if not modules then modules = { } end modules ['math-ini'] = {
    version   = 1.001,
    comment   = "companion to math-ini.mkiv",
    author    = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

-- The way we do math in \CONTEXT\ \MKIV\ differs from other macro packages so you
-- should not mix the somewhat unique (and bit weird) approach here with the more
-- traditional (\TEX) approach. Also, we use char-def.lua as starting point and that
-- file is quite \CONTEXT\ specific. When we added math to that there was no
-- interest (quite the contrary) so we didn't went generic there which in retrospect
-- also gives us the freedom to add more information, something that happens
-- occasionally. Because that file is shared between \MKIV\ and \LMTX\ some
-- information is only used by \LMTX. We also have quite some runs over the math
-- list but that has been so since we started and performance will not degrade much
-- by it; after all math is not that demanding. More details can be found in the
-- manuals that discuss math. Most code (and concepts) date from 2005 so maybe I
-- will upgrade the lot some day, although it has been adapted on the way to the
-- changes in the engine(s).

local next, type = next, type
local formatters, find, nospaces = string.formatters, string.find, string.nospaces
local utfchar, utfbyte = utf.char, utf.byte
local sortedhash = table.sortedhash
local toboolean = toboolean

local context               = context
local implement             = interfaces.implement

local ctx_doifelsesomething = commands.doifelsesomething

local trace_defining        = false  trackers.register("math.defining", function(v) trace_defining = v end)

local report_math           = logs.reporter("mathematics","initializing")

mathematics                 = mathematics or { }
local mathematics           = mathematics

mathematics.extrabase       = fonts.privateoffsets.mathextrabase -- here we push some virtuals
mathematics.privatebase     = fonts.privateoffsets.mathbase      -- here we push the ex

local unsetvalue            <const> = attributes.unsetvalue

local allocate              = utilities.storage.allocate
local chardata              = characters.data

local texsetattribute       = tex.setattribute
local setmathcode           = tex.setmathcode
----- setdelcode            = tex.setdelcode -- we no longer set these as the engine also accepts otherwise
local texintegerdef         = tex.integerdef

local getfontoffamily       = tex.getfontoffamily

local fontdata              = fonts.hashes.identifiers
local fontchardata          = fonts.hashes.characters

-- These are different from mkiv with luatex.

local classes          = allocate { unset = 64 } -- or -1
local classnames       = allocate { }
local maxengineclass   = 63
local lastengineclass  = 0
local lastprivateclass = maxengineclass

for k, v in next, nodes.noadcodes do
    if type(k) == "string" then
        classes[k] = v
--         local n = classnames[v]
--         if not n or #k < #n then
--             classnames[v] = k
--         end
    elseif k > lastengineclass then
        lastengineclass = k
    end
end

local ordinary_class    = classes.ordinary
local operator_class    = classes.operator
local binary_class      = classes.binary
local relation_class    = classes.relation
local open_class        = classes.open
local close_class       = classes.close
local variable_class    = classes.variable
local punctuation_class = classes.punctuation
local middle_class      = classes.middle
local accent_class      = classes.accent
local radical_class     = classes.radical
local fraction_class    = classes.fraction
local under_class       = classes.under
local over_class        = classes.over
local fenced_class      = classes.fenced
local ghost_class       = classes.ghost

-- these will go

classes.ord             = ordinary_class
classes.op              = operator_class
classes.bin             = binary_class
classes.rel             = relation_class
classes.opening         = open_class         -- will go
classes.closing         = close_class        -- will go
classes.punct           = punctuation_class
classes.frac            = fraction_class
classes.rad             = radical_class
classes.fen             = fenced_class
classes.gst             = ghost_class

-- these will go too

classes.limop           = operator_class
classes.limoperator     = operator_class
classes.nolop           = operator_class
classes.nolimoperator   = operator_class
classes.large           = operator_class
classes.largeoperator   = operator_class

-- special in the engine : variable active inner vcenter

local glyphcodes = nodes.glyphcodes

local function registerengineclass(name,short)
    local class = classes[name]
    if not class then
        if lastengineclass < maxengineclass then
            lastengineclass = lastengineclass + 1
            class = lastengineclass
            classnames[class] = short or name
        else
            class = ordinary_class
        end
    else
        classnames[class] = short or name
    end
    classes[class] = name
    classes[name] = class
    local subtype = class + 31 -- todo magic constant
    glyphcodes[subtype] = name
    glyphcodes[name] = subtype
    return class
end

-- predefined classes

registerengineclass("ordinary",    "ord")
registerengineclass("operator",    "ope")
registerengineclass("binary",      "bin")
registerengineclass("relation",    "rel")
registerengineclass("open",        "ope")
registerengineclass("close",       "clo")
registerengineclass("punctuation", "pun")
registerengineclass("variable",    "var") -- not used
registerengineclass("active",      "act") -- not used
registerengineclass("inner",       "inn") -- not used
registerengineclass("middle",      "mid")
registerengineclass("accent",      "acc")
registerengineclass("radical",     "rad")
registerengineclass("fraction",    "fra")
registerengineclass("under",       "und")
registerengineclass("over",        "ove")
registerengineclass("fenced",      "fen")
registerengineclass("ghost",       "gho")
registerengineclass("vcenter",     "vce") -- not used

-- additional classes

registerengineclass("explicit",        "xpl")
registerengineclass("imaginary",       "img")
registerengineclass("differential",    "dif")
registerengineclass("exponential",     "exp")
registerengineclass("integral",        "int")
registerengineclass("ellipsis",        "ell")
registerengineclass("function",        "fnc")
registerengineclass("digit",           "dig")  local division_class =
registerengineclass("division",        "div")
registerengineclass("factorial",       "fac")
registerengineclass("wrapped",         "wra")
registerengineclass("construct",       "con")
registerengineclass("dimension",       "dim")
registerengineclass("unary",           "una")
registerengineclass("textpunctuation", "tpu")
registerengineclass("unspaced",        "uns")
registerengineclass("experimental",    "exp")
registerengineclass("fake",            "fak")
registerengineclass("numbergroup",     "ngr")

registerengineclass("maybeordinary",   "mor")
registerengineclass("mayberelation",   "mre")
registerengineclass("maybebinary",     "mbi")

registerengineclass("chemicalbond",    "chb")
registerengineclass("implication",     "imp")

registerengineclass("continuation",    "ctn")

local specialclasses = tex.specialmathclasscodes

classes["all"]   = specialclasses["all"]    classnames[specialclasses["all"]  ] = "all"
classes["begin"] = specialclasses["begin"]  classnames[specialclasses["begin"]] = "beg"
classes["end"]   = specialclasses["end"]    classnames[specialclasses["end"]  ] = "end"

callbacks.register("get_noad_class", function(n) return classnames[n] end,"provide math class name")

-- inspect(classes) os.exit()

local function registerprivateclass(name,parent)
    local class = parent and classes[parent] or classes[name]
    if not class then
        lastprivateclass = lastprivateclass + 1
        class = lastprivateclass
        classes[name] = class
        -- also setup
    end
    return class
end

local function toengineclass(class)
    if type(class) == "string" then
        return classes[class] or ordinary_class
    elseif class > lastengineclass then
        return ordinary_class
    else
        return class
    end
end

implement {
    name      = "registerengineclass",
    public    = true,
    protected = true,
    arguments = { "optional", "optional" },
    actions   = registerengineclass,
}

local topaccent_class    = registerprivateclass("topaccent")
local bottomaccent_class = registerprivateclass("bottomaccent")
local delimiter_class    = registerprivateclass("delimiter")
local root_class         = registerprivateclass("root")
----- prime_class        = registerprivateclass("prime")

registerprivateclass("botaccent","bottomaccent")

local accents = allocate {
    accent       = true, -- some can be both
    topaccent    = true,  [topaccent_class]    = true,
    bottomaccent = true,  [bottomaccent_class] = true,
    botaccent    = true,
    under        = true,  [under_class]        = true,
    over         = true,  [over_class]         = true,
    unknown      = false,
}

local integer_value <const> = tokens.values.integer

implement {
    name      = "mathclassvalue",
 -- usage     = "value",
    public    = true,
    arguments = "string", -- here we also accent \mathclassvalue foo so no {}
    actions = function(name)
     -- return integer_value, classes[name] or ordinary_class
        context(tostring(classes[name] or ordinary_class))
    end
}

-- used in math-tag: so there we need to make things ord etc to fit within
-- mathml

local codes = allocate {
    variable       = variable_class,    [variable_class]    = "variable",
    ordinary       = ordinary_class,    [ordinary_class]    = "ordinary",
    largeoperator  = operator_class,    [operator_class]    = "largeoperator",
    binaryoperator = binary_class,      [binary_class]      = "binaryoperator",
    relation       = relation_class,    [relation_class]    = "relation",
    openingsymbol  = open_class,        [open_class]        = "openingsymbol",
    closingsymbol  = close_class,       [close_class]       = "closingsymbol",
    punctuation    = punctuation_class, [punctuation_class] = "punctuation",
    middlesymbol   = middle_class,      [middle_class]      = "middlesymbol",
}

local extensibles = allocate {
           unknown    = 0,
    l = 1, left       = 1,
    r = 2, right      = 2,
    h = 3, horizontal = 3,-- lr or rl
    u = 5, up         = 4,
    d = 5, down       = 5,
    v = 6, vertical   = 6,-- ud or du
    m = 7, mixed      = 7,
}

table.setmetatableindex(extensibles,function(t,k) t[k] = 0 return 0 end)

local virtualized = allocate {
}

function mathematics.virtualize(unicode,virtual)

    local function virtualize(k,v)
        local c = virtualized[k]
        if c == v then
            report_math("character %C is already virtualized to %C",k,v)
        elseif c then
            report_math("character %C is already virtualized to %C, ignoring mapping to %C",k,c,v)
        else
            virtualized[k] = v
        end
    end

    if type(unicode) == "table" then
        for k, v in next, unicode do
            virtualize(k,v)
        end
    elseif type(unicode) == "number" and type(virtual) == "number" then
        virtualize(unicode,virtual)
 -- else
        -- error
    end
end

mathematics.extensibles   = extensibles
mathematics.classes       = classes
mathematics.toengineclass = toengineclass
mathematics.classnames    = classnames
mathematics.codes         = codes
-----------.accents       = codes
mathematics.virtualized   = virtualized

-- This is relatively new and experimental:

do

    local dictionaries       = mathematics.dictionaries or { }
    mathematics.dictionaries = dictionaries

    local names    = dictionaries.names    or utilities.storage.allocate()
    local groups   = dictionaries.groups   or utilities.storage.allocate()
    local data     = dictionaries.data     or utilities.storage.allocate()
    local sets     = dictionaries.sets     or utilities.storage.allocate()
    local variants = dictionaries.variants or utilities.storage.allocate() -- todo: get from char-def
    local defaults = dictionaries.defaults or utilities.storage.allocate() -- todo: get from char-def

    storage.register("mathematics/dictionaries/names",    names,    "mathematics.dictionaries.names")
    storage.register("mathematics/dictionaries/groups",   groups,   "mathematics.dictionaries.groups")
    storage.register("mathematics/dictionaries/data",     data,     "mathematics.dictionaries.data")
    storage.register("mathematics/dictionaries/sets",     sets,     "mathematics.dictionaries.sets")
    storage.register("mathematics/dictionaries/variants", variants, "mathematics.dictionaries.variants")
    storage.register("mathematics/dictionaries/defaults", defaults, "mathematics.dictionaries.defaults")

    dictionaries.names    = dictionaries.names    or names
    dictionaries.groups   = dictionaries.groups   or groups
    dictionaries.data     = dictionaries.data     or data
    dictionaries.sets     = dictionaries.sets     or sets
    dictionaries.variants = dictionaries.variants or variants
    dictionaries.defaults = dictionaries.defaults or defaults

    local i_everygroup <const> = 0xFFFF
    local s_everygroup <const> = "everygroup"

    names [s_everygroup] = i_everygroup
    names [i_everygroup] = i_everygroup
    groups[i_everygroup] = s_everygroup
    data  [i_everygroup] = { }

    if not sets.n then
        sets.n = 0
    end

    function dictionaries.registergroup(name)
        local group = rawget(names,name)
        if not group then
            group = #groups + 1
            names[name]   = group
            names[group]  = group -- hm
            groups[group] = name
            data[group]   = { }
            local csname  = "math" .. nospaces(name) .. "dictionary"
            texintegerdef(csname,group,"immutable")
        end
        return group
    end

    function dictionaries.registergroupset(name,set)
        local s = sets[name]
        if not s then
            if set == "every" then
                s = {
                    group = i_everygroup,
                }
                sets[name] = s
            else
                local d = dictionaries.registergroup(name)
                local n = sets.n + 1
                local l = utilities.parsers.settings_to_array(set)
                local g = { }
                for i=1,#l do
                    local n = names[l[i]]
                    if n then
                        g[#g+1] = n -- ordered
                    end
                end
                s = {
                    names  = l,
                    groups = g,
                    group  = d,
                }
                sets[name] = s
                sets[d]    = s
            end
        end
    end

    -- TODO: check 'minus' as it reports true

    function dictionaries.groupset(name)
        return sets[name] or { }
    end

    function dictionaries.groupsetgroup(name)
        if name == "every" or name == s_everygroup then
            return i_everygroup
        else
            local s = sets[name]
            if s then
                return s.group
            else
                return names[name] or 0
            end
        end
    end

    function dictionaries.registercharacter(group,index,description,class,name) -- name is diagnostic
        local d = names[group] -- can be number or string
        if d then
            data[d][index] = description or true
            local v = variants[index]
            if type(class) == "string" then
                class = classes[class]
            end
            if not class then
                class = true
            end
            if v then
                v[d] = class
            else
                variants[index] = { [d] = class }
            end
            if not defaults[index] then
                defaults[index] = d
            end
        end
--         print(group,index,description,class,name)
    end

    function dictionaries.name(group,index) -- number, number
        group = names[group] or i_everygroup
        if group == i_everygroup then
            for i=1,#groups do
                local d = data[i]
                local n = d[index]
                if type(n) == "string" then
                    return n
                end
            end
        elseif group then
            local d = data[group]
            if d then
                local n = d[index]
                if type(n) == "string" then
                    return n
                end
            end
            local s = sets[group]
            if s then
                local g = s.groups
                for i=1,#g do
                    d = data[g[i]]
                    local n = d[index]
                    if type(n) == "string" then
                        return n
                    end
                end
            end
        end
        return false
    end

    implement {
        name      = "registergroupset",
        arguments = "2 arguments",
        actions   = dictionaries.registergroupset,
    }

    implement {
        name      = "groupsetgroup",
        arguments = "argument",
        actions   = { dictionaries.groupsetgroup, context },
    }

    local f_dictionary = false
    local whatdetail   = "all"

    local function trace(n,properties,group,index,font,char)
     -- local properties, group, index, font, char = nodes.nuts.getchardict(nodes.nuts.tonut(n))
        if whatdetail and (properties ~= 0 or group ~= 0 or index ~= 0) then
            local char = fontchardata[font][char]
            if char or whatdetail == "all" then
                local unicode = char and char.unicode
                if unicode then
                    local groupname = groups[group]
                    local indexname = false
                    if groupname then
                        indexname = data[group][index] -- dictionaries.data
                    else
                        groupname = "unknown"
                    end
                    if not indexname or indexname == true then
                        indexname = chardata[unicode]
                        indexname = indexname and indexname.description or "unknown"
                    end
                    if not f_dictionary then
                        f_dictionary = formatters["properties [%04X:%04X:%04X] [%s] %U : %s"]
                    end
                    return f_dictionary(properties,group,index,groupname,unicode,indexname)
                end
            end
        end
    end

    trackers.register("math.dictionaries",function(v) whatdetail = v end)

    callbacks.register("get_math_dictionary",trace,"provide math dictionary details")

    -- This is experimental and a prelude to the long pending "relate math rendering to
    -- some field" wish. In TeX characters and symbols are grouped by class but that is
    -- mostly related to spacing etc. while we actually want to group by meaning. A
    -- reasonable but incomplete starting point is:
    --
    -- https://www.w3.org/TR/MathML3/appendixa.html#parsing_DefEncAtt
    --
    -- But it has some weird short names mixed with long ones (and a strange suddenly
    -- uppercase: Differential-Operator) but we are not bound to that at all. We will
    -- probably remove and add categories anyway. This openmath stuff looks a bit
    -- abandoned but we can use it as a start and playground anyway.
    --
    -- The char-def.lua file will have mathgroup entries reflecting this.
    --
    -- This is a good one (with nice roll-overs too):
    --
    -- https://en.wikipedia.org/wiki/List_of_mathematical_symbols_by_subject

    if environment.initex then

        local registergroup = mathematics.dictionaries.registergroup

        registergroup("default")

        registergroup("binary relation")
        registergroup("binary set relation")
        registergroup("integral")
        registergroup("limit")
        registergroup("number set")
        registergroup("postfix operator")
        registergroup("prime")
        registergroup("binary operator")
        registergroup("binary vector")
        registergroup("binary arithmetic")     -- operator
        registergroup("binary logical")
        registergroup("binary set")
        registergroup("constant arithmetic")
        registergroup("constant set")
        registergroup("differential")
        registergroup("differential2")
        registergroup("factorial")
        registergroup("interval")
        registergroup("quantifier")
        registergroup("unary set")             -- check forall exists etc
        registergroup("constant logical")      -- new one
        registergroup("partial")               -- partial differential
        registergroup("nary operator")         -- new one
        registergroup("nary logical")
        registergroup("specifier")
        registergroup("specifier2")
        registergroup("pause")
        registergroup("punctuation")
     -- registergroup("grouped")
        registergroup("unary logical")
        registergroup("whatever")
        registergroup("whatever2")

     -- registergroup("binary linear algebra")
     -- registergroup("lambda")
     -- registergroup("nary arithmetic")       -- see operator
     -- registergroup("nary constructor")
     -- registergroup("nary functional")
     -- registergroup("nary linear algebra")
     -- registergroup("nary minmax")
     -- registergroup("nary relation")
     -- registergroup("nary set list")
     -- registergroup("nary set relation")
     -- registergroup("nary set")
     -- registergroup("nary statistics")
     -- registergroup("product")
     -- registergroup("unary arithmetic")      -- operator
     -- registergroup("unary elementary")      -- sin cos ln sqrt
     -- registergroup("unary functional")
     -- registergroup("unary linear algebra")
     -- registergroup("unary logical")
     -- registergroup("unary vector")

    end

    -- \Umathdictdef\vdash 1 \mathbinarylogicaldictionary "22A2 \mathrelationcode 0 "22A2
    --
    -- \startluacode
    --     mathematics.dictionaries.registercharacter("binary logical",0x22A2,"implies")
    -- \stopluacode

end

do

    local skip = {
       [accent_class]       = true,
       [topaccent_class]    = true,
       [bottomaccent_class] = true,
       [over_class]         = true,
       [under_class]        = true,
       [radical_class]      = true,
       [root_class]         = true,
    }

    local registercharacter = mathematics.dictionaries.registercharacter
    local groupnames        = mathematics.dictionaries.names

    local i_everygroup <const> = 0xFFFF

    local setmathcharacter = function(class,family,slot,unicode,mset,group,meaning)
        if mset and class ~= ordinary_class then
            setmathcode("global",slot,class,family,unicode)
            mset = false
        end
        if group then
            group = groupnames[group] or 0
            if group ~= 0 then
                -- which one
                registercharacter(group,unicode,meaning,class)
             -- registercharacter(group,slot,meaning,class)
            end
        end
        return mset
    end

    local function report(class,family,unicode,name,group)
        local nametype = type(name)
        if not group then
            group = "no group"
        end
        if nametype == "string" then
            report_math("class %a, family %a, char %C, name %a, group %a",class,family,unicode,name,group)
        elseif nametype == "number" then
            report_math("class %a, family %a, char %C, number %U, group %a",class,family,unicode,name,group)
        else
            report_math("class %a, family %a, char %C, group %a",class,family,unicode,group)
        end
    end

    local texmathchardef = tex.mathchardef

    local setmathsymbol = function(name,class,family,slot,stretch,group,meaning) -- hex is nicer for tracing
        if skip[class] then
            return -- only in mkiv
     -- elseif class == open_class or class == close_class or class == middle_class then
        else
            if class == delimiter_class then -- open close or middle (bars)
                class = ordinary_class
            end
            if group then
                group = groupnames[group] or 0
                if group ~= 0 then
                    texmathchardef(name,class,family,slot,"permanent",0x1,group,slot)
                    registercharacter(group,slot,meaning,class,name)
                    return
                end
            end
            texmathchardef(name,class,family,slot,"permanent")
        end
    end

    mathematics.setmathsymbol = setmathsymbol

    function mathematics.define()
        if trace_defining then
            logs.startfilelogging(report_math,"math defined from character definitions")
        end
        local family = 0
        local data   = characters.data
        --
        local function remap(first,last)
            for unicode=utfbyte(first),utfbyte(last) do
                setmathcode("global",unicode,ordinary_class,family,unicode)
            end
        end
        remap("0","9")
        remap("A","Z")
        remap("a","z")
        --
     -- setdelcode("global",0x2E,0,0,0,0) -- period is special -- still?
        --
        for unicode, character in sortedhash(data) do
            local symbol  = character.mathsymbol
            local mset    = true
            local class   = character.mathclass
            local spec    = character.mathspec
            local name    = character.mathname
            local stretch = character.mathstretch
            local group   = character.mathgroup
            local meaning = character.mathmeaning
            if symbol then
                local other = data[symbol]
                local class = other.mathclass
                if class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(engine,family,unicode,symbol,group)
                    end
                    mset = setmathcharacter(engine,family,unicode,symbol,mset,group,meaning)
                end
                local spec = other.mathspec
                if spec then
                    for i=1,#spec do
                        local m = spec[i]
                        local class = m.class
                        if class then
                            local engine = toengineclass(class)
                            -- todo: trace
                            mset = setmathcharacter(engine,family,unicode,symbol,mset,group,meaning)
                        end
                    end
                end
            end
            if spec then
                local done = false
                if class then
                    if name then
                        report_math("fatal error, conflicting mathclass and mathspec for %C",unicode)
                        os.exit()
                    else
                        class = classes[class] or ordinary_class
                        local engine = toengineclass(class)
                        if trace_defining then
                            report(engine,family,unicode,nil,group)
                        end
                        mset = setmathcharacter(engine,family,unicode,unicode,mset,group,meaning)
                        done = true
                    end
                end
                for i=1,#spec do
                    local m       = spec[i]
                    local name    = m.name
                    local class   = m.class   or class
                    local group   = m.group   or group
                    local stretch = m.stretch or stretch
                    local meaning = m.meaning or meaning
                    if class then
                        class = classes[class] or ordinary_class
                    else
                        class = ordinary_class
                    end
                    if class then
                        local engine = toengineclass(class)
                        if name then
                            if trace_defining then
                                report(engine,family,unicode,name,group)
                            end
                            setmathsymbol(name,engine,family,unicode,stretch,group,meaning)
                        else
                            name = (class == classes.ordinary or class == classes.digit) and "no name" -- character.adobename -- bad
                            if name and trace_defining then
                                report(engine,family,unicode,name,group)
                            end
                        end
                        if not done then
                            mset = setmathcharacter(engine,family,unicode,m.unicode or unicode,mset,group,meaning) -- see solidus
                            done = true
                        end
                    end
                end
            else
                if class then
                    class = classes[class] or ordinary_class
                else
                    class = ordinary_class
                end
                if name ~= nil then
                    local engine = toengineclass(class)
                    if name == false then
                        if trace_defining then
                            report(engine,family,unicode,name,group)
                        end
                        mset = setmathcharacter(engine,family,unicode,unicode,mset,group,meaning)
                    else
                     -- if not name then
                     --     name = character.contextname -- too dangerous, we loose textslash and a few more
                     -- end
                        if name then
                            if trace_defining then
                                report(engine,family,unicode,name,group)
                            end
                            if not group then
                                if class == variable_class then
                                 -- happens with greek where have a name but don't set a group .. somewhat messy
                                    group = i_everygroup
                                else
                                 -- report(engine,family,unicode,name) -- character.adobename)
                                end
                            end
                            setmathsymbol(name,engine,family,unicode,stretch,group,meaning)
                        else
                            if trace_defining then
                                report(engine,family,unicode,"no name",group) -- character.adobename)
                            end
                        end
                        mset = setmathcharacter(engine,family,unicode,unicode,mset,group,meaning)
                    end
                elseif class ~= ordinary_class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(engine,family,unicode,"no name",group) -- character.adobename)
                    end
                    mset = setmathcharacter(engine,family,unicode,unicode,mset,group,meaning)
                end
            end
        end
        --
        if trace_defining then
            logs.stopfilelogging()
        end
    end

end

-- needed for mathml analysis
-- string with # > 1 are invalid
-- we could cache

do

    local lpegmatch = lpeg.match
    local utf8byte  = lpeg.patterns.utf8byte * lpeg.P(-1)

    -- function somechar(c)
    --     local b = lpegmatch(utf8byte,c)
    --     return b and chardata[b]
    -- end

    local somechar = table.setmetatableindex(function(t,k)
        if k then
            local b = lpegmatch(utf8byte,k)
            local v = b and chardata[b] or false
            t[k] = v
            return v
        end
    end)

    local function utfmathclass(chr, default)
        local cd = somechar[chr]
        return cd and cd.mathclass or default or "unknown"
    end

    local function utfmathlimop(chr)
        local cd = somechar[chr]
        return cd and (cd.mathclass == "operator" or cd.mathclass == "integral") or false
    end

    local function utfmathaccent(chr,default,asked1,asked2)
        local cd = somechar[chr]
        if not cd then
            return default or false
        end
        if asked1 and asked1 ~= "" then
            local mc = cd.mathclass
            if mc and (mc == asked1 or mc == asked2) then
                return true
            end
            local ms = cd.mathspec
            if not ms then
                local mp = cd.mathparent
                if mp then
                    ms = chardata[mp].mathspec
                end
            end
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mc = msi.class
                    if mc and (mc == asked1 or mc == asked2) then
                        return true
                    end
                end
            end
        else
            local mc = cd.mathclass
            if mc then
                return accents[mc] or default or false
            end
            local ms = cd.mathspec
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mc = msi.class
                    if mc then
                        return accents[mc] or default or false
                    end
                end
            end
        end
        return default or false
    end

    local function utfmathstretch(chr,default) -- "h", "v", "b", ""
        local cd = somechar[chr]
        return cd and cd.mathstretch or default or ""
    end

    local function utfmathcommand(chr,default,asked1,asked2)
        local cd = somechar[chr]
        if not cd then
            return default or ""
        end
        if asked1 then
            local mn = cd.mathname
            local mc = cd.mathclass
            if mn and mc and (mc == asked1 or mc == asked2) then
                return mn
            end
            local ms = cd.mathspec
            if not ms then
                local mp = cd.mathparent
                if mp then
                    ms = chardata[mp].mathspec
                end
            end
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mn = msi.name
                    if mn then
                        local mc = msi.class
                        if mc == asked1 or mc == asked2 then
                            return mn
                        end
                    end
                end
            end
        else
            local mn = cd.mathname
            if mn then
                return mn
            end
            local ms = cd.mathspec
            if ms then
                for i=1,#ms do
                    local msi = ms[i]
                    local mn = msi.name
                    if mn then
                        return mn
                    end
                end
            end
        end
        return default or ""
    end

    local function utfmathfiller(chr, default)
        local cd = somechar[chr]
        local cmd = cd and cd.mathfiller -- or cd.mathname
        return cmd or default or ""
    end

    mathematics.utfmathclass   = utfmathclass
    mathematics.utfmathstretch = utfmathstretch
    mathematics.utfmathcommand = utfmathcommand
    mathematics.utfmathfiller  = utfmathfiller
    mathematics.utfmathaccent  = utfmathaccent

    -- interfaced

    implement {
        name      = "utfmathclass",
        public    = true,
        actions   = { utfmathclass, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathstretch",
        public    = true,
        actions   = { utfmathstretch, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathcommand",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathfiller",
        public    = true,
        actions   = { utfmathfiller, context },
        arguments = "argument"
    }

    implement {
        name      = "utfmathcommandabove",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = { "argument", false, "'topaccent'","'over'" }
    }

    implement {
        name      = "utfmathcommandbelow",
        public    = true,
        actions   = { utfmathcommand, context },
        arguments = { "argument", false, "'bottomaccent'","'under'" }
    }

    implement {
        name      = "utfmathcommandfiller",
        public    = true,
        actions   = { utfmathfiller, context },
        arguments = "argument"
    }

    -- todo: make this a helper:

    implement {
        name      = "doifelseutfmathabove",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = { "argument", false, "'topaccent'", "'over'" }
    }

    implement {
        name      = "doifelseutfmathbelow",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = { "argument", false, "'bottomaccent'", "'under'" }
    }

    implement {
        name      = "doifelseutfmathaccent",
        public    = true,
        actions   = { utfmathaccent, ctx_doifelsesomething },
        arguments = "argument",
    }

    implement {
        name      = "doifelseutfmathfiller",
        public    = true,
        actions   = { utfmathfiller, ctx_doifelsesomething },
        arguments = "argument",
    }

    implement {
        name      = "doifelseutfmathlimop",
        public    = true,
        actions   = { utfmathlimop, ctx_doifelsesomething },
        arguments = "argument"
    }

end

do

    -- 1: step 1
    -- 2: step 2
    -- 3: htdp * 1.33^n
    -- 4: size * 1.33^n
    -- 5: use lfg

    implement {
        name      = "mathvariantslot",
        public    = true,
        usage     = "value",
        arguments = "2 integers",
        actions   = function(fam,n)
            local b = fontdata[getfontoffamily(fam)].bigslots
            if b then
                n = (n > #b and b[#b]) or b[n] or n
            end
            return integer_value, n
+ 1
        end
    }

    -- will go away:

    function mathematics.big(tfmdata,unicode,n,method)
        local t = tfmdata.characters
        local c = t[unicode]
        if c and n > 0 then
            if method == 1 or method == 2 or method == 5 then
                if method == 5 then
                    local b = tfmdata.bigslots
                    if b then
                        n = (n > #b and b[#b]) or b[n] or n
                    end
                elseif method == 2 then -- large steps
                    n = n * 2
                end
                local next = c.next
                while next do
                    if n <= 1 then
                        return next
                    else
                        n = n - 1
                        local tn = t[next].next
                        if tn then
                            next = tn
                        else
                            return next
                        end
                    end
                end
            elseif method >= 3 then
                local size = 1.33^n
                if method == 4 then
                    size = tfmdata.parameters.size * size
                else -- if method == 3 then
                    size = (c.height + c.depth) * size
                end
                local next = c.next
                while next do
                    local cn = t[next]
                    if (cn.height + cn.depth) >= size then
                        return next
                    else
                        local tn = cn.next
                        if tn then
                            next = tn
                        else
                            return next
                        end
                    end
                end
            end
        end
        return unicode
    end

end

do -- experimental, not stored in the format

    local categories       = { }
    mathematics.categories = categories

    local a_mathcategory   <const> = attributes.private("mathcategory")
    local a_mathstack      <const> = attributes.private("mathstack")

    local functions        = storage.allocate()
    categories.functions   = functions
    local noffunctions     = 0

    local function identify(kind,tag,method)
        local n = functions[tag]
        if n then
            n = n.index
        else
            n = noffunctions + 1 ---
            local t = {
                kind   = kind,
                tag    = tag,
                method = method,
                index  = n,
            }
            functions[n] = t
            functions[tag] = t
            noffunctions = n
        end
        return n
    end

    implement {
        name      = "tagmfunctionlab", -- this one will be replaced by the next
        arguments = { "integer", "argument", "argument" },
        actions   = function(kind,tag,method)
            texsetattribute(a_mathcategory,identify(kind,tag,method))
        end
    }

    implement {
        name      = "tagmfunctionlabattribute",
        usage     = "value",
        arguments = { "integer", "argument", "argument" },
        actions   = function(kind,tag,method)
            return integer_value, identify(kind,tag,method)
        end
    }

    function mathematics.functiontype(n)
        local func = n and functions[n]
        local kind = func and func.kind or 0
        if kind == 1 then
            return "function"
        elseif kind == 2 then
            return "accent"
        elseif kind == 3 then
            return "fence"
        else
            return "unknown"
        end
    end

end

do

    local list

    function mathematics.resetattributes()
        if not list then
            list = { }
            for k, v in next, attributes.numbers do
                if find(k,"^math") then
                    list[#list+1] = v
                end
            end
        end
        for i=1,#list do
            texsetattribute(list[i],unsetvalue)
        end
    end

end

implement {
    name      = "resetmathattributes",
    public    = true,
    protected = true,
    actions   = mathematics.resetattributes
}

-- weird to do this here but it's a side affect of math anyway

implement {
    name     = "enableasciimode",
    onlyonce = true,
    actions  = resolvers.macros.enablecomment,
}

implement {
    name      = "nofmathvariants",
    public    = true,
    usage     = "value",
    arguments = "integer",
    actions   = function(n)
        local char = fontchardata[getfontoffamily(0)]
        local data = char[n]
        local size = 1
        while data do
            local next = data.next
            if next then
                size = size + 1
                data = char[next]
            else
                break
            end
        end
        return integer_value, size
    end,
}

implement {
    name      = "getmathvariant",
    public    = true,
    usage     = "value",
    arguments = "2 integers",
    actions   = function(m,n)
        local char = fontchardata[getfontoffamily(0)]
        local data = char[n]
        local slot = n
        if data then
            while data and m > 1 do
                local next = data.next
                if next then
                    m = m - 1
                    data = char[next]
                    slot = next
                else
                    break
                end
            end
        end
        return integer_value, slot
    end,
}

implement {
    name      = "getmathcharone",
    public    = true,
    usage     = "value",
    arguments = "integer",
    actions   = function(n)
        local char = fontchardata[getfontoffamily(0)]
        local data = char[n]
        return integer_value, data and data.smaller or n
    end,
}

implement {
    name      = "getmathchartwo",
    public    = true,
    usage     = "value",
    arguments = "integer",
    actions   = function(n)
        local char = fontchardata[getfontoffamily(0)]
        local data = char[n]
        local slot = data and data.smaller
        if slot then
            data = char[slot]
            n = slot
        end
        return integer_value, data and data.smaller or n
    end,
}