Task

Display a finite linear combination in an infinite vector basis 



(

e

1


,

e

2


,
…
)


{\displaystyle (e_{1},e_{2},\ldots )}

.

Write a function that, when given a finite list of scalars 



(

α

1


,

α

2


,
…
)


{\displaystyle (\alpha ^{1},\alpha ^{2},\ldots )}

, 
creates a string representing the linear combination 




∑

i



α

i



e

i




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

 in an explicit format often used in mathematics, that is:






α


i

1





e


i

1




±

|


α


i

2





|


e


i

2




±

|


α


i

3





|


e


i

3




±
…


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


where 




α


i

k




≠
0


{\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



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))
    }
}