%D \module
%D   [       file=m-polynomial,
%D        version=2023.8.18,
%D          title=\CONTEXT\ Math Module,
%D       subtitle=Polynomials,
%D         author={Mikael Sundqvist & Hans Hagen},
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

% maybe just m-polynomial like m-matrix

% built-in
%
% alternative=align:normal % uses align mechanism (carry over spacing)
% alternative=align:split  % uses align mechanism
% alternative=text:normal  % not aligned
% alternative=text:align   % uses alignhere etc
% alternative=default      % same as text:align (can be normal instead)
% alternative=none         % only processing
%
% user:
%
% alternative=somename     % \startsetups[math:polynomial:somename]

\startluacode
if not tex.issetup then -- will become a faster helper

    function tex.issetup(n) -- will become a faster helper
        return tex.isdefined(tokens.getters.macro("??setup") .. ":" .. n)
    end

end

local tonumber = tonumber

local context   = context
local copytable = table.copy
local round     = math.round

local shows   = { }
local helpers = { }

local implement = interfaces.implement

local v_none = interfaces.variables.none

local ctx_NC         = context.NC
local ctx_NR         = context.NR
local ctx_startcolor = context.startcolor
local ctx_stopcolor  = context.stopcolor

local result = {
    n           = 0,
    numerator   = { },
    denominator = { },
    steps       = { },
}

do

    local function show(t,split,symbol,mark)
        local n = #t
        local done = false
        for i=n,1,-1 do
            local tn = t[i]
            ctx_NC()
            if not tn or tn == 0 then
                if split then
                    ctx_NC()
                end
            else
                if mark then ctx_startcolor { mark } end
                if done and tn > 0 then
                    context("+")
                end
                if tn < 0 then
                    context("-")
                    tn = - tn
                end
                if split then
                    if mark then ctx_stopcolor() end
                    ctx_NC()
                    if mark then ctx_startcolor { mark } end
                end
                if i > 1 then
                    if tn ~= 1 then
                        context("%.3N",tn)
                    end
                    context(symbol)
                else
                   context("%.3N",tn)
                end
                if i > 2 then
                    context("^{%s}",i-1)
                end
                if mark then ctx_stopcolor() end
                done = true
            end
        end
        ctx_NR()
    end

    local function default(settings)
        local split  = settings.split
        local symbol = settings.symbol or "x"
        context.startalign {
            n     = (split and 2 or 1) * result.n,
            align = "all:right",
        }
            local steps    = result.steps
            local previous = result.numerator
            show(result.denominator,split,symbol,"blue")
            show(result.numerator,split,symbol)
            for i=1,#steps do
                local current = steps[i].numerator
                if previous then
                    show(helpers.subtract(previous,current),split,symbol,"red")
                end
                show(current,split,symbol)
                previous = current
            end
            show(result.quotient,split,symbol,"green")
         -- inspect(result)
        context.stopalign()
    end

    shows["align:normal"] = function(settings) default(settings,false) end
    shows["align:split"]  = function(settings) default(settings,true)  end

end

do

    local function show(t,symbol)
        local n = #t
        local done = false
        for i=n,1,-1 do
            local tn = t[i]
            if not tn or tn == 0 then
                -- ignore
            else
                if done and tn > 0 then
                    context("+")
                end
                if tn < 0 then
                    context("-")
                    tn = - tn
                end
                if i > 1 then
                    if tn ~= 1 then
                        context("%.3N",tn)
                    end
                    context(symbol)
                else
                   context("%.3N",tn)
                end
                if i > 2 then
                    context("^{%s}",i-1)
                end
                done = true
            end
        end
    end

    helpers.show = show

    local function show_n_over_d(n,d,index,symbol)
        local colors = result.colors
        local c  = colors and colors[index]
        local cn = c and (c.ns or c.n)
        local cd = c and (c.ds or c.d)
        context.frac(
            function()
                if cn then
                    ctx_startcolor { cn }
                        show(n,symbol)
                    ctx_stopcolor()
                else
                    show(n,symbol)
                end
            end,
            function()
                if cd then
                    ctx_startcolor { cd }
                        show(d,symbol)
                    ctx_stopcolor()
                else
                    show(d,symbol)
                end
            end
        )
    end

    local function show_what(w,what,index,symbol)
        local colors = result.colors
        local c = colors and colors[index]
        local cw = c and c[what]
        if cw then
            ctx_startcolor { cw }
                show(w,symbol)
            ctx_stopcolor()
        else
            show(w,symbol)
        end
    end

    local function show_n(n,index,symbol) show_what(n,"n",index,symbol) end
    local function show_d(d,index,symbol) show_what(d,"d",index,symbol) end
    local function show_q(q,index,symbol) show_what(q,"q",index,symbol) end

    helpers.show_n        = show_n
    helpers.show_d        = show_d
    helpers.show_q        = show_q
    helpers.show_n_over_d = show_n_over_d

    local function lines(settings,align)
        local steps    = result.steps
        local nofsteps = #steps
        local colors   = result.colors
        local symbol   = result.symbol or "x"
        show_n_over_d(result.numerator,result.denominator,0,symbol)
        if nofsteps > 0 then
            if align then
                context.alignhere()
            end
            context(steps[1].clipped and "≈" or "=")
            for i=1,nofsteps do
                local step = steps[i]
                show_q(step.quotient,i,symbol)
                if not helpers.iszero(step.numerator) then
                    context("+")
                    show_n_over_d(step.numerator,result.denominator,i,symbol)
                end
                if i < nofsteps then
                    if align then
                        context.breakhere()
                    end
                    context(step.clipped and "≈" or "=",symbol)
                end
            end
        else
         -- context.quad()
         -- context.mtext("(no quotient)")
        end
    end

    shows["text:normal"] = function(settings) lines(settings,false) end
    shows["text:align"]  = function(settings) lines(settings,true)  end

end

do

    local function subtract(n,d)
        local t = { }
        for i=1,#d do
             t[i] = n[i] - d[i]
        end
        return t
    end

    local function negate(v)
        local t = { }
        for i=1,#v do
            t[i] = -v[i]
        end
        return t
    end

    local function iszero(t)
        for i=1,#t do
            if t[i] ~= 0 then
                return false
            end
        end
        return true
    end

    local function last(t)
        for i=#t,1,-1 do
            local ti = t[i]
            if ti ~= 0 then
                return i
            end
        end
        return false
    end

    local meps <const> = -0.000001
    local peps <const> =  0.000001

    local function solve(settings)
        local numerator   = settings.numerator
        local denominator = settings.denominator
        if type(numerator) == "string" then
            numerator          = utilities.parsers.settings_to_array(numerator)
            settings.numerator = numerator
        end
        if type(denominator) == "string" then
            denominator          = utilities.parsers.settings_to_array(denominator)
            settings.denominator = denominator
        end
        local n = #numerator
        local d = #denominator
        for i=1,n do numerator  [i] = tonumber(numerator  [i]) or 0 end
        for i=1,d do denominator[i] = tonumber(denominator[i]) or 0 end -- proper numbers
        for i=1,n do denominator[i] = tonumber(denominator[i]) or 0 end
        --
        if d > n then
            logs.report("polynomial","denominator has a higher degree")
            -- kind of fatal error
        end
        --
        local nlast    = last(numerator)
        local dlast    = last(denominator)
        local steps    = { }
        local quotient = { }
        result   = {
            n           = n,
            numerator   = numerator,
            denominator = denominator,
            steps       = steps,
            colors      = settings.colors,
            symbol      = settings.symbol or "x",
        }
        for i=1,n do
            quotient[i] = 0
        end
        while nlast and dlast and nlast >= dlast do
            numerator = copytable(numerator)
            local shift  = nlast - dlast
            local nvalue = numerator[nlast]
            local dvalue = denominator[dlast]
         -- local factor = nvalue // dvalue
            local factor = nvalue / dvalue
            local clipped = false
            for i=1,n do
                 local ni = numerator[i]
                 local di = denominator[i-shift] or 0
                 local ni = ni - factor * di
                 if ni ~= 0 and ni > meps and ni < peps then
                     ni = 0
                     clipped = true
                 end
                 numerator[i] = ni
            end
            quotient[shift+1] = factor
            steps[#steps+1]  = {
                numerator = numerator,
                factor   = factor,
                nvalue   = nvalue,
                dvalue   = dvalue,
                shift    = shift,
                quotient = copytable(quotient),
                clipped  = clipped
            }
            local l = last(numerator)
            if l == nlast then
                break
            end
            nlast = l
        end
        return result
    end

    helpers.last     = last
    helpers.subtract = subtract
    helpers.negate   = negate
    helpers.iszero   = iszero
    helpers.solve    = solve

    shows[v_none] = function(settings)
        --
    end

    shows.default = shows["text:normal"]

    local function tocolors(colors)
        if type(colors) == "string" then
            local list = utilities.parsers.settings_to_hash(colors)
            local done = { }
            for k, v in next, list do
                done[tonumber(k) or 0] = utilities.parsers.settings_to_hash(v)
            end
            return done
        end
    end

    implement {
        name      = "polynomial",
        arguments =  {
            {
                { "alternative" },
                { "numerator" },
                { "denominator" },
                { "split", "boolean" },
                { "colors" },
                { "symbol" },
            },
        },
        actions   = function(settings)
            settings.colors = tocolors(settings.colors)
            result = solve(settings)
            local alternative = settings.alternative or "default"
            if shows[alternative] then
                shows[alternative](settings)
            else
                local s = "math:polynomial:" .. alternative
                if tex.issetup(s) then
                    context.formatted.directsetup(s)
                else
                    shows.default(settings)
                end
            end
        end
    }

    local show = helpers.show

    local function getcolor(n,what)
        local colors = result.colors
        local c = colors and colors[n]
        return c and c[what]
    end

    implement {
        name      = "polynomialsteps",
        usage     = "value",
        actions   = function()
            return tokens.values.integer, #result.steps
        end
    }

    implement {
        name      = "polynomialfactor",
        arguments = "integer",
        actions   = function(n)
            local s = result.steps[n]
            if s and s.factor then
                context(round(s.factor))
            else
                context(0)
            end
        end,
    }

    implement {
        name      = "polynomialshift",
        arguments = "integer",
        actions   = function(n)
            local s = result.steps[n]
            if s and s.shift then
                context(round(s.shift))
            else
                context(0)
            end
        end,
    }


-- tokens.converters = { }
--
-- local getexpansion = token.getexpansion
--
-- function tokens.converters.tonumber(s)
--     return tonumber(s and getexpansion([[\noexpand\the\numexpr ]] .. s)) or 0
-- end
--
-- interfaces.implement {
--     name      = "demo",
--     public    = true,
--     arguments = "optional",
--     actions = function(s)
--         context(tokens.converters.tonumber(s))
--     end
-- }


    local function whatever(kind,s)
        if kind == "-" then
            s = helpers.negate(s)
        end
        if kind == "+" or kind == '-' then
            for i=#s,1,-1 do
                if s[i] < 0 then
                    break
                elseif s[i] > 0 then
                    context("+")
                    break
                end
            end
        end
        helpers.show(s,result.symbol)
    end

    implement {
        name      = "polynomialnumerator",
        arguments = { "string", "integer" },
        actions   = function(kind,n)
            if n > 0 then
                local s = result.steps[n]
                if s then
                    whatever(kind,s.numerator)
                end
            else
                whatever(kind,result.numerator)
            end
        end
    }

    implement {
        name      = "polynomialdenominator",
        arguments = { "string", "integer" },
        actions   = function(kind,n)
            whatever(kind,result.denominator)
        end,
    }

    implement {
        name      = "polynomialquotient",
        arguments = { "string", "integer" },
        actions   = function(kind,n)
            if n > 0 then
                local s = result.steps[n]
                if s then
                    whatever(kind,s.quotient)
                end
            end
        end,
    }

    implement {
        name      = "polynomialstep",
        arguments = { "string", "integer" },
        actions   = function(kind,n)
            local s = n > 0 and result.steps[n] or result
            if s then
                helpers.show_n_over_d(s.numerator,result.denominator,n,result.symbol)
            end
        end
    }

    implement {
        name      = "polynomialquotientstep",
        arguments = { "string", "integer" },
        actions   = function(kind,n)
            local s = result.steps[n]
            if s then
                local f = s.factor
                if n > 1 then
                    local p = result.steps[n-1]
                    s = helpers.subtract(s.quotient,p.quotient)
                else
                    s = s.quotient
                end
                if kind == "-" then
                    if f > 0 then
                        context("-")
                    else
                        s = helpers.negate(s)
                        context("+")
                    end
                elseif kind == "+" then
                    if f > 0 then
                        context("+")
                    end
                end
                helpers.show_q(s,n,result.symbol)
            end
        end,
    }

    implement {
        name      = "ifpolynomialclipped",
        arguments = "integer",
        usage     = "condition",
        public    = true,
        actions   = function(n)
            local s = result.steps[n]
            return tokens.values.boolean, s and s.quotient
        end,
    }

    implement {
        name      = "ifpolynomialnumerator",
        arguments = "integer",
        usage     = "condition",
        public    = true,
        actions   = function(n)
            local s
            if n > 0 then
                s = result.steps[n]
            else
                s = result
            end
            return tokens.values.boolean, s and not helpers.iszero(s.numerator)
        end
    }

    implement {
        name      = "polynomialsymbol",
        public    = true,
        protected = true,
        actions   = function()
            context(result.symbol)
        end,
    }

end

\stopluacode

\unprotect

\installcorenamespace {polynomial}

\installparameterhandler\??polynomial {polynomial}
\installsetuphandler    \??polynomial {polynomial}

\setuppolynomial
  [\c!split=\v!no,
   \c!alternative=text:align,
   \c!symbol=x]

\tolerant\protected\def\polynomial[#S#1]#*[#2]#*[#3]%
  {\begingroup
   \ifhastok={#1}%
     \setupcurrentpolynomial[#1]%
     \donetrue
   \else
     \donefalse
   \fi
   \clf_polynomial {
      numerator   \ifdone{#2}\else{#1}\fi
      denominator \ifdone{#3}\else{#2}\fi
      alternative {\polynomialparameter\c!alternative}
      colors      {\polynomialparameter\c!color}
      symbol      {\polynomialparameter\c!symbol}
      split       \ifcstok{\polynomialparameter\c!split}\v!yes true \else false\fi
   }%
   \endgroup}

\tolerant\protected\def\polynomialsteps       {\the\clf_polynomialsteps}
\tolerant\protected\def\polynomialfactor      [#1]{\clf_polynomialfactor      \numexpr\ifparameter#1\or#1\else\zerocount\fi\relax}
\tolerant\protected\def\polynomialshift       [#1]{\clf_polynomialshift       \numexpr\ifparameter#1\or#1\else\zerocount\fi\relax}

\tolerant\def\module_polynomial_component[#1]#*[#2]#*[#3]%
  {\ifarguments
   \or
     #1{}\zerocount
   \or
     #1{}\numexpr\ifparameter#2\or#2\else\zerocount\fi\relax
   \else
     #1{#2}\numexpr\ifparameter#3\or#3\else\zerocount\fi\relax
   \fi}

\protected\def\polynomialnumerator   {\module_polynomial_component[\clf_polynomialnumerator   ]}
\protected\def\polynomialdenominator {\module_polynomial_component[\clf_polynomialdenominator ]}
\protected\def\polynomialquotient    {\module_polynomial_component[\clf_polynomialquotient    ]}
\protected\def\polynomialquotientstep{\module_polynomial_component[\clf_polynomialquotientstep]}
\protected\def\polynomialstep        {\module_polynomial_component[\clf_polynomialstep        ]}

\startsetups math:polynomial:complete
    \frac {
        \polynomialnumerator
    } {
        \polynomialdenominator
    }
    \alignhere
    \localcontrolledrepeat \polynomialsteps {
        =
        \ifnum\currentloopiterator>\plusone
            \polynomialquotient[\currentloopiterator - 1] +
        \fi
        \frac {
            \polynomialquotientstep[\currentloopiterator]
            (\polynomialdenominator)
            \polynomialnumerator[+][\currentloopiterator - 1]
% \polynomialnumerator[-][\currentloopiterator - 1]
            \polynomialquotientstep[-][\currentloopiterator]
% \polynomialquotientstep[+][\currentloopiterator]
            (\polynomialdenominator)
        } {
            \polynomialdenominator
        }
        \breakhere
        =
        \polynomialquotient[\currentloopiterator]
        \ifpolynomialnumerator\currentloopiterator
            +
            \frac {
                \polynomialnumerator[\currentloopiterator]
            } {
                \polynomialdenominator
            }
        \fi
        \ifnum\currentloopiterator<\polynomialsteps
            \breakhere
        \fi
    }
\stopsetups

\protect

\continueifinputfile{m-polynomial.mkxl}

\setuplayout[tight]

\setuppapersize[A4,landscape][A4,landscape]

\starttext

\setuppolynomial[symbol=z]

% \def\TempHack
%   {\scratchcounter\setmathoptions\mathbinarycode
%    \bitwiseflip\scratchcounter-\lookaheadforendclassoptioncode
%    \setmathoptions\mathbinarycode\scratchcounter}
%
% \startformula
% \TempHack
% \polynomial
%     [-5, -3,  3, -1, 1,  0, 2, -3, -2, -1, 4]
%     [-8, -7, -5,  2, 8, -9, 1]
% \stopformula

% \startformula
% \TempHack
% \polynomial
%     [split=yes]
%     [-5, -3,  3, -1, 1,  0, 2, -3, -2, -1, 4]
%     [-8, -7, -5,  2, 8, -9, 1]
% \stopformula

\def\TestPolynomial#1#2#3%
  {\startformula
   \polynomial
      [alternative=#1]
      [#2]
      [#3]
   \stopformula}

% \page

\def\TestPolynomials#1#2%
  {\page
   \TestPolynomial{text:normal} {#1}{#2}
   \blank[3*big]
   \TestPolynomial{text:align}  {#1}{#2}
   \page
   }

\TestPolynomials
    {7, -5,  2, 3}
    {3, 0, 1}

\TestPolynomials
    {7, -5,  2, 3}
    {3,  0,  2.7}

\TestPolynomials
    {7, -5,  2, 3}
    {3,  0,  1}

\startformula
\polynomial
  [color={1={n=red,d=green,q=blue},2={n=cyan,d=magenta,q=orange}}]
  [7, -5,  2, 3, 2]
  [3,  0,  1]
\stopformula

\polynomial
  [alternative=none,
   color={1={n=red,d=green,q=blue},2={n=cyan,d=magenta,q=orange,ds=darkgray}}]
  [7, -5,  2, 3, 2]
  [3,  0,  1]

numerator

\startformula
    \polynomialnumerator
\stopformula

numerator 2

\startformula
    \polynomialnumerator[2]
\stopformula

denominator

\startformula
    \polynomialdenominator
\stopformula

quotient 1/2/3

\startformula
    \polynomialquotient[1]/
    \polynomialquotient[2]/
    \polynomialquotient[3]
\stopformula

quotientstep 1/2/3

\startformula
    \polynomialquotientstep[1]/
    \polynomialquotientstep[2]/
    \polynomialquotientstep[3]
\stopformula

steps

\startformula
    \polynomialsteps
\stopformula

factor

\startformula
    \polynomialfactor[2]
\stopformula
a
shift

\startformula
    \polynomialshift[2]
\stopformula


\startformula
    \frac {\polynomialnumerator}{\polynomialdenominator}
    =
    \polynomialquotient[1]
    +
    \frac {\polynomialnumerator[1]}{\polynomialdenominator}
\stopformula

\startformula
\polynomial
  [alternative=complete,
   color={1={n=red,d=green,q=blue},2={n=cyan,d=magenta,q=orange,ds=darkgray}}]
  [7, -5,  2, 3, 2]
  [3,  0,  1]
\stopformula

% \ifpolynomialclipped1 YES \else NOP \fi

\dorecurse\polynomialsteps{
    \startformula
        \polynomialstep[#1]
    \stopformula
}

\input tufte

\startformula
    \polynomialdenominator
    \polynomialnumerator[2]
    \frac{3x^3+2x^2-5x+7}{x^2+3}
    \alignhere
    = 3x + \frac{2x^2 - 14x + 7}{x^2+3}
    \breakhere
    = 3x + 2 + \frac{-14x+1}{x^2+3}
\stopformula

\input tufte

\startformula
    \frac{3x^3+2x^2-5x+7}{x^2+3}
    \alignhere
    = 3x + \frac{2x^2 - 14x + 7}{x^2+3}
    \breakhere
    = 3x + 2 + \frac{-14x+1}{x^2+3}
\stopformula

% \input tufte

\TestPolynomials
    {-5, -3,  3, -1, 1,  0, 2, -3, -2, -1, 4}
    {-8, -7, -5,  2, 8, -9, 1}

\TestPolynomials
    {-1, 0, 1}
    {-1, 1}

% \input tufte

\TestPolynomials
    {-1, 1}
    {-1, 0, 1}

% \input tufte

\stoptext