays;

public class LinearCombination {
private static String linearCombo(int[] c) {
StringBuilder sb = new StringBuilder();
for (int i = 0; i < c.length; ++i) {
if (c[i] == 0) continue;
String op;
if (c[i] < 0 && sb.length() == 0) {
op = "-";
} else if (c[i] < 0) {
op = " - ";
} else if (c[i] > 0 && sb.length() == 0) {
op = "";
} else {
op = " + ";
}
int av = Math.abs(c[i]);
String coeff = av == 1 ? "" : "" + av + "*";
sb.append(op).append(coeff).append("e(").append(i + 1).append(')');
}
if (sb.length() == 0) {
return "0";
}
return sb.toString();
}

public static void main(String[] args) {
int[][] combos = new int[][]{
new int[]{1, 2, 3},
new int[]{0, 1, 2, 3},
new int[]{1, 0, 3, 4},
new int[]{1, 2, 0},
new int[]{0, 0, 0},
new int[]{0},
new int[]{1, 1, 1},
new int[]{-1, -1, -1},
new int[]{-1, -2, 0, -3},
new int[]{-1},
};
for (int[] c : combos) {
System.out.printf("%-15s  ->  %s\n", Arrays.toString(c), linearCombo(c));
}
}
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)

## jq

def linearCombo:
reduce to_entries[] as {key: $k,value:$v} ("";
if $v == 0 then . else (if$v < 0 and length==0 then   "-"
elif $v < 0 then " - " elif$v > 0 and length==0 then ""
else                           " + "
end) as $sign | ($v|fabs) as $av | (if ($av == 1) then "" else "\($av)*" end) as$coeff
| .  + "\($sign)\($coeff)e\($k)" end) | if length==0 then "0" else . end ; # The exercise def lpad($len): tostring | ($len - length) as$l | (" " * $l)[:$l] + .;

[1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1]
| "\(lpad(15)) => \(linearCombo)"
Output:
        [1,2,3] => e0 + 2*e1 + 3*e2
[0,1,2,3] => e1 + 2*e2 + 3*e3
[1,0,3,4] => e0 + 3*e2 + 4*e3
[1,2,0] => e0 + 2*e1
[0,0,0] => 0
[0] => 0
[1,1,1] => e0 + e1 + e2
[-1,-1,-1] => -e0 - e1 - e2
[-1,-2,0,-3] => -e0 - 2*e1 - 3*e3
[-1] => -e0


## Julia

# v0.6

linearcombination(coef::Array) = join(collect("$c * e($i)" for (i, c) in enumerate(coef) if c != 0), " + ")

for c in [[1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1],
[-1, -1, -1], [-1, -2, 0, -3], [-1]]
@printf("%20s -> %s\n", c, linearcombination(c))
end

Output:
           [1, 2, 3] -> 1 * e(1) + 2 * e(2) + 3 * e(3)
[0, 1, 2, 3] -> 1 * e(2) + 2 * e(3) + 3 * e(4)
[1, 0, 3, 4] -> 1 * e(1) + 3 * e(3) + 4 * e(4)
[1, 2, 0] -> 1 * e(1) + 2 * e(2)
[0, 0, 0] ->
[0] ->
[1, 1, 1] -> 1 * e(1) + 1 * e(2) + 1 * e(3)
[-1, -1, -1] -> -1 * e(1) + -1 * e(2) + -1 * e(3)
[-1, -2, 0, -3] -> -1 * e(1) + -2 * e(2) + -3 * e(4)
[-1] -> -1 * e(1)

## Kotlin

// version 1.1.2

fun linearCombo(c: IntArray): String {
val sb = StringBuilder()
for ((i, n) in c.withIndex()) {
if (n == 0) continue
val op = when {
n < 0 && sb.isEmpty() -> "-"
n < 0                 -> " - "
n > 0 && sb.isEmpty() -> ""
else                  -> " + "
}
val av = Math.abs(n)
val coeff = if (av == 1) "" else "$av*" sb.append("$op${coeff}e(${i + 1})")
}
return if(sb.isEmpty()) "0" else sb.toString()
}

fun main(args: Array<String>) {
val combos = arrayOf(
intArrayOf(1, 2, 3),
intArrayOf(0, 1, 2, 3),
intArrayOf(1, 0, 3, 4),
intArrayOf(1, 2, 0),
intArrayOf(0, 0, 0),
intArrayOf(0),
intArrayOf(1, 1, 1),
intArrayOf(-1, -1, -1),
intArrayOf(-1, -2, 0, -3),
intArrayOf(-1)
)
for (c in combos) {
println("${c.contentToString().padEnd(15)} ->${linearCombo(c)}")
}
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)


## Lambdatalk

{def linearcomb
{def linearcomb.r
{lambda {:a :n :i}
{if {= :i :n}
then
else {let { {:e e({+ :i 1})}
{:v {abs {A.get :i :a}}}
{:s {if {< {A.get :i :a} 0} then - else +}}
} {if {= :v 0} then  else
{if {= :v 1} then :s :e else :s :v*:e}}}
{linearcomb.r :a :n {+ :i 1}} }}}
{lambda {:a}
{S.replace _LAMB_[^\s]+ by 0 in
{let { {:r {linearcomb.r {A.new :a} {S.length :a} 0}}
} {if {W.equal? {S.first :r} +} then {S.rest :r} else :r} }}}}
-> linearcomb

{linearcomb 1 2 3}      -> e(1) + 2*e(2) + 3*e(3)
{linearcomb -1 -2 0 -3} -> - e(1) - 2*e(2) - 3*e(4)
{linearcomb 0 1 2 3}    -> e(2) + 2*e(3) + 3*e(4)
{linearcomb 1 0 3 4}    -> e(1) + 3*e(3) + 4*e(4)
{linearcomb 1 2 0}      -> e(1) + 2*e(2)
{linearcomb 0 0 0}      -> 0
{linearcomb 0}          -> 0
{linearcomb 1 1 1}      -> e(1) + e(2) + e(3)
{linearcomb -1 -1 -1}   -> - e(1) - e(2) - e(3)
{linearcomb -1}         -> - e(1)


## Lua

Translation of: C#
function t2s(t)
local s = "["
for i,v in pairs(t) do
if i > 1 then
s = s .. ", " .. v
else
s = s .. v
end
end
return s .. "]"
end

function linearCombo(c)
local sb = ""
for i,n in pairs(c) do
local skip = false

if n < 0 then
if sb:len() == 0 then
sb = sb .. "-"
else
sb = sb .. " - "
end
elseif n > 0 then
if sb:len() ~= 0 then
sb = sb .. " + "
end
else
skip = true
end

if not skip then
local av = math.abs(n)
if av ~= 1 then
sb = sb .. av .. "*"
end
sb = sb .. "e(" .. i .. ")"
end
end
if sb:len() == 0 then
sb = "0"
end
return sb
end

function main()
local combos = {
{  1,  2,  3},
{  0,  1,  2,  3 },
{  1,  0,  3,  4 },
{  1,  2,  0 },
{  0,  0,  0 },
{  0 },
{  1,  1,  1 },
{ -1, -1, -1 },
{ -1, -2, 0, -3 },
{ -1 }
}

for i,c in pairs(combos) do
local arr = t2s(c)
print(string.format("%15s -> %s", arr, linearCombo(c)))
end
end

main()

Output:
      [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)

## Mathematica / Wolfram Language

tests = {{1, 2, 3}, {0, 1, 2, 3}, {1, 0, 3, 4}, {1, 2, 0}, {0, 0, 0}, {0}, {1, 1, 1}, {-1, -1, -1}, {-1, -2, 0, -3}, {-1}};
Column[TraditionalForm[Total[MapIndexed[#1 e[#2[[1]]] &, #]]] & /@ tests]

Output:
e(1)+2e(2)+3e(3)
e(2)+2e(3)+3e(4)
e(1)+3e(3)+4e(4)
e(1)+2e(2)
0
0
e(1)+e(2)+e(3)
-e(1)-e(2)-e(3)
-e(1)-2e(2)-3e(4)
-e(1)

## Modula-2

MODULE Linear;
FROM FormatString IMPORT FormatString;

PROCEDURE WriteInt(n : INTEGER);
VAR buf : ARRAY[0..15] OF CHAR;
BEGIN
FormatString("%i", buf, n);
WriteString(buf)
END WriteInt;

PROCEDURE WriteLinear(c : ARRAY OF INTEGER);
VAR
buf : ARRAY[0..15] OF CHAR;
i,j : CARDINAL;
b : BOOLEAN;
BEGIN
b := TRUE;
j := 0;

FOR i:=0 TO HIGH(c) DO
IF c[i]=0 THEN CONTINUE END;

IF c[i]<0 THEN
IF b THEN WriteString("-")
ELSE      WriteString(" - ") END;
ELSIF c[i]>0 THEN
IF NOT b THEN WriteString(" + ") END;
END;

IF c[i] > 1 THEN
WriteInt(c[i]);
WriteString("*")
ELSIF c[i] < -1 THEN
WriteInt(-c[i]);
WriteString("*")
END;

FormatString("e(%i)", buf, i+1);
WriteString(buf);

b := FALSE;
INC(j)
END;

IF j=0 THEN WriteString("0") END;
WriteLn
END WriteLinear;

TYPE
Array1 = ARRAY[0..0] OF INTEGER;
Array3 = ARRAY[0..2] OF INTEGER;
Array4 = ARRAY[0..3] OF INTEGER;
BEGIN
WriteLinear(Array3{1,2,3});
WriteLinear(Array4{0,1,2,3});
WriteLinear(Array4{1,0,3,4});
WriteLinear(Array3{1,2,0});
WriteLinear(Array3{0,0,0});
WriteLinear(Array1{0});
WriteLinear(Array3{1,1,1});
WriteLinear(Array3{-1,-1,-1});
WriteLinear(Array4{-1,-2,0,-3});
WriteLinear(Array1{-1});

END Linear.


## Nim

Translation of: Kotlin
import strformat

proc linearCombo(c: openArray[int]): string =

for i, n in c:
if n == 0: continue
let op = if n < 0:
if result.len == 0: "-" else: " - "
else:
if n > 0 and result.len == 0: "" else: " + "
let av = abs(n)
let coeff = if av == 1: "" else: $av & '*' result &= fmt"{op}{coeff}e({i + 1})" if result.len == 0: result = "0" const Combos = [@[1, 2, 3], @[0, 1, 2, 3], @[1, 0, 3, 4], @[1, 2, 0], @[0, 0, 0], @[0], @[1, 1, 1], @[-1, -1, -1], @[-1, -2, 0, -3], @[-1]] for c in Combos: echo fmt"{($c)[1..^1]:15}  →  {linearCombo(c)}"

Output:
[1, 2, 3]        →  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     →  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     →  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        →  e(1) + 2*e(2)
[0, 0, 0]        →  0
[0]              →  0
[1, 1, 1]        →  e(1) + e(2) + e(3)
[-1, -1, -1]     →  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  →  -e(1) - 2*e(2) - 3*e(4)
[-1]             →  -e(1)

## OCaml

let fmt_linear_comb =
let rec head e = function
| 0 :: t -> head (succ e) t
| 1 :: t -> Printf.sprintf "e(%u)%s" e (tail (succ e) t)
| -1 :: t -> Printf.sprintf "-e(%u)%s" e (tail (succ e) t)
| a :: t -> Printf.sprintf "%d*e(%u)%s" a e (tail (succ e) t)
| _ -> "0"
and tail e = function
| 0 :: t -> tail (succ e) t
| 1 :: t -> Printf.sprintf " + e(%u)%s" e (tail (succ e) t)
| -1 :: t -> Printf.sprintf " - e(%u)%s" e (tail (succ e) t)
| a :: t when a < 0 -> Printf.sprintf " - %u*e(%u)%s" (-a) e (tail (succ e) t)
| a :: t -> Printf.sprintf " + %u*e(%u)%s" a e (tail (succ e) t)
| _ -> ""
in

let () =
List.iter (fun v -> print_endline (fmt_linear_comb v)) [
[1; 2; 3];
[0; 1; 2; 3];
[1; 0; 3; 4];
[1; 2; 0];
[0; 0; 0];
[0];
[1; 1; 1];
[-1; -1; -1];
[-1; -2; 0; -3];
[-1]]

Output:
e(1) + 2*e(2) + 3*e(3)
e(2) + 2*e(3) + 3*e(4)
e(1) + 3*e(3) + 4*e(4)
e(1) + 2*e(2)
0
0
e(1) + e(2) + e(3)
-e(1) - e(2) - e(3)
-e(1) - 2*e(2) - 3*e(4)
-e(1)


## Perl

use strict;
use warnings;
use feature 'say';

sub linear_combination {
my(@coef) = @$_; my$e = '';
for my $c (1..+@coef) {$e .= "$coef[$c-1]*e($c) + " if$coef[$c-1] }$e =~ s/ \+ $//;$e =~ s/1\*//g;
$e =~ s/\+ -/- /g;$e or 0;
}

say linear_combination($_) for [1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, -3], [-1 ]  Output: e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) - 3*e(4) -e(1) ## Phix Translation of: Tcl with javascript_semantics function linear_combination(sequence f) string res = "" for e=1 to length(f) do integer fe = f[e] if fe!=0 then if fe=1 then if length(res) then res &= "+" end if elsif fe=-1 then res &= "-" elsif fe>0 and length(res) then res &= sprintf("+%d*",fe) else res &= sprintf("%d*",fe) end if res &= sprintf("e(%d)",e) end if end for if res="" then res = "0" end if return res end function constant tests = {{1,2,3}, {0,1,2,3}, {1,0,3,4}, {1,2,0}, {0,0,0}, {0}, {1,1,1}, {-1,-1,-1}, {-1,-2,0,-3}, {-1}} for i=1 to length(tests) do sequence ti = tests[i] printf(1,"%12s -> %s\n",{sprint(ti), linear_combination(ti)}) end for  Output:  {1,2,3} -> e(1)+2*e(2)+3*e(3) {0,1,2,3} -> e(2)+2*e(3)+3*e(4) {1,0,3,4} -> e(1)+3*e(3)+4*e(4) {1,2,0} -> e(1)+2*e(2) {0,0,0} -> 0 {0} -> 0 {1,1,1} -> e(1)+e(2)+e(3) {-1,-1,-1} -> -e(1)-e(2)-e(3) {-1,-2,0,-3} -> -e(1)-2*e(2)-3*e(4) {-1} -> -e(1)  ## PureBasic ; Process and output values. Procedure WriteLinear(Array c.i(1)) Define buf$,
i.i, j.i, b,i

b = #True
j = 0

For i = 0 To ArraySize(c(), 1)
If c(i) = 0 : Continue : EndIf

If c(i) < 0
If b : Print("-") : Else : Print(" - ") : EndIf
ElseIf c(i) > 0
If Not b : Print(" + ") : EndIf
EndIf

If c(i) > 1
Print(Str(c(i))+"*")
ElseIf c(i) < -1
Print(Str(-c(i))+"*")
EndIf

Print("e("+Str(i+1)+")")

b = #False
j+1
Next

If j = 0 : Print("0") : EndIf
PrintN("")
EndProcedure

; 1. Output of the input values
Define buf$= "[", *adr_ptr For *adr_ptr = Adr_Start To Adr_Stop - SizeOf(Integer) Step SizeOf(Integer) buf$ + Str(PeekI(*adr_ptr))
buf$+ "] -> " Else buf$ + ", "
EndIf
Next
buf$= RSet(buf$, 25)
Print(buf$) ; 2. Reserve memory, pass and process values. Dim a.i((Adr_Stop - Adr_Start) / SizeOf(Integer) -1) CopyMemory(Adr_Start, @a(0), Adr_Stop - Adr_Start) WriteLinear(a()) EndMacro If OpenConsole("") ; Pass memory addresses of the data. VectorHdl(?V1, ?_V1) VectorHdl(?V2, ?_V2) VectorHdl(?V3, ?_V3) VectorHdl(?V4, ?_V4) VectorHdl(?V5, ?_V5) VectorHdl(?V6, ?_V6) VectorHdl(?V7, ?_V7) VectorHdl(?V8, ?_V8) VectorHdl(?V9, ?_V9) VectorHdl(?V10, ?_V10) Input() EndIf End 0 DataSection V1: Data.i 1,2,3 _V1: V2: Data.i 0,1,2,3 _V2: V3: Data.i 1,0,3,4 _V3: V4: Data.i 1,2,0 _V4: V5: Data.i 0,0,0 _V5: V6: Data.i 0 _V6: V7: Data.i 1,1,1 _V7: V8: Data.i -1,-1,-1 _V8: V9: Data.i -1,-2,0,-3 _V9: V10: Data.i -1 _V10: EndDataSection Output:  [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1)  ## Python def linear(x): return ' + '.join(['{}e({})'.format('-' if v == -1 else '' if v == 1 else str(v) + '*', i + 1) for i, v in enumerate(x) if v] or ['0']).replace(' + -', ' - ') list(map(lambda x: print(linear(x)), [[1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, 3], [-1]]))  Output: e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) + 3*e(4) -e(1)  ## Racket #lang racket/base (require racket/match racket/string) (define (linear-combination->string es) (let inr ((es es) (i 1) (rv "")) (match* (es rv) [((list) "") "0"] [((list) rv) rv] [((list (? zero?) t ...) rv) (inr t (add1 i) rv)] [((list n t ...) rv) (define ±n (match* (n rv) ;; zero is handled above [(1 "") ""] [(1 _) "+"] [(-1 _) "-"] [((? positive? n) (not "")) (format "+~a*" n)] [(n _) (format "~a*" n)])) (inr t (add1 i) (string-append rv ±n "e("(number->string i)")"))]))) (for-each (compose displayln linear-combination->string) '((1 2 3) (0 1 2 3) (1 0 3 4) (1 2 0) (0 0 0) (0) (1 1 1) (-1 -1 -1) (-1 -2 0 -3) (-1)))  Output: e(1)+2*e(2)+3*e(3) e(2)+2*e(3)+3*e(4) e(1)+3*e(3)+4*e(4) e(1)+2*e(2) 0 0 e(1)+e(2)+e(3) -e(1)-e(2)-e(3) -e(1)-2*e(2)-3*e(4) -e(1) ## Raku (formerly Perl 6) sub linear-combination(@coeff) { (@coeff Z=> map { "e($_)" }, 1 .. *)
.grep(+*.key)
.map({ .key ~ '*' ~ .value })
.join(' + ')
.subst('+ -', '- ', :g)
.subst(/<|w>1\*/, '', :g)
|| '0'
}

say linear-combination($_) for [1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, -3], [-1 ] ;  Output: e(1) + 2*e(2) + 3*e(3) e(2) + 2*e(3) + 3*e(4) e(1) + 3*e(3) + 4*e(4) e(1) + 2*e(2) 0 0 e(1) + e(2) + e(3) -e(1) - e(2) - e(3) -e(1) - 2*e(2) - 3*e(4) -e(1) ## REXX /*REXX program displays a finite liner combination in an infinite vector basis. */ @.= .; @.1 = ' 1, 2, 3 ' /*define a specific test case for build*/ @.2 = ' 0, 1, 2, 3 ' /* " " " " " " " */ @.3 = ' 1, 0, 3, 4 ' /* " " " " " " " */ @.4 = ' 1, 2, 0 ' /* " " " " " " " */ @.5 = ' 0, 0, 0 ' /* " " " " " " " */ @.6 = 0 /* " " " " " " " */ @.7 = ' 1, 1, 1 ' /* " " " " " " " */ @.8 = ' -1, -1, -1 ' /* " " " " " " " */ @.9 = ' -1, -2, 0, -3 ' /* " " " " " " " */ @.10 = -1 /* " " " " " " " */ do j=1 while @.j\==.; n= 0 /*process each vector; zero element cnt*/ y= space( translate(@.j, ,',') ) /*elide commas and superfluous blanks. */$=                                             /*nullify  output  (liner combination).*/
do k=1  for words(y);     #= word(y, k)   /* ◄───── process each of the elements.*/
if #=0  then iterate;     a= abs(# / 1)   /*if the value is zero, then ignore it.*/
if #<0  then s= '- '                      /*define the sign:   minus (-).        */
else s= '+ '                      /*   "    "    "     plus  (+).        */
n= n + 1                                  /*bump the number of elements in vector*/
if n==1  then s= strip(s)                 /*if the 1st element used, remove blank*/
if a\==1    then s= s  ||  a'*'           /*if multiplier is unity, then ignore #*/
$=$  s'e('k")"                           /*construct a liner combination element*/
end   /*k*/
$= strip( strip($), 'L', "+")                  /*strip leading plus sign (1st element)*/
if $=='' then$= 0                            /*handle special case of no elements.  */
say right( space(@.j), 20)  ' ──► '   strip() /*align the output for presentation. */ end /*j*/ /*stick a fork in it, we're all done. */  output when using the default inputs:  1, 2, 3 ──► e(1) + 2*e(2) + 3*e(3) 0, 1, 2, 3 ──► e(2) + 2*e(3) + 3*e(4) 1, 0, 3, 4 ──► e(1) + 3*e(3) + 4*e(4) 1, 2, 0 ──► e(1) + 2*e(2) 0, 0, 0 ──► 0 0 ──► 0 1, 1, 1 ──► e(1) + e(2) + e(3) -1, -1, -1 ──► -e(1) - e(2) - e(3) -1, -2, 0, -3 ──► -e(1) - 2*e(2) - 3*e(4) -1 ──► -e(1)  ## Ring # Project : Display a linear combination scalars = [[1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, -3], [-1]] for n=1 to len(scalars) str = "" for m=1 to len(scalars[n]) scalar = scalars[n] [m] if scalar != "0" if scalar = 1 str = str + "+e" + m elseif scalar = -1 str = str + "" + "-e" + m else if scalar > 0 str = str + char(43) + scalar + "*e" + m else str = str + "" + scalar + "*e" + m ok ok ok next if str = "" str = "0" ok if left(str, 1) = "+" str = right(str, len(str)-1) ok see str + nl next Output: e1+2*e2+3*e3 e2+2*e3+3*e4 e1+3*e3+4*e4 e1+2*e2 0 0 e1+e2+e3 -e1-e2-e3 -e1-2*e2-3*e4 -e1  ## RPL RPL can handle both stack-based program flows and algebraic expressions, which is quite useful for tasks such as this one. Works with: Halcyon Calc version 4.2.7 ### Straightforward approach This version has the disadvantage of sometimes interchanging some terms when simplifying the expression by the COLCT function. ≪ → scalars ≪ '0' 1 scalars SIZE FOR j scalars j GET "e" j →STR + STR→ * + NEXT COLCT COLCT ≫ ≫ 'COMB→' STO  ### Full-compliant version The constant π is here simply used to facilitate the construction of the algebraic expression; it is then eliminated during the conversion into a string. ≪ → scalars ≪ "" 1 scalars SIZE FOR j 'π' scalars j GET "e" j →STR + STR→ * + →STR OVER SIZE NOT OVER 3 3 SUB "+" AND 4 3 IFTE OVER SIZE 1 - SUB + NEXT ≫ IF DUP "" == THEN DROP "0" END ≫ 'COMB→' STO   ≪ { { 1 2 3 } { 0 1 2 3 } { 1 0 3 4 } { 1 2 0 } {0 0 0 } { 0 } { 1 1 1 } { -1 -1 -1} { -1 -2 0 -3} { -1 } } { } 1 3 PICK SIZE FOR j OVER j GET COMB→ + NEXT SWAP DROP ≫ EVAL  Output: 1: { "e1+2*e2+3*e3" "e2+2*e3+3*e4" "e1+3*e3+4*e4" "e1+2*e2" "0" "0" "e1+e2+e3" "-e1-e2-e3" "-e1-2*e2-3*e4" "-e1" }  ## Ruby Translation of: D def linearCombo(c) sb = "" c.each_with_index { |n, i| if n == 0 then next end if n < 0 then if sb.length == 0 then op = "-" else op = " - " end elsif n > 0 then if sb.length > 0 then op = " + " else op = "" end else op = "" end av = n.abs() if av != 1 then coeff = "%d*" % [av] else coeff = "" end sb = sb + "%s%se(%d)" % [op, coeff, i + 1] } if sb.length == 0 then return "0" end return sb end def main combos = [ [1, 2, 3], [0, 1, 2, 3], [1, 0, 3, 4], [1, 2, 0], [0, 0, 0], [0], [1, 1, 1], [-1, -1, -1], [-1, -2, 0, -3], [-1], ] for c in combos do print "%-15s -> %s\n" % [c, linearCombo(c)] end end main()  Output: [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3) [0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4) [1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4) [1, 2, 0] -> e(1) + 2*e(2) [0, 0, 0] -> 0 [0] -> 0 [1, 1, 1] -> e(1) + e(2) + e(3) [-1, -1, -1] -> -e(1) - e(2) - e(3) [-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4) [-1] -> -e(1) ## Rust use std::fmt::{Display, Formatter, Result}; use std::process::exit; struct Coefficient(usize, f64); impl Display for Coefficient { fn fmt(&self, f: &mut Formatter<'_>) -> Result { let i = self.0; let c = self.1; if c == 0. { return Ok(()); } write!( f, " {} {}e({})", if c < 0. { "-" } else if f.alternate() { " " } else { "+" }, if (c.abs() - 1.).abs() < f64::EPSILON { "".to_string() } else { c.abs().to_string() + "*" }, i + 1 ) } } fn usage() { println!("Usage: display-linear-combination a1 [a2 a3 ...]"); } fn linear_combination(coefficients: &[f64]) -> String { let mut string = String::new(); let mut iter = coefficients.iter().enumerate(); // find first nonzero argument loop { match iter.next() { Some((_, &c)) if c == 0. => { continue; } Some((i, &c)) => { string.push_str(format!("{:#}", Coefficient(i, c)).as_str()); break; } None => { string.push('0'); return string; } } } // print subsequent arguments for (i, &c) in iter { string.push_str(format!("{}", Coefficient(i, c)).as_str()); } string } fn main() { let mut coefficients = Vec::new(); let mut args = std::env::args(); args.next(); // drop first argument // parse arguments into floats for arg in args { let c = arg.parse::<f64>().unwrap_or_else(|e| { eprintln!("Failed to parse argument \"{}\": {}", arg, e); exit(-1); }); coefficients.push(c); } // no arguments, print usage and exit if coefficients.is_empty() { usage(); return; } println!("{}", linear_combination(&coefficients)); }  Output: 1 2 3 -> e(1) + 2*e(2) + 3*e(3)  ## Scala object LinearCombination extends App { val combos = Seq(Seq(1, 2, 3), Seq(0, 1, 2, 3), Seq(1, 0, 3, 4), Seq(1, 2, 0), Seq(0, 0, 0), Seq(0), Seq(1, 1, 1), Seq(-1, -1, -1), Seq(-1, -2, 0, -3), Seq(-1)) private def linearCombo(c: Seq[Int]): String = { val sb = new StringBuilder for {i <- c.indices term = c(i) if term != 0} { val av = math.abs(term) def op = if (term < 0 && sb.isEmpty) "-" else if (term < 0) " - " else if (term > 0 && sb.isEmpty) "" else " + " sb.append(op).append(if (av == 1) "" else s"av*").append("e(").append(i + 1).append(')')
}
if (sb.isEmpty) "0" else sb.toString
}
for (c <- combos) {
println(f"${c.mkString("[", ", ", "]")}%-15s ->${linearCombo(c)}%s")
}
}


## Sidef

Translation of: Tcl
func linear_combination(coeffs) {
var res = ""
for e,f in (coeffs.kv) {
given(f) {
when (1) {
res += "+e(#{e+1})"
}
when (-1) {
res += "-e(#{e+1})"
}
case (.> 0) {
res += "+#{f}*e(#{e+1})"
}
case (.< 0) {
res += "#{f}*e(#{e+1})"
}
}
}
res -= /^\+/
res || 0
}

var tests = [
%n{1 2 3},
%n{0 1 2 3},
%n{1 0 3 4},
%n{1 2 0},
%n{0 0 0},
%n{0},
%n{1 1 1},
%n{-1 -1 -1},
%n{-1 -2 0 -3},
%n{-1},
]

tests.each { |t|
printf("%10s -> %-10s\n", t.join(' '), linear_combination(t))
}

Output:
     1 2 3 -> e(1)+2*e(2)+3*e(3)
0 1 2 3 -> e(2)+2*e(3)+3*e(4)
1 0 3 4 -> e(1)+3*e(3)+4*e(4)
1 2 0 -> e(1)+2*e(2)
0 0 0 -> 0
0 -> 0
1 1 1 -> e(1)+e(2)+e(3)
-1 -1 -1 -> -e(1)-e(2)-e(3)
-1 -2 0 -3 -> -e(1)-2*e(2)-3*e(4)
-1 -> -e(1)     

## Tcl

This solution strives for legibility rather than golf.

proc lincom {factors} {
set exp 0
set res ""
foreach f $factors { incr exp if {$f == 0} {
continue
} elseif {$f == 1} { append res "+e($exp)"
} elseif {$f == -1} { append res "-e($exp)"
} elseif {$f > 0} { append res "+$f*e($exp)" } else { append res "$f*e($exp)" } } if {$res eq ""} {set res 0}
regsub {^\+} $res {} res return$res
}

foreach test {
{1 2 3}
{0 1 2 3}
{1 0 3 4}
{1 2 0}
{0 0 0}
{0}
{1 1 1}
{-1 -1 -1}
{-1 -2 0 -3}
{-1}
} {
puts [format "%10s -> %-10s" $test [lincom$test]]
}

Output:
     1 2 3 -> e(1)+2*e(2)+3*e(3)
0 1 2 3 -> e(2)+2*e(3)+3*e(4)
1 0 3 4 -> e(1)+3*e(3)+4*e(4)
1 2 0 -> e(1)+2*e(2)
0 0 0 -> 0
0 -> 0
1 1 1 -> e(1)+e(2)+e(3)
-1 -1 -1 -> -e(1)-e(2)-e(3)
-1 -2 0 -3 -> -e(1)-2*e(2)-3*e(4)
-1 -> -e(1)     

## Visual Basic .NET

Translation of: C#
Imports System.Text

Module Module1

Function LinearCombo(c As List(Of Integer)) As String
Dim sb As New StringBuilder
For i = 0 To c.Count - 1
Dim n = c(i)
If n < 0 Then
If sb.Length = 0 Then
sb.Append("-")
Else
sb.Append(" - ")
End If
ElseIf n > 0 Then
If sb.Length <> 0 Then
sb.Append(" + ")
End If
Else
Continue For
End If

Dim av = Math.Abs(n)
If av <> 1 Then
sb.AppendFormat("{0}*", av)
End If
sb.AppendFormat("e({0})", i + 1)
Next
If sb.Length = 0 Then
sb.Append("0")
End If
Return sb.ToString()
End Function

Sub Main()
Dim combos = New List(Of List(Of Integer)) From {
New List(Of Integer) From {1, 2, 3},
New List(Of Integer) From {0, 1, 2, 3},
New List(Of Integer) From {1, 0, 3, 4},
New List(Of Integer) From {1, 2, 0},
New List(Of Integer) From {0, 0, 0},
New List(Of Integer) From {0},
New List(Of Integer) From {1, 1, 1},
New List(Of Integer) From {-1, -1, -1},
New List(Of Integer) From {-1, -2, 0, -3},
New List(Of Integer) From {-1}
}

For Each c In combos
Dim arr = "[" + String.Join(", ", c) + "]"
Console.WriteLine("{0,15} -> {1}", arr, LinearCombo(c))
Next
End Sub

End Module

Output:
      [1, 2, 3] -> e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3] -> e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4] -> e(1) + 3*e(3) + 4*e(4)
[1, 2, 0] -> e(1) + 2*e(2)
[0, 0, 0] -> 0
[0] -> 0
[1, 1, 1] -> e(1) + e(2) + e(3)
[-1, -1, -1] -> -e(1) - e(2) - e(3)
[-1, -2, 0, -3] -> -e(1) - 2*e(2) - 3*e(4)
[-1] -> -e(1)

## V (Vlang)

Translation of: Go
import strings

fn linear_combo(c []int) string {
mut sb := strings.new_builder(128)
for i, n in c {
if n == 0 {
continue
}
mut op := ''
match true {
n < 0 && sb.len == 0 {
op = "-"
}
n < 0{
op = " - "
}
n > 0 && sb.len == 0 {
op = ""
}
else{
op = " + "
}
}
mut av := n
if av < 0 {
av = -av
}
mut coeff := "$av*" if av == 1 { coeff = "" } sb.write_string("$op${coeff}e(${i+1})")
}
if sb.len == 0 {
return "0"
} else {
return sb.str()
}
}

fn main() {
combos := [
[1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1],
]
for c in combos {
println("${c:-15} ->${linear_combo(c)}")
}
}
Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)


## Wren

Translation of: Kotlin
Library: Wren-fmt
import "./fmt" for Fmt

var linearCombo = Fn.new { |c|
var sb = ""
var i = 0
for (n in c) {
if (n != 0) {
var op = (n < 0 && sb == "") ? "-"   :
(n < 0)             ? " - " :
(n > 0 && sb == "") ? ""    : " + "
var av = n.abs
var coeff = (av == 1) ? "" : "%(av)*"
sb = sb + "%(op)%(coeff)e(%(i + 1))"
}
i = i + 1
}
return (sb == "") ? "0" : sb
}

var combos = [
[1, 2, 3],
[0, 1, 2, 3],
[1, 0, 3, 4],
[1, 2, 0],
[0, 0, 0],
[0],
[1, 1, 1],
[-1, -1, -1],
[-1, -2, 0, -3],
[-1]
]
for (c in combos) {
Fmt.print("$-15s ->$s", c.toString, linearCombo.call(c))
}

Output:
[1, 2, 3]        ->  e(1) + 2*e(2) + 3*e(3)
[0, 1, 2, 3]     ->  e(2) + 2*e(3) + 3*e(4)
[1, 0, 3, 4]     ->  e(1) + 3*e(3) + 4*e(4)
[1, 2, 0]        ->  e(1) + 2*e(2)
[0, 0, 0]        ->  0
[0]              ->  0
[1, 1, 1]        ->  e(1) + e(2) + e(3)
[-1, -1, -1]     ->  -e(1) - e(2) - e(3)
[-1, -2, 0, -3]  ->  -e(1) - 2*e(2) - 3*e(4)
[-1]             ->  -e(1)


## zkl

Translation of: Raku
fcn linearCombination(coeffs){
[1..].zipWith(fcn(n,c){ if(c==0) "" else "%s*e(%s)".fmt(c,n) },coeffs)
.filter().concat("+").replace("+-","-").replace("1*","")
or 0
}
T(T(1,2,3),T(0,1,2,3),T(1,0,3,4),T(1,2,0),T(0,0,0),T(0),T(1,1,1),T(-1,-1,-1),
T(-1,-2,0,-3),T(-1),T)
.pump(Console.println,linearCombination);
Output:
e(1)+2*e(2)+3*e(3)
e(2)+2*e(3)+3*e(4)
e(1)+3*e(3)+4*e(4)
e(1)+2*e(2)
0
0
e(1)+e(2)+e(3)
-e(1)-e(2)-e(3)
-e(1)-2*e(2)-3*e(4)
-e(1)
0