# Unicode polynomial equation

This task has been flagged for clarification due to it being believed to be too difficult to implement in a reasonable amount of effort in more than one (usually very specialised) language. It may need to be divided into multiple tasks or modified substantially so that multiple implementations are practical, and that may cause code on this page in its current state to be flagged incorrect afterwards. See this page's Talk page for discussion.
Unicode polynomial equation 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 objective of this task is to parse in a difficult polynomial, and generate a "pretty" representation of the polynomial in Unicode.

In the target language define a "polynomial" object (or structure or record). Using this object also define the routines for parsing a polynomial as input, and generating a normalised Unicode representation of the polynomial as output.

Given a string containing an untidy Unicode polynomial, e.g.

```-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹
```

Coerce (or convert) the string into the "polynomial" object, at the same time normalise the polynomial to a canonical form. The ideal normalised output (in this example) would be:

```x⁵ - 2x⁴ + 42x³ + 40x + 1
```
Specific examples of Unicode and polynomial texts to be parsed as test cases.
Description Input example test cases
"Zero" coefficients are removed x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
The "0" polynomial case 0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
"One" coefficients are normalised 1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
Signs are normalised +x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
ASCII representations are parsed x^5 - 2x**4 + 42x^3 + 40x + 1
Non-ASCII representations are parsed x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1 (c.f. & ·)
Specifically permit non-polynomials where terms have negative exponents x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰ (n.b. Unicode Fraction)
Spaces in numbers and between operators are ignored x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
Single commas are ignored in numbers x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
A coefficient may be duplicated, zero, or missing 0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
Support Scientific notation and optionally
support Unicode Decimal Exponent Symbol U+23E8/⏨
1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
Unicode characters that must be specifically supported are: ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁻ ⁺ · × ⁄ ↑ ⏨.
Where · & × are multiplication, and ⁄ is Unicode Fraction.
Support fractions for both input and output. x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
On output round the decimal to appropriate fraction.
Optionally support Unicode Vulgar fractions for both input and output.
¼ ½ ¾ ⅐ ⅑ ⅒ ⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞ ↉
x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
On output round the decimal to appropriate fraction.

There are (at least) three possible ways of achieving this task.

• Using an external parsing library.
• Using a built-in parsing/formatting library.
• Coding a custom polynomial parsing routing.

Either one, or all of these approaches are accepted and appear as a subtitle.

## Go

Although this program provides full support for Unicode vulgar fractions, note that there is no guarantee that they (or arithmetic on them) will successfully 'round trip' due to floating point arithmetic being used in the underlying calculations and some of them being recurring rather than exact decimals in any case.

```package main

import (
"fmt"
"log"
"math"
"regexp"
"strconv"
"strings"
)

var powers = strings.NewReplacer(
"0", "⁰",
"1", "¹",
"2", "²",
"3", "³",
"4", "⁴",
"5", "⁵",
"6", "⁶",
"7", "⁷",
"8", "⁸",
"9", "⁹",
"-", "⁻",
)

var fractions = [][2]string{
{".25", "¼"},
{".5", "½"},
{".75", "¾"},
{".14285714285714285", "⅐"},
{".1111111111111111", "⅑"},
{".1", "⅒"},
{".3333333333333333", "⅓"},
{".6666666666666666", "⅔"},
{".2", "⅕"},
{".4", "⅖"},
{".6", "⅗"},
{".8", "⅘"},
{".16666666666666666", "⅙"},
{".8333333333333334", "⅚"},
{".125", "⅛"},
{".375", "⅜"},
{".625", "⅝"},
{".875", "⅞"},
}

func printEquation(coefs map[int]float64) {
fmt.Print("=> ")
if len(coefs) == 0 {
fmt.Println("0\n")
return
}
max, min := math.MinInt32, math.MaxInt32
for k := range coefs {
if k > max {
max = k
}
if k < min {
min = k
}
}
for p := max; p >= min; p-- {
if c := coefs[p]; c != 0 {
if p < max {
sign := "+"
if c < 0 {
sign = "-"
c = -c
}
fmt.Printf(" %s ", sign)
}
if c != 1 || (c == 1 && p == 0) {
cs := fmt.Sprintf("%v", c)
ix := strings.Index(cs, ".")
if ix >= 0 {
dec := cs[ix:]
for _, frac := range fractions {
if dec == frac[0] {
cs = strings.Replace(cs, dec, frac[1], 1)
break
}
}
}
if cs[0] == '0' && len(cs) > 1 && cs[1] != '.' {
cs = cs[1:]
}
fmt.Print(cs)
}
if p != 0 {
ps := strconv.Itoa(p)
ps = powers.Replace(ps)
if ps == "¹" {
ps = ""
}
fmt.Printf("x%s", ps)
}
}
}
fmt.Println("\n")
}

func check(err error) {
if err != nil {
log.Fatal(err)
}
}

func main() {
equs := []string{
`-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹`,
`x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1`,
`0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵`,
`1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰`,
`+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1`,
`x^5 - 2x**4 + 42x^3 + 40x + 1`,
`x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1`,
`x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰`,
`x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1`,
`x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1`,
`0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1`,
`1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1`,
`x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2`,
`x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5`,
`x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x`,
`⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝`,
}
rgx := regexp.MustCompile(`\s+(\+|-)\s+`)
rep := strings.NewReplacer(
",", "",
" ", "",
"¼", ".25",
"½", ".5",
"¾", ".75",
"⅐", ".14285714285714285",
"⅑", ".1111111111111111",
"⅒", ".1",
"⅓", ".3333333333333333",
"⅔", ".6666666666666666",
"⅕", ".2",
"⅖", ".4",
"⅗", ".6",
"⅘", ".8",
"⅙", ".16666666666666666",
"⅚", ".8333333333333334",
"⅛", ".125",
"⅜", ".375",
"⅝", ".625",
"⅞", ".875",
"↉", ".0",
"⏨", "e",
"⁄", "/",
)
rep2 := strings.NewReplacer(
"⁰", "0",
"¹", "1",
"²", "2",
"³", "3",
"⁴", "4",
"⁵", "5",
"⁶", "6",
"⁷", "7",
"⁸", "8",
"⁹", "9",
"⁻⁻", "",
"⁻", "-",
"⁺", "",
"**", "",
"^", "",
"↑", "",
"⁄", "/",
)
var err error
for _, equ := range equs {
fmt.Println(equ)
terms := rgx.Split(equ, -1)
ops := rgx.FindAllString(equ, -1)
for i := 0; i < len(ops); i++ {
ops[i] = strings.TrimSpace(ops[i])
}
coefs := make(map[int]float64)
for i, term := range terms {
s := strings.Split(term, "x")
t := s[0]
t = strings.TrimRight(t, "·× ")
t = rep.Replace(t)
c := 1.0
inverse := false
if t == "" || t == "+" || t == "-" {
t += "1"
}
ix := strings.Index(t, "/")
if ix == len(t)-1 {
inverse = true
t = t[0 : len(t)-1]
c, err = strconv.ParseFloat(t, 64)
check(err)
} else if ix >= 0 {
u := strings.Split(t, "/")
m, err := strconv.ParseFloat(u[0], 64)
check(err)
n, err := strconv.ParseFloat(u[1], 64)
check(err)
c = m / n
} else {
c, err = strconv.ParseFloat(t, 64)
check(err)
}
if i > 0 && ops[i-1] == "-" {
c = -c
}
if c == -0.0 {
c = 0
}
if len(s) == 1 {
coefs[0] += c
continue
}
u := s[1]
u = strings.TrimSpace(u)
if u == "" {
p := 1
if inverse {
p = -1
}
if c != 0 {
coefs[p] += c
}
continue
}
u = rep2.Replace(u)
jx := strings.Index(u, "/")
p := 1
if jx >= 0 {
v := strings.Split(u, "/")
p, err = strconv.Atoi(v[0])
if (err != nil) {
p = 1
}
d, err := strconv.ParseFloat(v[1], 64)
check(err)
c /= d
} else {
p, err = strconv.Atoi(strings.TrimSpace(u))
if (err != nil) {
p = 1
}
}
if inverse {
p = -p
}
if c != 0 {
coefs[p] += c
}
}
printEquation(coefs)
}
}
```
Output:
```-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
=> 0

1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x^5 - 2x**4 + 42x^3 + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰
=> 1 + 40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵

x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x
=> -40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵

⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝
=> ⅐x⁵ - x⁴ + 42⅕x³ + ⅑x - 40¾
```

## Julia

The task allows the "polynomials" to be parsed to have negative exponents. This makes them Laurent polynomials, not ordinary polynomials.

```import Base.print

struct LaurentPolynomial{T}
powtocoef::Dict{Int,T}
varname::Char
end

function tosuper(i)
s = ""
if i != 1
if i < 0
s = "\u207b"
i = -i
end
s *= prod([reverseudi[x] for x in reverse(digits(i))])
end
return s
end

function print(io::IO, lp::LaurentPolynomial)
if isempty(lp.powtocoef) || all(iszero, values(lp.powtocoef))
print("0")
return
end
firstterm = true
dorev = minimum(keys(lp.powtocoef)) >= 0
for p in sort!(collect(lp.powtocoef), lt =(a,b)->a[1]<b[1], rev=dorev)
e, c = p[1], p[2]
if c != 0
if !firstterm
print(c < 0 ? " - " : " + ")
c = abs(c)
end
sfrac = get(tofracs, c - trunc(c), "")
sint = string(Int(trunc(c)))
s = round(c) == c ? sint : sfrac == "" ? string(c) :
sint == "0" ? sfrac : sint * sfrac
print(c == 1 && e != 0 ? "" : s)
e != 0 && print(lp.varname, tosuper(e))
firstterm = false
end
end
end

const uniexp = [['\u2070', '\u00b9', '\u00b2', '\u00b3']; collect('\u2074':'\u2079')]
const allsuper = String(vcat(uniexp, ['\u207a', '\u207b']))
const udi = Dict([u => i-1 for (i, u) in enumerate(uniexp)])
const reverseudi = Dict([v => k for (k, v) in udi])
const uch = Dict(['\u207a' => '+', '\u207b' => '-', '\u00b7' => ' ',
'\u00d7' => ' ', '\u2091' => '^', '\u23e8' => 'E'])
const fracs = Dict(['¼' => "\$(1/4)", '½' => "\$(1/2)", '¾' => "\$(3/4)", '⅐' => "\$(1/7)",
'⅑' => "\$(1/9)", '⅒' => "\$(1/10)", '⅓' => "\$(1/3)", '⅔' => "\$(2/3)", '⅕' => "\$(1/5)",
'⅖' => "\$(2/5)", '⅗' => "\$(3/5)", '⅘' => "\$(4/5)", '⅙' => "(1/6)", '⅚' => "\$(5/6)",
'⅛' => "\$(1/8)", '⅜' => "\$(3/8)", '⅝' => "\$(5/8)", '⅞' => "\$(7/8)", '↉' => "\$(0/3)"])
const tofracs = Dict(0.25 => '¼', 0.5 => '½', 0.75 => '¾', 0.2 => '⅕')
allfrac = join(vcat(collect(keys(fracs))), "|")

utoascii(c) = (x = haskey(udi, c) ? Char('0' + udi[c]) : haskey(uch, c) ? uch[c] : c)

function fcoef(termstring, varname)
m = match(r"(\d+)⁄(\d+)", termstring).captures
return "\$(parse(Float64, m[1])/parse(Float64, m[2]))\$varname^0"
end

function xcoef(termstring, varname)
m = match(Regex("(\\d+)\$varname([^⁄\\+]*)⁄(\\d+)"), termstring).captures
coe = parse(Float64, m[1])/parse(Float64, m[3])
return "\$(coe)\$varname\$(m[2])"
end

function fromvfrac(termstring)
m = match(r"(\d*)(\D+)", termstring).captures
s = string((m[1] == "" ? 0 : parse(Float64, m[1])) + parse(Float64, fracs[m[2][1]]))
end

function normalizeexpression(s, varname='x')
s = replace(s, Regex("\\d*(" * allfrac * ")") => (x) -> fromvfrac(x))
s = replace(replace(s, r"[^\+].+" => (x) -> "+\$x"), r".+[^\+]\$" => (x) -> "\$x+")
s = replace(replace(replace(s, r"\s+" => ""), r"\*\*|↑" => "^"), "\u23e8" => "e")
s = replace(s, Regex(varname * "(?=[\$allsuper]+)") => "\$varname^")
s = replace(prod([utoascii(c) for c in s]), r"\s+" => "")
s = replace(s, r"[\-\+]+" => (x) -> isodd(count(y -> y == '-', x)) ? "+-" : "+")
s = replace(replace(s, r"\^\+\-" => "^-"), r"\^\+" => "^")
s = replace(s, Regex("(?<=[\\-\\+])\$varname") => "1\$varname")
s = replace(s, r"(\d+)x([^⁄\+]*)⁄(\d+)" => (x) -> xcoef(x, varname))
s = replace(s, r"(?<=[0-9])(,)(?=[0-9])" => "")
s = replace(s, r"\d+⁄\d+" => (x) -> fcoef(x, varname))
s = replace(s, r"\+([\d\.]+)\+" => SubstitutionString("+\\1\$varname^0+"))
return replace(s, Regex("(⁄|/)(" * varname * ")\\^?") =>
(x) -> varname * (x[end] == '^' ? "^-" : "^-1"))
end

function topoly(s::String, varname='x')
allcoef = Dict{Int,Float64}(0 => 0.0)
s = normalizeexpression(s, varname)
reg = Regex("[\\.\\-\\+\\deE\\/]*" * varname * "(?:\\^[\\d\\-]+)?(?=(?:[^\\+\\-]?(?:\\+|\\-)))")
matched = collect(eachmatch(reg, s))
pairs = [split(x.match, varname * "^") for x in matched]
for p in pairs
p[1] = replace(p[1], "+-" => "-")
if length(p) == 1
push!(p, "1")
p[1] = replace(p[1], Regex(varname * "\\$") => "")
end
coef, expo = tryparse(Float64, p[1]), tryparse(Int, p[2])
coef = coef == nothing ? 1.0 : coef
expo = expo == nothing ? 1 : expo
coef += allcoef[expo]
end
allcoef[expo] = coef
end
return LaurentPolynomial(allcoef, varname)
end

testcases = [
"1x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1",
"0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵",
"1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰",
"+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1",
"x^5 - 2x**4 + 42x^3 + 40x + 1",
"x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1",
"x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰",
"x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1",
"x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1",
"0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1",
"1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1",
"x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2",
"x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½",
]

for s in testcases
println(lpad(s, 48), "  =>  ", topoly(s, 'x'))
end
```
Output:
```                1x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵  =>  0
1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
x^5 - 2x**4 + 42x^3 + 40x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰  =>  x⁻⁵ - 2x⁻⁴ + 42x⁻³ + 40x⁻¹ + 1
x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1  =>  x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2  =>  x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½  =>  x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
```

## Nim

Translation of: Go
```import re, sequtils, strutils, tables
from unicode import toRunes

const

Powers = [("0", "⁰"), ("1", "¹"), ("2", "²"), ("3", "³"), ("4", "⁴"),
("5", "⁵"), ("6", "⁶"), ("7", "⁷"), ("8", "⁸"), ("9", "⁹")]

Fractions = [(".25", "¼"), (".5", "½"), (".75", "¾"), (".14285714285714", "⅐"),
(".11111111111111", "⅑"), (".1", "⅒"), (".33333333333333", "⅓"),
(".66666666666667", "⅔"), (".2", "⅕"), (".4", "⅖"), (".6", "⅗"),
(".8", "⅘"), (".16666666666667", "⅙"), (".83333333333333", "⅚"),
(".125", "⅛"), (".375", "⅜"), (".625", "⅝"), (".875", "⅞")]

Reps1 = [(",", ""), (" ", ""), ("¼", ".25"), ("½", ".5"), ("¾", ".75"),
("⅐", ".14285714285714"), ("⅑", ".11111111111111"), ("⅒", ".1"),
("⅓", ".33333333333333"), ("⅔", ".66666666666667"), ("⅕", ".2"),
("⅖", ".4"), ("⅗", ".6"), ("⅘", ".8"), ("⅙", ".16666666666667"),
("⅚", ".83333333333333"), ("⅛", ".125"), ("⅜", ".375"), ("⅝", ".625"),
("⅞", ".875"), ("↉", ".0"), ("⏨", "e"), ("⁄", "/")]

Reps2 = [("⁰", "0"), ("¹", "1"), ("²", "2"), ("³", "3"), ("⁴", "4"), ("⁵", "5"),
("⁶", "6"), ("⁷", "7"), ("⁸", "8"), ("⁹", "9"), ("⁻⁻", ""), ("⁻", "-"),
("⁺", ""), ("**", ""), ("^", ""), ("↑", ""), ("⁄", "/")]

Eqs = [
"-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹",
"x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1",
"0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵",
"1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰",
"+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1",
"x^5 - 2x**4 + 42x^3 + 40x + 1",
"x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1",
"x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰",
"x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1",
"x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1",
"0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1",
"1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1",
"x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2",
"x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5",
"x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x",
"⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝"]

type Coefs = Table[int, float]

proc printEquation(coefs: Coefs) =
stdout.write "=> "
if coefs.len == 0:
echo "0\n"
return

var max = int.low
var min = int.high
for k in coefs.keys:
if k > max: max = k
if k < min: min = k

for p in countdown(max, min):
var c = coefs.getOrDefault(p)
if c != 0:
if p < max:
var sign = '+'
if c < 0:
sign = '-'
c = -c
stdout.write ' ', sign, ' '

if c != 1 or (c == 1 and p == 0):
var cs = \$c
cs.trimZeros()
let ix = cs.find('.')
if ix >= 0:
let d = cs[ix..^1]
for frac in Fractions:
if d == frac[0]:
cs = cs.replace(d, frac[1])
break
if cs[0] == '0' and cs.len > 1 and cs[1] != '.':
cs = cs[1..^1]
stdout.write cs

if p != 0:
var ps = (\$p).multiReplace(Powers)
if ps == "¹": ps = ""
stdout.write 'x', ps

echo '\n'

template getFloat(s: string): float =
try:
s.parseFloat()
except ValueError:
quit "Expected float, got: " & s, QuitFailure

let rgx = re"\s+(\+|-)\s+"

for eq in Eqs:
echo eq
let terms = eq.split(rgx)
let ops = toSeq(eq.findAll(rgx)).mapIt(it.strip())
var coefs: Coefs
for i, term in terms:

let s = term.split("x")
var t = s[0]
t = unicode.strip(t, runes = "·× ".toRunes)
t = t.multiReplace(Reps1)
var c = 1.0
var inverse = false
if t == "" or t == "+" or t == "-": t &= '1'

let ix = t.find('/')
if ix == t.high:
inverse = true
t.setLen(t.high)
c = t.getFloat()
elif ix >= 0:
let u = t.split('/')
let m = u[0].getFloat()
let n = u[1].getFloat()
c = m / n
else:
c = t.getFloat()
if i > 0 and ops[i - 1] == "-": c = -c
if c == -0.0: c = 0.0

if s.len == 1:
coefs[0] = coefs.getOrDefault(0) + c
continue

var u = s[1].strip()
if u.len == 0:
let p = if inverse: -1 else: 1
if c != 0:
coefs[p] = coefs.getOrDefault(p) + c
continue

u = u.multiReplace(Reps2)
let jx = u.find('/')
var p: int
if jx >= 0:
let v = u.split('/')
p = try: v[0].parseInt() except ValueError: 1
let d = v[1].getFloat()
c /= d
else:
p = try: u.strip().parseInt() except ValueError: 1
if inverse: p = -p
if c != 0: coefs[p] = coefs.getOrDefault(p) + c

printEquation(coefs)
```
Output:
```-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
=> 0

1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x^5 - 2x**4 + 42x^3 + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰
=> 1 + 40x-¹ + 42x-³ - 2x-⁴ + x-⁵

x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x
=> -40x-¹ + 42x-³ - 2x-⁴ + x-⁵

⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝
=> ⅐x⁵ - x⁴ + 42⅕x³ + ⅑x - 40¾```

## Phix

To simplify this task I first created a test file (save as utf8, Unicode_polynomial_equation.e):

```constant raw_text = """
-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
===> x^5 - 2x^4 + 42x^3 + 40x + 1
x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
==> 0
1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x^5 - 2x**4 + 42x^3 + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰
==> 1 + 40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵
===> 1 + 40x^-1 + 42x^-3 - 2x^-4 + x^-5
x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
==> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
===> x^5 - 0.5x^4 + 101.25x^3 + 100.75x + 2.5
x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
==> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½
x<sup>5</sup> - 2x<sup>4</sup> + 42x<sup>3</sup> + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x^5 - 2x^4 + 42x^3 + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x⁵ - 2x⁴ + 42x³ + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
x5 - 2x4 + 42x3 + 40x + 1
==> x⁵ - 2x⁴ + 42x³ + 40x + 1
"""
global function get_lines()
return split(raw_text,"\n")
end function
```

Explanation:
On finding a line beginning with "==> ", parse the previous line and check that the output matches the rest of the line.
Lines beginning "===> " contain alternative (valid) representations of the previous line, for use when uni_frac is false. Note these equivalences can then be used further on, eg the result on line 5 maps to line 3 via 2, not that it matters should the same equivalent be defined twice, and also note that "==> " should always be the unicode version and "===> " the ascii one.

Obviously this is not well tested and //will// fail on the next thing thrown at it, but it shows the basic approach. Error handling omitted using that good ol' standby excuse "for clarity".

Note that space is not skipped when getting exponents, otherwise it might wrongly treat say "x + 2" as "x^2", since we /are/ allowing exponentiation symbols to be omitted. At the start of parse() we strip spaces around '^' (etc) to help with that.

Processing the input in utf32 form is a complete no-brainer; whereas constructing utf8 output is a little more subtle, but avoids creating a utf32 "string" just because all bytes happen to be less than 255, which would not necessarily be valid utf8/32.

```-- demo\rosetta\Unicode_polynomial_equation.exw
constant uni_frac = platform()!=WINDOWS -- if true output unicode superscripts and vulgar fractions

constant UTF8BOM = {#EF,#BB,#BF},
SPTWO = #00B2,         -- superscript two
STHRE = #00B3,         -- superscript three
MIDOT = #00B7,         -- middle dot
SPONE = #00B9,         -- superscript one
QUART = #00BC,         -- one quarter
AHALF = #00BD,         -- one half
THQTR = #00BE,         -- three quarters
MULTY = #00D7,         -- multiplication sign
DIVDE = #2044,         -- division sign
SZERO = #2070,         -- superscript zero
SFOUR = #2074,         -- superscript four
SFIVE = #2075,         -- superscript five
SPSIX = #2076,         -- superscript six
SSEVN = #2077,         -- superscript seven
SEGHT = #2078,         -- superscript eight
SNINE = #2079,         -- superscript nine
SPLUS = #207A,         -- superscript plus
SMNUS = #207B,         -- superscript minus
SVNTH = #2150,         -- one seventh
NINTH = #2151,         -- one ninth
TENTH = #2152,         -- one tenth
THIRD = #2153,         -- one third
TWTHD = #2154,         -- two thirds
FIFTH = #2155,         -- one fifth
TWFTH = #2156,         -- two fifths
THFTH = #2157,         -- three fifths
FRFTH = #2158,         -- four fifths
SIXTH = #2159,         -- one sixth
FVSIX = #215A,         -- five sixths
EIGTH = #215B,         -- one eigth
THEGH = #215C,         -- three eigths
FVEGH = #215D,         -- five eigths
UPARW = #2191,         -- uparrow
BASET = #23E8,         -- base 10
SPACE = ' ',           -- space
T = 10             -- align nxt tbl

constant {vulgar_fractions,unicode_vulgar_fractions} = columnize({{{1,4},QUART},
{{1,2},AHALF},
{{3,4},THQTR},
{{1,7},SVNTH},
{{1,9},NINTH},
{{1,T},TENTH},
{{1,3},THIRD},
{{2,3},TWTHD},
{{1,5},FIFTH},
{{2,5},TWFTH},
{{3,5},THFTH},
{{4,5},FRFTH},
{{1,6},SIXTH},
{{5,6},FVSIX},
{{1,8},EIGTH},
{{3,8},THEGH},
{{5,8},FVEGH}})

constant EXPONENTS = {SZERO,SPONE,SPTWO,STHRE,SFOUR,SFIVE,SPSIX,SSEVN,SEGHT,SNINE}

function skip(sequence s, integer sdx, sequence set)
while sdx<=length(s)
and find(s[sdx],set) do
sdx += 1
end while
return sdx
end function

function get_sign(sequence s, integer sdx, bool allow_superscripts)
integer sgn = +1, ch
for i=sdx to length(s) do
ch = s[sdx]
if allow_superscripts then
ch = iff(ch=SPLUS?'+':
iff(ch=SMNUS?'-':
iff(ch=SPACE?'?':ch))) -- (do not skip spaces, see note)
end if
if ch!='+'
and ch!=' ' then
if ch!='-' then exit end if
sgn *= -1
end if
sdx += 1
end for
return {sgn,sdx}
end function

function get_num(sequence s, integer sdx, atom n=0, bool allow_superscripts=false, as_fraction=false)
integer sgn = +1, ch, f, e10, d = 1
atom p10 = 10
bool none = not as_fraction -- (cope with "x" == "1x^1" and != "0x^0")
-- (but not when processing the "34" of "12.34", obvs)
if not as_fraction then
{sgn,sdx} = get_sign(s,sdx,allow_superscripts)
end if
if not allow_superscripts then
sdx = skip(s,sdx,{' '})
end if
for i=sdx to length(s) do
ch = s[sdx]
if ch>='0' and ch<='9' then
if as_fraction then
n += (ch-'0')/p10
p10 *= 10
else
n = n*10+ch-'0'
end if
none = false
elsif allow_superscripts then
f = find(ch,EXPONENTS)
if f=0 then exit end if
n = n*10+f-1
none = false
elsif not find(ch," ,") then
exit
end if
sdx += 1
end for
if not allow_superscripts then
if find(ch,{'e','E',BASET}) then
{e10,f,sdx} = get_num(s,sdx+1)
if f!=1 then ?9/0 end if
n *= power(10,e10)
elsif ch='.' then
if as_fraction then ?9/0 end if
{n,f,sdx} = get_num(s,sdx+1,n,as_fraction:=true)
if f!=1 then ?9/0 end if
none = false
else
f = find(ch,unicode_vulgar_fractions)
if f!=0 then
if as_fraction then ?9/0 end if
integer {vfn,vfd} = vulgar_fractions[f]
if uni_frac then
n = n*vfd + vfn
if d!=1 then ?9/0 end if
d = vfd
else
n += vfn/vfd
end if
sdx += 1
none = false
end if
end if
end if
if none then n = 1 end if
n *= sgn
return {n,d,sdx}
end function

function get_term(sequence s, integer sdx)
integer last_sdx = sdx, -- (infinite loop check/prevent)
e = 0
atom c, d = 1, f
bool sdiv = false
{c,d,sdx} = get_num(s,sdx)
sdx = skip(s,sdx,{' ',MIDOT,MULTY})
if sdx<=length(s)
and (s[sdx]='/' or
s[sdx]=DIVDE) then
sdx += 1
if sdx<=length(s) and s[sdx]!='x' then
{d,f,sdx} = get_num(s,sdx)
if f!=1 then ?9/0 end if
if not uni_frac then
c /= d
d = 1
end if
else
sdiv = true
end if
end if
if sdx<=length(s) and s[sdx]='x' then
sdx = skip(s,sdx+1,{'^','*',SPLUS,UPARW})
{e,f,sdx} = get_num(s,sdx,allow_superscripts:=true)
if f!=1 then ?9/0 end if
if sdiv then e = -e end if
else
if sdiv then ?9/0 end if
end if
if sdx<=length(s)
and (s[sdx]='/' or
s[sdx]=DIVDE) then
if d!=1 then ?9/0 end if
{d,f,sdx} = get_num(s,sdx+1)
if f!=1 then ?9/0 end if
if not uni_frac then
c /= d
d = 1
end if
end if
if sdx=last_sdx then ?9/0 end if
return {e,c,d,sdx}
end function

function unicode_superscripts(integer e)
-- display helper
string res = ""
if e>9 then
res = unicode_superscripts(floor(e/10))
e = remainder(e,10)
end if
res &= utf32_to_utf8({EXPONENTS[e+1]})
return res
end function

enum EXP, COEF, FRAC    -- contents of terms[i]

function poly(sequence terms)
-- display helper
string r = ""
for t=length(terms) to 1 by -1 do
{integer e, atom c, integer f} = terms[t]
if c!=0 then
if c=1 and f=1 and e!=0 then
r &= iff(r=""? "":" + ")
elsif c=-1 and f=1 and e!=0 then
r &= iff(r=""?"-":" - ")
else
if r!="" then
r &= iff(c<0?" - ":" + ")
c = abs(c)
end if
if f!=1 then    -- (hence/only when uni_frac==true)
integer k = find({remainder(c,f),f},vulgar_fractions)
if k then
c = floor(c/f)
if c!=0 then r &= sprintf("%d",c) end if
r &= utf32_to_utf8({unicode_vulgar_fractions[k]})
else
r &= sprintf("%g",c/f)
end if
else
r &= sprintf("%g",c)
end if
end if
if e!=0 then
r &= 'x'
if e!=1 then
if uni_frac then
if e<0 then
r &= utf32_to_utf8({SMNUS})
e = -e
end if
r &= unicode_superscripts(e)
else
r &= sprintf("^%d",e)
end if
end if
end if
end if
end for
if r="" then r="0" end if
return r
end function

function parse(sequence s)
sequence terms = {}
integer sdx = 1, e, f
atom c
s = match_replace("<sup>",s,"^")
s = match_replace("</sup>",s,"")
s = match_replace("**",s,"^")
s = match_replace(" ^",s,"^")
s = match_replace("^ ",s,"^")
s = match_replace({' ',SPLUS},s,{SPLUS})
s = match_replace({' ',SMNUS},s,{SMNUS})
for i=1 to length(EXPONENTS) do
e = EXPONENTS[i]
s = match_replace({' ',e},s,{e})
end for
while sdx<=length(s) do
{e,c,f,sdx} = get_term(s,sdx)
if c!=0 then -- (aside: +5 -5 may yet leave c==0)
terms = append(terms,{e,c,f})
end if
end while
terms = sort(terms)
-- merge, eg "10x^2 + 10x^2" -> 20x^2
for i=length(terms) to 2 by -1 do
if terms[i][EXP] = terms[i-1][EXP] then
if terms[i-1][FRAC]!=terms[i][FRAC] then
?9/0 -- placeholder for more code
else
terms[i-1][COEF] += terms[i][COEF]
end if
terms[i..i] = {} -- (delete 2nd)
end if
end for
return poly(terms)
end function

include Unicode_polynomial_equation.e

sequence alts = {},     -- (unicode versions)
altn = {},     -- (idx of ascii equivalents)
lines = get_lines()

if lines[1][1..3] = UTF8BOM then
-- remove/ignore any utf8 byte order mark
lines[1] = lines[1][4..\$]
end if

for i=2 to length(lines) do
if length(lines[i])>5
and lines[i][1..5] = "===> " then
alts = append(alts,lines[i-1][5..\$])
altn = append(altn,i)
end if
end for

for i=2 to length(lines) do
if length(lines[i])>4
and lines[i][1..4] = "==> " then
sequence line = utf8_to_utf32(lines[i-1]),
res = parse(line),
expected = lines[i][5..\$]
if res=expected then
-- (res is the unicode version)
if platform()!=WINDOWS or res="0" then
printf(1,"%2d: %40s   ok\n",{i-1,res})
else
-- (unicode output on windows consoles is fiddly...)
printf(1,"%2d: ok\n",i-1)
end if
else
integer k = find(expected,alts)
if k and res=lines[altn[k]][6..\$] then
-- (res is the ascii equivalent)
printf(1,"%2d: %40s   ok\n",{i-1,res})
else
printf(1,"%d: error - %s\n",{i-1,res})
end if
end if
end if
end for

?"done"
{} = wait_key()
```
Output:

uni_frac = false (ie windows)

``` 1:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
4:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
6:                                        0   ok
8:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
10:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
12:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
14:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
16:       1 + 40x^-1 + 42x^-3 - 2x^-4 + x^-5   ok
19:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
21:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
23:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
25:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
27: x^5 - 0.5x^4 + 101.25x^3 + 100.75x + 2.5   ok
30: x^5 - 0.5x^4 + 101.25x^3 + 100.75x + 2.5   ok
32:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
34:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
36:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
38:             x^5 - 2x^4 + 42x^3 + 40x + 1   ok
```

uni_frac = true (linux or pwa/p2js only, unless you have managed to find and install a decent windows console unicode font, which I haven't)

``` 1:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
4:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
6:                                        0   ok
8:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
10:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
12:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
14:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
16:           1 + 40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵   ok
19:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
21:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
23:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
25:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
27:           x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½   ok
30:           x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½   ok
32:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
34:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
36:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
38:                x⁵ - 2x⁴ + 42x³ + 40x + 1   ok
```

## Wren

Translation of: Go
Library: Wren-pattern
```import "./pattern" for Pattern

var powers = [
["0", "⁰"],
["1", "¹"],
["2", "²"],
["3", "³"],
["4", "⁴"],
["5", "⁵"],
["6", "⁶"],
["7", "⁷"],
["8", "⁸"],
["9", "⁹"],
["-", "⁻"]
]

var fractions = [
[".25", "¼"],
[".5", "½"],
[".75", "¾"],
[".14285714285714", "⅐"],
[".11111111111111", "⅑"],
[".1", "⅒"],
[".33333333333333", "⅓"],
[".66666666666667", "⅔"],
[".2", "⅕"],
[".4", "⅖"],
[".6", "⅗"],
[".8", "⅘"],
[".16666666666667", "⅙"],
[".83333333333333", "⅚"],
[".125", "⅛"],
[".375", "⅜"],
[".625", "⅝"],
[".875", "⅞"]
]

var printEquation = Fn.new { |coefs|
System.write("=> ")
if (coefs.isEmpty) {
System.print("0\n")
return
}
var keys = coefs.keys.toList
var max = keys[0]
var min = keys[0]
for (k in keys.skip(1)) {
if (k > max) max = k
if (k < min) min = k
}
for (p in max..min) {
var c = coefs[p] ? coefs[p] : 0
if (c != 0) {
if (p < max) {
var sign = "+"
if (c < 0) {
sign = "-"
c = -c
}
System.write(" %(sign) ")
}
if (c != 1 || (c == 1 && p == 0)) {
var cs = c.toString
var ix = cs.indexOf(".")
if (ix >= 0) {
var dec = cs[ix..-1]
for (frac in fractions) {
if (dec == frac[0]) {
cs = cs[0...ix] + frac[1]
break
}
}
}
if (cs[0] == "0" && cs.count > 1 && cs[1] != ".") cs = cs[1..-1]
System.write(cs)
}
if (p != 0) {
var ps = p.toString
for (power in powers) ps = ps.replace(power[0], power[1])
if (ps == "¹") ps = ""
System.write("x%(ps)")
}
}
}
System.print("\n")
}

var equs = [
"-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹",
"x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1",
"0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵",
"1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰",
"+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1",
"x^5 - 2x**4 + 42x^3 + 40x + 1",
"x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1",
"x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰",
"x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1",
"x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1",
"0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1",
"1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1",
"x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2",
"x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5",
"x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x",
"⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝"
]

var pattern = Pattern.new("+1/s/n+1/s")

var reps = [
[",", ""],
[" ", ""],
["¼", ".25"],
["½", ".5"],
["¾", ".75"],
["⅐", ".14285714285714"],
["⅑", ".11111111111111"],
["⅒", ".1"],
["⅓", ".33333333333333"],
["⅔", ".66666666666667"],
["⅕", ".2"],
["⅖", ".4"],
["⅗", ".6"],
["⅘", ".8"],
["⅙", ".16666666666667"],
["⅚", ".83333333333333"],
["⅛", ".125"],
["⅜", ".375"],
["⅝", ".625"],
["⅞", ".875"],
["↉", ".0"],
["⏨", "e"],
["⁄", "/"]
]

var reps2 = [
["⁰", "0"],
["¹", "1"],
["²", "2"],
["³", "3"],
["⁴", "4"],
["⁵", "5"],
["⁶", "6"],
["⁷", "7"],
["⁸", "8"],
["⁹", "9"],
["⁻⁻", ""],
["⁻", "-"],
["⁺", ""],
["**", ""],
["^", ""],
["↑", ""],
["⁄", "/"]
]

for (equ in equs) {
System.print(equ)
var terms = pattern.splitAll(equ)
var ops = pattern.findAll(equ).map { |m| m.text.trim() }.toList
var coefs = {}
var i = 0
for (term in terms) {
var s = term.split("x")
var t = s[0].trimEnd("·× ")
for (rep in reps) t = t.replace(rep[0], rep[1])
var c = 1
var inverse = false
if (t == "" || t == "+" || t == "-") t = t + "1"
var ix = t.indexOf("/")
if (ix == t.count - 1) {
inverse = true
t = t[0..-2]
c = Num.fromString(t)
} else if (ix >= 0) {
var u = t.split("/")
var m = Num.fromString(u[0])
var n = Num.fromString(u[1])
c = m / n
} else {
c = Num.fromString(t)
}
if (i > 0 && ops[i-1] == "-") c = -c
if (c == -0) c = 0
var cont = false
if (s.count == 1) {
coefs[0] = coefs[0] ? coefs[0] + c : c
cont = true
}
if (!cont) {
var u = s[1].trim()
if (u == "") {
var p = 1
if (inverse) p = -1
if (c != 0) coefs[p] = coefs[p] ? coefs[p] + c : c
cont = true
}
if (!cont) {
for (rep in reps2) u = u.replace(rep[0], rep[1])
var jx = u.indexOf("/")
var p = 1
if (jx >= 0) {
var v = u.split("/")
p = Num.fromString(v[0])
if (p == null) p = 1
var d = Num.fromString(v[1])
c = c / d
} else {
p = Num.fromString(u.trim())
if (p == null) p = 1
}
if (inverse) p = -p
if (c != 0) coefs[p] = coefs[p] ? coefs[p] + c : c
}
}
i = i + 1
}
printEquation.call(coefs)
}
```
Output:
```-0.00x⁺¹⁰ + 1.0·x ** 5 + -2e0x^4 + +0,042.00 × x ⁺³ + +.0x² + 20.000 000 000x¹ - -1x⁺⁰ + .0x⁻¹ + 20.x¹
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵
=> 0

1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x^5 - 2x**4 + 42x^3 + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰
=> 1 + 40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵

x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

0x⁷ + 10x + 10x + x⁵ - 2x⁴ + 42x³ + 20x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1
=> x⁵ - 2x⁴ + 42x³ + 40x + 1

x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5
=> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½

x⁻⁵ - 2⁄x⁴ + 42x⁻³ - 40/x
=> -40x⁻¹ + 42x⁻³ - 2x⁻⁴ + x⁻⁵

⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝
=> ⅐x⁵ - x⁴ + 42⅕x³ + ⅑x - 40¾
```