path: root/tex/context/base/mkxl/math-ini.lmt

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 commands              = commands
local implement             = interfaces.implement

local ctx_sprint            = context.sprint
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            = attributes.unsetvalue
local allocate              = utilities.storage.allocate
local chardata              = characters.data

local texsetattribute       = tex.setattribute
local setmathcode           = tex.setmathcode
local setdelcode            = tex.setdelcode
local texintegerdef         = tex.integerdef

setdelcode = function() end

-- 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

    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
            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
            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

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

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

    function dictionaries.registercharacter(group,index,description,class)
        local d = names[group] -- can be number or string
        if d then
            data[d][index] = description or true
            local v = variants[index]
            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
    end

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

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

    local fontchardata = fonts.hashes.characters
    local f_dictionary = false
    local register     = callback.register
    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 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
        if whatdetail then
            register("get_math_dictionary",trace)
        else
            register("get_math_dictionary")
        end
    end)

    register("get_math_dictionary",trace)

    -- 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 arithmetic")
        registergroup("binary linear algebra")
        registergroup("binary logical")
        registergroup("binary relation")
        registergroup("binary set")
        registergroup("constant arithmetic")
        registergroup("constant set")
        registergroup("differential")
        registergroup("integral")
        registergroup("interval")
        registergroup("lambda")
        registergroup("limit")
        registergroup("nary arithmetic")
        registergroup("nary constructor")
        registergroup("nary functional")
        registergroup("nary linear algebra")
        registergroup("nary logical")
        registergroup("nary minmax")
        registergroup("nary relation")
        registergroup("nary set list")
        registergroup("nary set relation")
        registergroup("nary set")
        registergroup("nary statistics")
        registergroup("partial") -- partial differential
        registergroup("product")
        registergroup("quantifier")
        registergroup("unary arithmetic")
        registergroup("unary elementary")
        registergroup("unary functional")
        registergroup("unary linear algebra")
        registergroup("unary logical")
        registergroup("unary set")
        registergroup("unary vector")

    end

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

end

-- 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 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

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

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 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
        classes[name] = class
    end
    return class
end

registerengineclass("explicit",        "xpl")
registerengineclass("imaginary",       "img")
registerengineclass("differential",    "dif")
registerengineclass("exponential",     "exp")
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")
registerengineclass("experimental")
registerengineclass("fake")
registerengineclass("numbergroup",     "ngr")

registerengineclass("maybeordinary")
registerengineclass("mayberelation")
registerengineclass("maybebinary")

local specialclasses = tex.specialmathclasscodes

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

callback.register("get_noad_class", function(n) return classnames[n] end)

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")
local 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 = tokens.values.integer

implement {
    name      = "mathclassvalue",
 -- usage     = "value",
    public    = true,
    arguments = "string",
    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 {
    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

do

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

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

    local function report(class,engine,family,unicode,name)
        local nametype = type(name)
        if nametype == "string" then
            report_math("class %a, engine %a, family %a, char %C, name %a",class,engine,family,unicode,name)
        elseif nametype == "number" then
            report_math("class %a, engine %a, family %a, char %C, number %U",class,engine,family,unicode,name)
        else
            report_math("class %a, engine %a, family %a, char %C",class,engine,family,unicode)
        end
    end

    local f_accent            = formatters[ [[\defUmathtopaccent \%s{%X}{%X}{%X}]] ]
    local f_fixedtopaccent    = formatters[ [[\defUmathfixedtopaccent \%s{%X}{%X}{%X}]] ]
    local f_fixedbottomaccent = formatters[ [[\defUmathfixedbottomaccent \%s{%X}{%X}{%X}]] ]
    local f_topaccent         = formatters[ [[\defUmathtopaccent \%s{%X}{%X}{%X}]] ]
    local f_bottomaccent      = formatters[ [[\defUmathbottomaccent \%s{%X}{%X}{%X}]] ]
    local f_over              = formatters[ [[\defUdelimiterover \%s{%X}{%X}{%X}]] ]
    local f_under             = formatters[ [[\defUdelimiterunder\%s{%X}{%X}{%X}]] ]
    local f_fence             = formatters[ [[\defUdelimiter \%s{%X}{%X}{%X}]] ]
    local f_delimiter         = formatters[ [[\defUdelimiter \%s{%X}{%X}{%X}]] ]
    local f_radical           = formatters[ [[\defUradical \%s{%X}{%X}]]     ]
    local f_root              = formatters[ [[\defUroot \%s{%X}{%X}]]     ]
    local f_char              = formatters[ [[\defUmathchar \%s{%X}{%X}{%X}]] ]

    local texmathchardef = tex.mathchardef

    local setmathsymbol = function(name,class,engine,family,slot,stretch,group) -- hex is nicer for tracing
        if class == accent_class then
            ctx_sprint(f_topaccent(name,0,family,slot))
        elseif class == topaccent_class then
            -- only widegrave widehat widetilde : still needed?
            ctx_sprint((stretch and f_topaccent or f_fixedtopaccent)(name,0,family,slot))
        elseif class == bottomaccent_class then
            ctx_sprint((stretch and f_bottomaccent or f_fixedbottomaccent)(name,0,family,slot))
        elseif class == over_class then
            ctx_sprint(f_over(name,0,family,slot))
        elseif class == under_class then
            ctx_sprint(f_under(name,0,family,slot))
        elseif class == open_class or class == close_class or class == middle_class then
            setdelcode("global",slot,family,slot,0,0)
            ctx_sprint(f_fence(name,engine,family,slot))
        elseif class == delimiter_class then
            setdelcode("global",slot,family,slot,0,0)
            ctx_sprint(f_delimiter(name,0,family,slot))
        elseif class == radical_class then
            ctx_sprint(f_radical(name,family,slot))
        elseif class == root_class then
            ctx_sprint(f_root(name,family,slot))
        elseif texmathchardef then
            if group then
                group = groupnames[group] or 0
                if group ~= 0 then
                    texmathchardef(name,engine,family,slot,"permanent",0x1,group,slot)
                    return
                end
            end
            texmathchardef(name,engine,family,slot,"permanent")
        else
            -- beware, open/close and other specials should not end up here
            ctx_sprint(f_char(name,engine,family,slot))
        end
    end

    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
        --
        for unicode, character in sortedhash(data) do
            local symbol = character.mathsymbol
            local mset   = true
            local dset   = true
            if symbol then
                local other = data[symbol]
                local class = other.mathclass
                if class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(class,engine,family,unicode,symbol)
                    end
                    mset, dset = setmathcharacter(engine,family,unicode,symbol,mset,dset,group)
                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, dset = setmathcharacter(engine,family,unicode,symbol,mset,dset,group)
                        end
                    end
                end
            end
            local class   = character.mathclass
            local spec    = character.mathspec
            local name    = character.mathname
            local stretch = character.mathstretch
            local group   = character.mathgroup
            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(class,engine,family,unicode)
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset,group)
                        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
                    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(class,engine,family,unicode,name)
                            end
                            setmathsymbol(name,class,engine,family,unicode,stretch,group)
                        else
                            name = (class == classes.ordinary or class == classes.digit) and character.adobename -- bad
                            if name and trace_defining then
                                report(class,engine,family,unicode,name)
                            end
                        end
                        if not done then
                            mset, dset = setmathcharacter(engine,family,unicode,m.unicode or unicode,mset,dset,group) -- 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(class,engine,family,unicode,name)
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset,group)
                    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(class,engine,family,unicode,name)
                            end
                            setmathsymbol(name,class,engine,family,unicode,stretch,group)
                        else
                            if trace_defining then
                                report(class,engine,family,unicode,character.adobename)
                            end
                        end
                        mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset,group)
                    end
                elseif class ~= ordinary_class then
                    local engine = toengineclass(class)
                    if trace_defining then
                        report(class,engine,family,unicode,character.adobename)
                    end
                    mset, dset = setmathcharacter(engine,family,unicode,unicode,mset,dset,group)
                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 == "limop" 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

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

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

do -- experimental

    -- local categories = { } -- indexed + hashed
    --
    -- local a_mathcategory = attributes.private("mathcategory")
    --
    -- local function registercategory(category,tag,data) -- always same data for tag
    --     local c = categories[category]
    --     if not c then
    --         c = { }
    --         categories[category] = c
    --     end
    --     local n = c[tag]
    --     if not n then
    --         n = #c + 1
    --         c[n] = data
    --         n = n * 1000 + category
    --         c[tag] = n
    --     end
    --     return n
    -- end
    --
    -- function mathematics.getcategory(n)
    --     local category = n % 1000
    --     return category, categories[category][floor(n/1000)]
    -- end
    --
    -- mathematics.registercategory = registercategory
    --
    -- function commands.taggedmathfunction(tag,label)
    --     if label then
    --         texsetattribute(a_mathcategory,registercategory(1,tag,tag))
    --         context.mathlabeltext(tag)
    --     else
    --         texsetattribute(a_mathcategory,1)
    --         context(tag)
    --     end
    -- end

    local categories       = { }
    mathematics.categories = categories

    local a_mathcategory   = attributes.private("mathcategory")

    local functions        = storage.allocate()
    categories.functions   = functions
    local noffunctions     = 1000 -- offset

    implement {
        name      = "tagmfunctiontxt",
        arguments = { "string", "conditional" },
        actions   = function(tag,apply)
            local delta = apply and 1000 or 0
            texsetattribute(a_mathcategory,1000 + delta)
        end
    }

    implement {
        name      = "tagmfunctionlab",
        arguments = { "string", "conditional" },
        actions   = function(tag,apply)
            local delta = apply and 1000 or 0
            local n = functions[tag]
            if not n then
                noffunctions = noffunctions + 1
                functions[noffunctions] = tag
                functions[tag] = noffunctions
                texsetattribute(a_mathcategory,noffunctions + delta)
            else
                texsetattribute(a_mathcategory,n + delta)
            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,
}