Unicode polynomial equation: Difference between revisions

← Older edit

Unicode polynomial equation (view source)

Revision as of 10:19, 15 February 2024

107,968 bytes added , 3 months ago

m

→‎{{header|Wren}}: Minor tidy

PureFox

9,476

edits

Revision as of 16:50, 25 October 2018 (view source) Petelomax (talk \| contribs) (Phix) ← Older edit		Latest revision as of 10:19, 15 February 2024 (view source) PureFox (talk \| contribs) m (→‎{{header\|Wren}}: Minor tidy)
(13 intermediate revisions by 5 users not shown)
Line 58: [[Category:Mathematics]] =={{header\|~~Phix~~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. ~~To simplify this task I first created a test file (save as utf8, Unicode_polynomial_equation.txt):~~ <syntaxhighlight lang="go">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 - 2x4 + 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) } }</syntaxhighlight> {{out}} <pre> -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~~0.5x⁴ + 101¼x.25x³ + 100¾x.75x + 2½.5 ==> x⁵ - ½x⁴ + 101¼x³ + 100¾x + 2½ ~~x<sup>5</sup> - 2x<sup>4</sup> + 42x<sup>3</sup> + 40x + 1~~ ~~==> x⁵~~x⁻⁵ - ~~2x⁴~~2⁄x⁴ + ~~42x~~42x⁻³ ~~+ 40x +~~- 140/x ~~x^5~~=> - ~~2x^4~~40x⁻¹ + ~~42x^3~~42x⁻³ +- ~~40x~~2x⁻⁴ + 1x⁻⁵ ~~==> x⁵ - 2x⁴ + 42x³ + 40x + 1~~ x⁵⅐x⁵ - ~~2x⁴~~⅓x⁴ - ⅔x⁴ + ~~42x~~42⅕x³ + ~~40x~~⅑x +- 40⅛ - 1⅝ ==> x⁵⅐x⁵ - ~~2x⁴~~x⁴ + ~~42x~~42⅕x³ + ~~40x~~⅑x +- 140¾ ~~x5 - 2x4 + 42x3 + 40x + 1~~ ~~==> x⁵ - 2x⁴ + 42x³ + 40x + 1~~ </pre> ~~Explanation: <br>~~ ~~On finding a line beginning with "==> ", parse the previous line and check that the output matches the rest of the line.<br>~~ 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. =={{header\|Julia}}== ~~Obviously this is not well tested and //will// fail on the next thing thrown at it, but~~ The task allows the "polynomials" to be parsed to have negative exponents. This makes them <em>Laurent</em> polynomials, not ordinary polynomials. ~~it shows the basic approach. Error handling omitted using that good ol' standby excuse~~ <syntaxhighlight lang="julia">import Base.print ~~"for clarity".~~ struct LaurentPolynomial{T} ~~Note that space is not skipped when getting exponents, otherwise it might wrongly treat~~ powtocoef::Dict{Int,T} ~~say "x + 2" as "x^2", since we /are/ allowing exponentiation symbols to be omitted. At~~ varname::Char ~~the start of parse() we strip spaces around '^' (etc) to help with that.~~ end function tosuper(i) ~~Processing the input in utf32 form is a complete no-brainer; whereas constructing utf8~~ s = "" ~~output is a little more subtle, but avoids creating a utf32 "string" just because all~~ if i != 1 ~~bytes happen to be less than 255, which would not necessarily be valid utf8/32.~~ 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) ~~<lang Phix>-- demo\rosetta\Unicode_polynomial_equation.exw~~ if isempty(lp.powtocoef) \|\| all(iszero, values(lp.powtocoef)) ~~constant uni_frac = false -- if true output unicode superscripts and vulgar fractions~~ 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')] ~~constant UTF8BOM = {#EF,#BB,#BF},~~ const allsuper = String(vcat(uniexp, ['\u207a', '\u207b'])) ~~SPTWO = #00B2, -- superscript two~~ const udi = Dict([u => i-1 for (i, u) in enumerate(uniexp)]) ~~STHRE = #00B3, -- superscript three~~ const reverseudi = Dict([v => k for (k, v) in udi]) ~~MIDOT = #00B7, -- middle dot~~ const uch = Dict(['\u207a' => '+', '\u207b' => '-', '\u00b7' => ' ', ~~SPONE = #00B9, -- superscript one~~ '\u00d7' => ' ', ~~QUART~~'\u2091' => ~~#00BC~~'^', '\u23e8' => ~~-- one quarter~~'E']) const fracs = Dict(['¼' => "$(1/4)", '½' => "$(1/2)", '¾' => "$(3/4)", '⅐' => "$(1/7)", ~~AHALF = #00BD, -- one half~~ '⅑' => "$(1/9)", '⅒' => "$(1/10)", '⅓' => "$(1/3)", '⅔' => "$(2/3)", '⅕' => "$(1/5)", ~~THQTR = #00BE, -- three quarters~~ '⅖' => "$(2/5)", '⅗' => "$(3/5)", '⅘' => "$(4/5)", '⅙' => "(1/6)", '⅚' => "$(5/6)", ~~MULTY = #00D7, -- multiplication sign~~ '⅛' => "$(1/8)", '⅜' => "$(3/8)", '⅝' => "$(5/8)", '⅞' => "$(7/8)", '↉' => "$(0/3)"]) ~~DIVDE = #2044, -- division sign~~ const tofracs = Dict(0.25 => '¼', 0.5 => '½', 0.75 => '¾', 0.2 => '⅕') ~~SZERO = #2070, -- superscript zero~~ allfrac = join(vcat(collect(keys(fracs))), "\|") ~~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~~ ~~-- ZTHRD = #2189, -- zero thirds[??]~~ ~~UPARW = #2191, -- uparrow~~ ~~BASET = #23E8, -- base 10~~ ~~SPACE = ' ', -- space~~ ~~T = 10, -- align nxt tbl~~ $ utoascii(c) = (x = haskey(udi, c) ? Char('0' + udi[c]) : haskey(uch, c) ? uch[c] : c) ~~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}})~~ function fcoef(termstring, varname) ~~constant EXPONENTS = {SZERO,SPONE,SPTWO,STHRE,SFOUR,SFIVE,SPSIX,SSEVN,SEGHT,SNINE}~~ m = match(r"(\d+)⁄(\d+)", termstring).captures return "$(parse(Float64, m[1])/parse(Float64, m[2]))$varname^0" end function ~~skip~~xcoef(~~sequence s~~termstring, ~~integer sdx, sequence set~~varname) m = match(Regex("(\\d+)$varname([^⁄\\+])⁄(\\d+)"), termstring).captures ~~while sdx<=length(s)~~ coe = parse(Float64, m[1])/parse(Float64, m[3]) ~~and find(s[sdx],set) do~~ return "$(coe)$varname$(m[2])" ~~sdx += 1~~ end ~~while~~ ~~return sdx~~ ~~end function~~ function fromvfrac(termstring) ~~function get_sign(sequence s, integer sdx, bool allow_superscripts)~~ m = match(r"(\d)(\D+)", termstring).captures ~~integer sgn = +1, ch~~ s = string((m[1] == "" ? 0 : parse(Float64, m[1])) + parse(Float64, fracs[m[2][1]])) ~~for sdx=sdx to length(s) do~~ end ~~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~~ ~~end for~~ ~~return {sgn,sdx}~~ ~~end function~~ function normalizeexpression(s, varname='x') ~~function get_num(sequence s, integer sdx, atom n=0, bool allow_superscripts=false, as_fraction=false)~~ s = replace(s, Regex("\\d(" * allfrac * ")") => (x) -> fromvfrac(x)) ~~integer sgn = +1, ch, f, e10, d = 1~~ s = replace(replace(s, r"[^\+].+" => (x) -> "+$x"), r".+[^\+]$" => (x) -> "$x+") ~~atom p10 = 10~~ ~~bool~~ ~~none~~ = ~~not~~ ~~as_fraction~~s --= replace(~~cope~~replace(replace(s, ~~with~~r"\s+" => "x"), r"\\\|↑" ==> "1x^1"), ~~and~~"\u23e8" !=> "~~0x^0~~e") s = replace(s, Regex(varname * "(?=[$allsuper]+)") => "$varname^") ~~-- (but not when processing the "34" of "12.34", obvs)~~ s = replace(prod([utoascii(c) for c in s]), r"\s+" => "") ~~if not as_fraction then~~ s = replace(s, r"[\-\+]+" => (x) -> isodd(count(y -> y == '-', x)) ? "+-" : "+") ~~{sgn,sdx} = get_sign(s,sdx,allow_superscripts)~~ s = replace(replace(s, r"\^\+\-" => "^-"), r"\^\+" => "^") ~~end if~~ s = replace(s, Regex("(?<=[\\-\\+])$varname") => "1$varname") ~~if not allow_superscripts then~~ s = replace(s, r"(\d+)x([^⁄\+])⁄(\d+)" => (x) -> xcoef(x, varname)) ~~sdx = skip(s,sdx,{' '})~~ s = replace(s, r"(?<=[0-9])(,)(?=[0-9])" => "") ~~end if~~ s = replace(s, r"\d+⁄\d+" => (x) -> fcoef(x, varname)) ~~for sdx=sdx to length(s) do~~ s = replace(s, r"\+([\d\.]+)\+" => SubstitutionString("+\\1$varname^0+")) ~~ch = s[sdx]~~ return replace(s, Regex("(⁄\|/)(" varname * ")\\^?") => ~~if ch>='0' and ch<='9' then~~ (x) -> varname * if(x[end] ~~as_fraction~~== ~~then~~'^' ? "^-" : "^-1")) end ~~n += (ch-'0')/p10~~ ~~p10 = 10~~ ~~else~~ ~~n = n10+ch-'0'~~ ~~end if~~ ~~none = false~~ ~~elsif allow_superscripts then~~ ~~f = find(ch,EXPONENTS)~~ ~~if f=0 then exit end if~~ ~~n = n10+f-1~~ ~~none = false~~ ~~elsif not find(ch," ,") then~~ ~~exit~~ ~~end if~~ ~~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 = nvfd + 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~~topoly(~~sequence~~ s::String, ~~integer sdx~~varname='x') allcoef = Dict{Int,Float64}(0 => 0.0) ~~integer last_sdx = sdx, -- (infinite loop check/prevent)~~ s = normalizeexpression(s, varname) ~~e = 0~~ reg = Regex("[\\.\\-\\+\\deE\\/]" varname * "(?:\\^[\\d\\-]+)?(?=(?:[^\\+\\-]?(?:\\+\|\\-)))") ~~atom c, d = 1, f~~ matched = collect(eachmatch(reg, s)) ~~bool sdiv = false~~ pairs = [split(x.match, varname * "^") for x in matched] ~~{c,d,sdx} = get_num(s,sdx)~~ for p in pairs ~~sdx = skip(s,sdx,{' ',MIDOT,MULTY})~~ p[1] = replace(p[1], "+-" => "-") ~~if sdx<=length(s)~~ ~~and~~ if length(~~s[sdx]~~p) ==~~'/'~~ or1 ~~s[sdx]=DIVDE)~~ ~~then~~ push!(p, "1") p[1] = replace(p[1], Regex(varname * "\$") => "") ~~sdx += 1~~ end ~~if sdx<=length(s) and s[sdx]!='x' then~~ coef, expo = tryparse(Float64, {dp[1]),~~f,sdx}~~ ~~= get_num~~tryparse(sInt,~~sdx~~ p[2]) coef = coef ~~if f!~~=1= ~~then~~nothing ?9/ 1.0 ~~end~~: ifcoef expo = expo == ifnothing ~~not~~? ~~uni_frac~~1 ~~then~~: expo if haskey(allcoef, ~~c /= d~~expo) coef d += 1allcoef[expo] end if ~~else~~allcoef[expo] = coef end ~~sdiv = true~~ return LaurentPolynomial(allcoef, varname) ~~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~~ testcases = [ ~~function unicode_superscripts(integer e)~~ "1x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1", ~~-- display helper~~ "0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵", ~~string res = ""~~ "1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰", ~~if e>9 then~~ "+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1", ~~res = unicode_superscripts(floor(e/10))~~ "x^5 - 2x4 + 42x^3 + 40x + 1", ~~e = remainder(e,10)~~ "x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1", ~~end if~~ "x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰", ~~res &= utf32_to_utf8({EXPONENTS[e+1]})~~ "x⁵ - 2x⁴ + 42.000 000x³ + 40x + 1", ~~return res~~ "x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1", ~~end function~~ "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 ~~enum EXP, COEF, FRAC -- contents of terms[i]~~ println(lpad(s, 48), " => ", topoly(s, 'x')) end </syntaxhighlight>{{out}} <pre> 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 - 2x4 + 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 </pre> =={{header\|Nim}}== ~~function poly(sequence terms)~~ {{trans\|Go}} ~~-- display helper~~ <syntaxhighlight lang="nim">import re, sequtils, strutils, tables ~~string r = ""~~ from unicode import toRunes ~~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~~ const ~~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~~ Powers = [("0", "⁰"), ("1", "¹"), ("2", "²"), ("3", "³"), ("4", "⁴"), ~~sequence alts = {}, -- (unicode versions)~~ ~~altn~~ = {} ("5", "⁵"), ("6", "⁶"), ("7", --"⁷"), (~~idx~~"8", of"⁸"), ~~ascii~~("9", ~~equivalents~~"⁹")] ~~lines = read_lines("Unicode_polynomial_equation.txt")~~ Fractions = [(".25", "¼"), (".5", "½"), (".75", "¾"), (".14285714285714", "⅐"), ~~if lines[1][1..3] = UTF8BOM then~~ (".11111111111111", "⅑"), (".1", "⅒"), (".33333333333333", "⅓"), ~~-- remove/ignore any utf8 byte order mark~~ (".66666666666667", "⅔"), (".2", "⅕"), (".4", "⅖"), (".6", "⅗"), ~~lines[1] = lines[1][4..$]~~ (".8", "⅘"), (".16666666666667", "⅙"), (".83333333333333", "⅚"), ~~end if~~ (".125", "⅛"), (".375", "⅜"), (".625", "⅝"), (".875", "⅞")] Reps1 = [(",", ""), (" ", ""), ("¼", ".25"), ("½", ".5"), ("¾", ".75"), ~~for i=2 to length(lines) do~~ ("⅐", ".14285714285714"), ("⅑", ".11111111111111"), ("⅒", ".1"), ~~if length(lines[i])>5~~ ("⅓", ".33333333333333"), ("⅔", ".66666666666667"), ("⅕", ".2"), ~~and lines[i][1..5] = "===> " then~~ ("⅖", ".4"), ("⅗", ".6"), ("⅘", ".8"), ("⅙", ".16666666666667"), ~~alts = append(alts,lines[i-1][5..$])~~ ("⅚", ".83333333333333"), ("⅛", ".125"), ("⅜", ".375"), ("⅝", ".625"), ~~altn = append(altn,i)~~ ("⅞", ".875"), ("↉", ".0"), ("⏨", "e"), ("⁄", "/")] ~~end if~~ ~~end for~~ Reps2 = [("⁰", "0"), ("¹", "1"), ("²", "2"), ("³", "3"), ("⁴", "4"), ("⁵", "5"), ~~for i=2 to length(lines) do~~ ("⁶", "6"), ("⁷", "7"), ("⁸", "8"), ("⁹", "9"), ("⁻⁻", ""), ("⁻", "-"), ~~if length(lines[i])>4~~ ("⁺", ""), ("", ""), ("^", ""), ("↑", ""), ("⁄", "/")] ~~and lines[i][1..4] = "==> " then~~ ~~sequence line = utf8_to_utf32(lines[i-1])~~ Eqs = [ ~~sequence res = parse(line)~~ "-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", ~~sequence expected = lines[i][5..$]~~ "x⁵ - 2x⁴ + 42x³ + 0x² + 40x + 1", ~~if res=expected then~~ "0e+0x⁰⁰⁷ + 00e-00x + 0x + .0x⁰⁵ - 0.x⁴ + 0×x³ + 0x⁻⁰ + 0/x + 0/x³ + 0x⁻⁵", ~~-- (res is the unicode version)~~ "1x⁵ - 2x⁴ + 42x³ + 40x + 1x⁰", ~~if platform()!=WINDOWS or res="0" then~~ "+x⁺⁵ + -2x⁻⁻⁴ + 42x⁺⁺³ + +40x - -1", ~~printf(1,"%2d: %40s ok\n",{i-1,res})~~ "x^5 - 2x4 + 42x^3 + 40x + ~~else~~1", "x↑5 - 2.00·x⁴ + 42.00·x³ + 40.00·x + 1", ~~-- (unicode output on windows consoles is fiddly...)~~ "x⁻⁵ - 2⁄x⁴ + 42x⁻³ + 40/x + 1x⁻⁰", ~~printf(1,"%2d: ok\n",i-1)~~ "x⁵ - 2x⁴ + 42.000 000x³ + 40x ~~end~~+ if1", "x⁵ - 2x⁴ + 0,042x³ + 40.000,000x + 1", ~~else~~ "0x⁷ + 10x + 10x + x⁵ - ~~integer~~2x⁴ k+ =42x³ ~~find(expected~~+ 20x + 1",~~alts)~~ "1E0x⁵ - 2,000,000.e-6x⁴ + 4.2⏨1x³ + .40e+2x + 1", ~~if k and res=lines[altn[k]][6..$] then~~ "x⁵ - x⁴⁄2 + 405x³⁄4 + 403x⁄4 + 5⁄2", ~~-- (res is the ascii equivalent)~~ "x⁵ - 0.5x⁴ + 101.25x³ + 100.75x + 2.5", ~~printf(1,"%2d: %40s ok\n",{i-1,res})~~ "x⁻⁵ - 2⁄x⁴ + 42x⁻³ - ~~else~~40/x", "⅐x⁵ - ⅓x⁴ - ⅔x⁴ + 42⅕x³ + ⅑x - 40⅛ - ⅝"] ~~printf(1,"%d: error - %s\n",{i-1,res})~~ ~~end if~~ type Coefs = Table[int, float] ~~end if~~ ~~end if~~ proc printEquation(coefs: Coefs) = ~~end for</lang>~~ 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)</syntaxhighlight> {{out}} <pre>-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 - 2x4 + 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</pre> =={{header\|Phix}}== To simplify this task I first created a test file (save as utf8, Unicode_polynomial_equation.e): <!--<syntaxhighlight lang="phix">(phixonline)--> <span style="color: #008080;">constant</span> <span style="color: #000000;">raw_text</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""" -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 """</span> <span style="color: #008080;">global</span> <span style="color: #008080;">function</span> <span style="color: #000000;">get_lines</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">raw_text</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <!--</syntaxhighlight>--> Explanation: <br> On finding a line beginning with "==> ", parse the previous line and check that the output matches the rest of the line.<br> 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. <!--<syntaxhighlight lang="phix">(phixonline)--> <span style="color: #000080;font-style:italic;">-- demo\rosetta\Unicode_polynomial_equation.exw</span> <span style="color: #008080;">constant</span> <span style="color: #000000;">uni_frac</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">WINDOWS</span> <span style="color: #000080;font-style:italic;">-- if true output unicode superscripts and vulgar fractions</span> <span style="color: #008080;">constant</span> <span style="color: #000000;">UTF8BOM</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">#EF</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#BB</span><span style="color: #0000FF;">,</span><span style="color: #000000;">#BF</span><span style="color: #0000FF;">},</span> <span style="color: #000000;">SPTWO</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00B2</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript two</span> <span style="color: #000000;">STHRE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00B3</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript three</span> <span style="color: #000000;">MIDOT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00B7</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- middle dot</span> <span style="color: #000000;">SPONE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00B9</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript one</span> <span style="color: #000000;">QUART</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00BC</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one quarter</span> <span style="color: #000000;">AHALF</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00BD</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one half</span> <span style="color: #000000;">THQTR</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00BE</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- three quarters</span> <span style="color: #000000;">MULTY</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#00D7</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- multiplication sign</span> <span style="color: #000000;">DIVDE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2044</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- division sign</span> <span style="color: #000000;">SZERO</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2070</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript zero</span> <span style="color: #000000;">SFOUR</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2074</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript four</span> <span style="color: #000000;">SFIVE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2075</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript five</span> <span style="color: #000000;">SPSIX</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2076</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript six</span> <span style="color: #000000;">SSEVN</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2077</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript seven</span> <span style="color: #000000;">SEGHT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2078</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript eight</span> <span style="color: #000000;">SNINE</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2079</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript nine</span> <span style="color: #000000;">SPLUS</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#207A</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript plus</span> <span style="color: #000000;">SMNUS</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#207B</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- superscript minus</span> <span style="color: #000000;">SVNTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2150</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one seventh</span> <span style="color: #000000;">NINTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2151</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one ninth</span> <span style="color: #000000;">TENTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2152</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one tenth</span> <span style="color: #000000;">THIRD</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2153</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one third</span> <span style="color: #000000;">TWTHD</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2154</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- two thirds</span> <span style="color: #000000;">FIFTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2155</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one fifth</span> <span style="color: #000000;">TWFTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2156</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- two fifths</span> <span style="color: #000000;">THFTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2157</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- three fifths</span> <span style="color: #000000;">FRFTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2158</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- four fifths</span> <span style="color: #000000;">SIXTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2159</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one sixth</span> <span style="color: #000000;">FVSIX</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#215A</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- five sixths</span> <span style="color: #000000;">EIGTH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#215B</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- one eigth</span> <span style="color: #000000;">THEGH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#215C</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- three eigths</span> <span style="color: #000000;">FVEGH</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#215D</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- five eigths</span> <span style="color: #000000;">UPARW</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#2191</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- uparrow</span> <span style="color: #000000;">BASET</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">#23E8</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- base 10</span> <span style="color: #000000;">SPACE</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- space</span> <span style="color: #000000;">T</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span> <span style="color: #000080;font-style:italic;">-- align nxt tbl</span> <span style="color: #008080;">constant</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">vulgar_fractions</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unicode_vulgar_fractions</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span><span style="color: #000000;">QUART</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},</span><span style="color: #000000;">AHALF</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span><span style="color: #000000;">THQTR</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span><span style="color: #000000;">SVNTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span><span style="color: #000000;">NINTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">T</span><span style="color: #0000FF;">},</span><span style="color: #000000;">TENTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},</span><span style="color: #000000;">THIRD</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},</span><span style="color: #000000;">TWTHD</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span><span style="color: #000000;">FIFTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span><span style="color: #000000;">TWFTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span><span style="color: #000000;">THFTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span><span style="color: #000000;">FRFTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span><span style="color: #000000;">SIXTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span><span style="color: #000000;">FVSIX</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span><span style="color: #000000;">EIGTH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span><span style="color: #000000;">THEGH</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span><span style="color: #000000;">FVEGH</span><span style="color: #0000FF;">}})</span> <span style="color: #008080;">constant</span> <span style="color: #000000;">EXPONENTS</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">SZERO</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SPONE</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SPTWO</span><span style="color: #0000FF;">,</span><span style="color: #000000;">STHRE</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SFOUR</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SFIVE</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SPSIX</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SSEVN</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SEGHT</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SNINE</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">function</span> <span style="color: #000000;">skip</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">while</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">],</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span> <span style="color: #008080;">return</span> <span style="color: #000000;">sdx</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">get_sign</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">allow_superscripts</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">sdx</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">if</span> <span style="color: #000000;">allow_superscripts</span> <span style="color: #008080;">then</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SPLUS</span><span style="color: #0000FF;">?</span><span style="color: #008000;">'+'</span><span style="color: #0000FF;">:</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SMNUS</span><span style="color: #0000FF;">?</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">:</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #000000;">SPACE</span><span style="color: #0000FF;">?</span><span style="color: #008000;">'?'</span><span style="color: #0000FF;">:</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">)))</span> <span style="color: #000080;font-style:italic;">-- (do not skip spaces, see note)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">'+'</span> <span style="color: #008080;">and</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">' '</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">'-'</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sgn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">allow_superscripts</span><span style="color: #0000FF;">=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">as_fraction</span><span style="color: #0000FF;">=</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sgn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">p10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">none</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">not</span> <span style="color: #000000;">as_fraction</span> <span style="color: #000080;font-style:italic;">-- (cope with "x" == "1x^1" and != "0x^0") -- (but not when processing the "34" of "12.34", obvs)</span> <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">as_fraction</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sgn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_sign</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">allow_superscripts</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">allow_superscripts</span> <span style="color: #008080;">then</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">skip</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">sdx</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">ch</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">if</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">>=</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">and</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;"><=</span><span style="color: #008000;">'9'</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">as_fraction</span> <span style="color: #008080;">then</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">-</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">p10</span> <span style="color: #000000;">p10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span> <span style="color: #008080;">else</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"></span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">-</span><span style="color: #008000;">'0'</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">none</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #008080;">elsif</span> <span style="color: #000000;">allow_superscripts</span> <span style="color: #008080;">then</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">EXPONENTS</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"></span><span style="color: #000000;">10</span><span style="color: #0000FF;">+</span><span style="color: #000000;">f</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #000000;">none</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #008080;">elsif</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ,"</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">allow_superscripts</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">'e'</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'E'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">BASET</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">e10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e10</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">elsif</span> <span style="color: #000000;">ch</span><span style="color: #0000FF;">=</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">as_fraction</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">as_fraction</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">none</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #008080;">else</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ch</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unicode_vulgar_fractions</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">as_fraction</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">vfn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vfd</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vulgar_fractions</span><span style="color: #0000FF;">[</span><span style="color: #000000;">f</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">if</span> <span style="color: #000000;">uni_frac</span> <span style="color: #008080;">then</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"></span><span style="color: #000000;">vfd</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">vfn</span> <span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">vfd</span> <span style="color: #008080;">else</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">vfn</span><span style="color: #0000FF;">/</span><span style="color: #000000;">vfd</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #000000;">none</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">none</span> <span style="color: #008080;">then</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sgn</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">get_term</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">last_sdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (infinite loop check/prevent)</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span> <span style="color: #004080;">bool</span> <span style="color: #000000;">sdiv</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">skip</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">MIDOT</span><span style="color: #0000FF;">,</span><span style="color: #000000;">MULTY</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'/'</span> <span style="color: #008080;">or</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">DIVDE</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'x'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">uni_frac</span> <span style="color: #008080;">then</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">d</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">else</span> <span style="color: #000000;">sdiv</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'x'</span> <span style="color: #008080;">then</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">skip</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">'^'</span><span style="color: #0000FF;">,</span><span style="color: #008000;">''</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SPLUS</span><span style="color: #0000FF;">,</span><span style="color: #000000;">UPARW</span><span style="color: #0000FF;">})</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">allow_superscripts</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdiv</span> <span style="color: #008080;">then</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">e</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">else</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdiv</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'/'</span> <span style="color: #008080;">or</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">DIVDE</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_num</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">uni_frac</span> <span style="color: #008080;">then</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">d</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">last_sdx</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">unicode_superscripts</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- display helper</span> <span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span> <span style="color: #008080;">if</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">></span><span style="color: #000000;">9</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unicode_superscripts</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">))</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">utf32_to_utf8</span><span style="color: #0000FF;">({</span><span style="color: #000000;">EXPONENTS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">e</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]})</span> <span style="color: #008080;">return</span> <span style="color: #000000;">res</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">enum</span> <span style="color: #000000;">EXP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">COEF</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">FRAC</span> <span style="color: #000080;font-style:italic;">-- contents of terms[i]</span> <span style="color: #008080;">function</span> <span style="color: #000000;">poly</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- display helper</span> <span style="color: #004080;">string</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span> <span style="color: #008080;">for</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> <span style="color: #0000FF;">{</span><span style="color: #004080;">integer</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span><span style="color: #0000FF;">?</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">elsif</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" - "</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">else</span> <span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">!=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">" - "</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" + "</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (hence/only when uni_frac==true)</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">({</span><span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">f</span><span style="color: #0000FF;">},</span><span style="color: #000000;">vulgar_fractions</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">/</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">utf32_to_utf8</span><span style="color: #0000FF;">({</span><span style="color: #000000;">unicode_vulgar_fractions</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]})</span> <span style="color: #008080;">else</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%g"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">/</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">else</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%g"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">if</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">'x'</span> <span style="color: #008080;">if</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">uni_frac</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">e</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">utf32_to_utf8</span><span style="color: #0000FF;">({</span><span style="color: #000000;">SMNUS</span><span style="color: #0000FF;">})</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">e</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">unicode_superscripts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">else</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"^%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"0"</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">return</span> <span style="color: #000000;">r</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">parse</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">sdx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">c</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"<sup>"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"^"</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"</sup>"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"^"</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" ^"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"^"</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"^ "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"^"</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SPLUS</span><span style="color: #0000FF;">},</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">SPLUS</span><span style="color: #0000FF;">})</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">SMNUS</span><span style="color: #0000FF;">},</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">SMNUS</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">EXPONENTS</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">EXPONENTS</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">},</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">while</span> <span style="color: #000000;">sdx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_term</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sdx</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (aside: +5 -5 may yet leave c==0)</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span> <span style="color: #000000;">terms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- merge, eg "10x^2 + 10x^2" -> 20x^2</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> <span style="color: #008080;">if</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">EXP</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">EXP</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #008080;">if</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">FRAC</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">FRAC</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- placeholder for more code</span> <span style="color: #008080;">else</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COEF</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">COEF</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000000;">terms</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span> <span style="color: #000080;font-style:italic;">-- (delete 2nd)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">return</span> <span style="color: #000000;">poly</span><span style="color: #0000FF;">(</span><span style="color: #000000;">terms</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">include</span> <span style="color: #000000;">Unicode_polynomial_equation</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">alts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000080;font-style:italic;">-- (unicode versions)</span> <span style="color: #000000;">altn</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000080;font-style:italic;">-- (idx of ascii equivalents) -- lines = read_lines("Unicode_polynomial_equation.txt")</span> <span style="color: #000000;">lines</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_lines</span><span style="color: #0000FF;">()</span> <span style="color: #008080;">if</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">UTF8BOM</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- remove/ignore any utf8 byte order mark</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">4</span><span style="color: #0000FF;">..$]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])></span><span style="color: #000000;">5</span> <span style="color: #008080;">and</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"===> "</span> <span style="color: #008080;">then</span> <span style="color: #000000;">alts</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">alts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">5</span><span style="color: #0000FF;">..$])</span> <span style="color: #000000;">altn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">altn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])></span><span style="color: #000000;">4</span> <span style="color: #008080;">and</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"==> "</span> <span style="color: #008080;">then</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">line</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">utf8_to_utf32</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]),</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">parse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">line</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">expected</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">5</span><span style="color: #0000FF;">..$]</span> <span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">=</span><span style="color: #000000;">expected</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (res is the unicode version)</span> <span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">WINDOWS</span> <span style="color: #008080;">or</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"0"</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %40s ok\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- (unicode output on windows consoles is fiddly...)</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: ok\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">else</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expected</span><span style="color: #0000FF;">,</span><span style="color: #000000;">alts</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">and</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">=</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">altn</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">6</span><span style="color: #0000FF;">..$]</span> <span style="color: #008080;">then</span> <span style="color: #000080;font-style:italic;">-- (res is the ascii equivalent)</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %40s ok\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">else</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: error - %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> <span style="color: #0000FF;">?</span><span style="color: #008000;">"done"</span> <span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">wait_key</span><span style="color: #0000FF;">()</span> <!--</syntaxhighlight>--> {{out}} uni_frac = false (ie windows) <pre> 1: x^5 - 2x^4 + 42x^3 + 40x + 1 ok Line 474 ⟶ 1,155: 38: x^5 - 2x^4 + 42x^3 + 40x + 1 ok </pre> 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) ~~uni_frac = true (linux only)~~ <pre> 1: x⁵ - 2x⁴ + 42x³ + 40x + 1 ok Line 494 ⟶ 1,175: 36: x⁵ - 2x⁴ + 42x³ + 40x + 1 ok 38: x⁵ - 2x⁴ + 42x³ + 40x + 1 ok </pre> =={{header\|Wren}}== {{trans\|Go}} {{libheader\|Wren-pattern}} <syntaxhighlight lang="wren">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 - 2x4 + 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) }</syntaxhighlight> {{out}} <pre> -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 - 2x4 + 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 </pre>