;Task:
Display a finite [[wp:linear combination|linear combination]] in an infinite vector basis <big><math>(e_1, e_2,\ldots)</math></big>.

Write a function that, when given a finite list of scalars <big><math>(\alpha^1,\alpha^2,\ldots)</math></big>, <br>creates a string representing the linear combination <big><math>\sum_i\alpha^i e_i</math></big> in an explicit format often used in mathematics, that is:

:<big><math>\alpha^{i_1}e_{i_1}\pm|\alpha^{i_2}|e_{i_2}\pm|\alpha^{i_3}|e_{i_3}\pm\ldots</math></big>

where <big><math>\alpha^{i_k}\neq 0</math></big>


<br>
The output must comply to the following rules:
* &nbsp; don't show null terms, unless the whole combination is null. 
:::::::  '''e(1)''' &nbsp; &nbsp; is fine, &nbsp; &nbsp; '''e(1) + 0*e(3)''' &nbsp; &nbsp; or &nbsp; &nbsp; '''e(1) + 0''' &nbsp; &nbsp; is wrong.
* &nbsp; don't show scalars when they are equal to one or minus one. 
:::::::  '''e(3)''' &nbsp; &nbsp; is fine, &nbsp; &nbsp; '''1*e(3)''' &nbsp; &nbsp; is wrong.
* &nbsp; don't prefix by a minus sign if it follows a preceding term. &nbsp; Instead you use subtraction. 
:::::::  '''e(4) - e(5)''' &nbsp; &nbsp; is fine, &nbsp; &nbsp; '''e(4) + -e(5)''' &nbsp; &nbsp; is wrong.

<br>
Show here output for the following lists of scalars:
<pre>
 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
</pre>
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