Display a linear combination

Display a linear combination is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The purpose of this task is to display a finite linear combination in an infinite vector basis $(e_{0},e_{1},\ldots )$.

Write a function that, when given a finite list of scalars $(\alpha ^{1},\alpha ^{2},\ldots )$, creates a string representing the linear combination

$\sum _{i}\alpha ^{i}e_{i}$

Your output must comply to the following rules:

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

Perl 6

<lang perl6>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 ]

</lang>

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)

zkl

Translation of: Perl 6

<lang zkl>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

}</lang> <lang zkl>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);</lang>

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