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.