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>my @examples =

sub linear-combination(@coeff) {

   my @terms = @coeff Z=> map { "e($_)" }, 1 .. *;

   @terms.=grep(+*.key);

   return '0' unless @terms;

   my $result = join '+',
   map { .key ~ '*' ~ .value },
   @terms;

   $result ~~ s:g/'+-'/-/;
   $result ~~ s:g/<|w>1\*//;
   return $result;

}

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)