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|
if not modules then modules = { } end modules ['x-mathml'] = {
version = 1.001,
comment = "companion to x-mathml.mkiv",
author = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
copyright = "PRAGMA ADE / ConTeXt Development Team",
license = "see context related readme files"
}
-- This needs an upgrade to the latest greatest mechanisms.
local type, next = type, next
local format, lower, find, gsub = string.format, string.lower, string.find, string.gsub
local strip = string.strip
local xmlsprint, xmlcprint, xmltext, xmlcontent = xml.sprint, xml.cprint, xml.text, xml.content
local getid = lxml.getid
local utfchar, utfcharacters, utfvalues = utf.char, utf.characters, utf.values
local lpegmatch = lpeg.match
local mathml = { }
moduledata.mathml = mathml
lxml.mathml = mathml -- for the moment
-- an alternative is to remap to private codes, where we can have
-- different properties .. to be done; this will move and become
-- generic; we can then make the private ones active in math mode
-- todo: handle opening/closing mo's here ... presentation mml is such a mess ...
characters.registerentities()
local doublebar = utfchar(0x2016)
local n_replacements = {
-- [" "] = utfchar(0x2002), -- "&textspace;" -> tricky, no &; in mkiv
["."] = "{.}",
[","] = "{,}",
[" "] = "",
}
local l_replacements = { -- in main table
["|"] = "\\mmlleftdelimiter\\vert",
["{"] = "\\mmlleftdelimiter\\lbrace",
["("] = "\\mmlleftdelimiter(",
["["] = "\\mmlleftdelimiter[",
["<"] = "\\mmlleftdelimiter<",
[doublebar] = "\\mmlleftdelimiter\\Vert",
}
local r_replacements = { -- in main table
["|"] = "\\mmlrightdelimiter\\vert",
["}"] = "\\mmlrightdelimiter\\rbrace",
[")"] = "\\mmlrightdelimiter)",
["]"] = "\\mmlrightdelimiter]",
[">"] = "\\mmlrightdelimiter>",
[doublebar] = "\\mmlrightdelimiter\\Vert",
}
-- todo: play with asciimode and avoid mmlchar
local o_replacements = { -- in main table
["@l"] = "\\mmlleftdelimiter.",
["@r"] = "\\mmlrightdelimiter.",
["{"] = "\\mmlleftdelimiter \\lbrace",
["}"] = "\\mmlrightdelimiter\\rbrace",
["|"] = "\\mmlleftorrightdelimiter\\vert",
["/"] = "\\mmlleftorrightdelimiter\\solidus",
[doublebar] = "\\mmlleftorrightdelimiter\\Vert",
["("] = "\\mmlleftdelimiter(",
[")"] = "\\mmlrightdelimiter)",
["["] = "\\mmlleftdelimiter[",
["]"] = "\\mmlrightdelimiter]",
-- ["<"] = "\\mmlleftdelimiter<",
-- [">"] = "\\mmlrightdelimiter>",
["#"] = "\\mmlchar{35}",
["$"] = "\\mmlchar{36}", -- $
["%"] = "\\mmlchar{37}",
["&"] = "\\mmlchar{38}",
["^"] = "\\mmlchar{94}{}", -- strange, sometimes luatex math sees the char instead of \char
["_"] = "\\mmlchar{95}{}", -- so we need the {}
["~"] = "\\mmlchar{126}",
[" "] = "",
["°"] = "^\\circ", -- hack
-- [utfchar(0xF103C)] = "\\mmlleftdelimiter<",
[utfchar(0xF1026)] = "\\mmlchar{38}",
[utfchar(0x02061)] = "", -- function applicator sometimes shows up in font
-- [utfchar(0xF103E)] = "\\mmlleftdelimiter>",
-- [utfchar(0x000AF)] = '\\mmlchar{"203E}', -- 0x203E
}
local simpleoperatorremapper = utf.remapper(o_replacements)
--~ languages.data.labels.functions
local i_replacements = {
["sin"] = "\\sin",
["cos"] = "\\cos",
["abs"] = "\\abs",
["arg"] = "\\arg",
["codomain"] = "\\codomain",
["curl"] = "\\curl",
["determinant"] = "\\det",
["divergence"] = "\\div",
["domain"] = "\\domain",
["gcd"] = "\\gcd",
["grad"] = "\\grad",
["identity"] = "\\id",
["image"] = "\\image",
["lcm"] = "\\lcm",
["lim"] = "\\lim",
["max"] = "\\max",
["median"] = "\\median",
["min"] = "\\min",
["mode"] = "\\mode",
["mod"] = "\\mod",
["polar"] = "\\Polar",
["exp"] = "\\exp",
["ln"] = "\\ln",
["log"] = "\\log",
["sin"] = "\\sin",
["arcsin"] = "\\arcsin",
["sinh"] = "\\sinh",
["arcsinh"] = "\\arcsinh",
["cos"] = "\\cos",
["arccos"] = "\\arccos",
["cosh"] = "\\cosh",
["arccosh"] = "\\arccosh",
["tan"] = "\\tan",
["arctan"] = "\\arctan",
["tanh"] = "\\tanh",
["arctanh"] = "\\arctanh",
["cot"] = "\\cot",
["arccot"] = "\\arccot",
["coth"] = "\\coth",
["arccoth"] = "\\arccoth",
["csc"] = "\\csc",
["arccsc"] = "\\arccsc",
["csch"] = "\\csch",
["arccsch"] = "\\arccsch",
["sec"] = "\\sec",
["arcsec"] = "\\arcsec",
["sech"] = "\\sech",
["arcsech"] = "\\arcsech",
[" "] = "",
["false"] = "{\\mathrm false}",
["notanumber"] = "{\\mathrm NaN}",
["otherwise"] = "{\\mathrm otherwise}",
["true"] = "{\\mathrm true}",
["declare"] = "{\\mathrm declare}",
["as"] = "{\\mathrm as}",
}
-- we could use a metatable or when accessing fallback on the
-- key but at least we now have an overview
local csymbols = {
arith1 = {
lcm = "lcm",
big_lcm = "lcm",
gcd = "gcd",
big_gcd = "big_gcd",
plus = "plus",
unary_minus = "minus",
minus = "minus",
times = "times",
divide = "divide",
power = "power",
abs = "abs",
root = "root",
sum = "sum",
product = "product",
},
fns = {
domain = "domain",
range = "codomain",
image = "image",
identity = "ident",
-- left_inverse = "",
-- right_inverse = "",
inverse = "inverse",
left_compose = "compose",
lambda = "labmda",
},
linalg1 = {
vectorproduct = "vectorproduct",
scalarproduct = "scalarproduct",
outerproduct = "outerproduct",
transpose = "transpose",
determinant = "determinant",
vector_selector = "selector",
-- matrix_selector = "matrix_selector",
},
logic1 = {
equivalent = "equivalent",
["not"] = "not",
["and"] = "and",
-- big_and = "",
["xor"] = "xor",
-- big_xor = "",
["or"] = "or",
-- big-or = "",
implies = "implies",
["true"] = "true",
["false"] = "false",
},
nums1 = {
-- based_integer = "based_integer"
rational = "rational",
inifinity = "infinity",
e = "expenonentiale",
i = "imaginaryi",
pi = "pi",
gamma = "gamma",
NaN = "NaN",
},
relation1 = {
eq = "eq",
lt = "lt",
gt = "gt",
neq = "neq",
leq = "leq",
geq = "geq",
approx = "approx",
},
set1 = {
cartesian_product = "cartesianproduct",
empty_set = "emptyset",
map = "map",
size = "card",
-- suchthat = "suchthat",
set = "set",
intersect = "intersect",
-- big_intersect = "",
union = "union",
-- big_union = "",
setdiff = "setdiff",
subset = "subset",
["in"] = "in",
notin = "notin",
prsubset = "prsubset",
notsubset = "notsubset",
notprsubset = "notprsubset",
},
veccalc1 = {
divergence = "divergence",
grad = "grad",
curl = "curl",
laplacian = "laplacian",
Laplacian = "laplacian",
},
calculus1 = {
diff = "diff",
-- nthdiff = "",
partialdiff = "partialdiff",
int = "int",
-- defint = "defint",
},
integer1 = {
factorof = "factorof",
factorial = "factorial",
quotient = "quotient",
remainder = "rem",
},
linalg2 = {
vector = "vector",
matrix = "matrix",
matrixrow = "matrixrow",
},
mathmkeys = {
-- equiv = "",
-- contentequiv = "",
-- contentequiv_strict = "",
},
rounding1 = {
ceiling = "ceiling",
floor = "floor",
-- trunc = "trunc",
-- round = "round",
},
setname1 = {
P = "primes",
N = "naturalnumbers",
Z = "integers",
rationals = "rationals",
R = "reals",
complexes = "complexes",
},
complex1 = {
-- complex_cartesian = "complex_cartesian", -- ci ?
real = "real",
imaginary = "imaginary",
-- complex_polar = "complex_polar", -- ci ?
argument = "arg",
conjugate = "conjugate",
},
interval1 = { -- not an apply
-- integer_interval = "integer_interval",
interval = "interval",
interval_oo = { tag = "interval", closure = "open" },
interval_cc = { tag = "interval", closure = "closed" },
interval_oc = { tag = "interval", closure = "open-closed" },
interval_co = { tag = "interval", closure = "closed-open" },
},
linalg3 = {
-- vector = "vector.column",
-- matrixcolumn = "matrixcolumn",
-- matrix = "matrix.column",
},
minmax1 = {
min = "min",
-- big_min = "",
max = "max",
-- big_max = "",
},
piece1 = {
piecewise = "piecewise",
piece = "piece",
otherwise = "otherwise",
},
error1 = {
-- unhandled_symbol = "",
-- unexpected_symbol = "",
-- unsupported_CD = "",
},
limit1 = {
-- limit = "limit",
-- both_sides = "both_sides",
-- above = "above",
-- below = "below",
-- null = "null",
tendsto = "tendsto",
},
list1 = {
-- map = "",
-- suchthat = "",
-- list = "list",
},
multiset1 = {
size = { tag = "card", type = "multiset" },
cartesian_product = { tag = "cartesianproduct", type = "multiset" },
empty_set = { tag = "emptyset", type = "multiset" },
-- multi_set = { tag = "multiset", type = "multiset" },
intersect = { tag = "intersect", type = "multiset" },
-- big_intersect = "",
union = { tag = "union", type = "multiset" },
-- big_union = "",
setdiff = { tag = "setdiff", type = "multiset" },
subset = { tag = "subset", type = "multiset" },
["in"] = { tag = "in", type = "multiset" },
notin = { tag = "notin", type = "multiset" },
prsubset = { tag = "prsubset", type = "multiset" },
notsubset = { tag = "notsubset", type = "multiset" },
notprsubset = { tag = "notprsubset", type = "multiset" },
},
quant1 = {
forall = "forall",
exists = "exists",
},
s_dist = {
-- mean = "mean.dist",
-- sdev = "sdev.dist",
-- variance = "variance.dist",
-- moment = "moment.dist",
},
s_data = {
mean = "mean",
sdev = "sdev",
variance = "vriance",
mode = "mode",
median = "median",
moment = "moment",
},
transc1 = {
log = "log",
ln = "ln",
exp = "exp",
sin = "sin",
cos = "cos",
tan = "tan",
sec = "sec",
csc = "csc",
cot = "cot",
sinh = "sinh",
cosh = "cosh",
tanh = "tanh",
sech = "sech",
csch = "cscs",
coth = "coth",
arcsin = "arcsin",
arccos = "arccos",
arctan = "arctan",
arcsec = "arcsec",
arcscs = "arccsc",
arccot = "arccot",
arcsinh = "arcsinh",
arccosh = "arccosh",
arctanh = "arstanh",
arcsech = "arcsech",
arccsch = "arccsch",
arccoth = "arccoth",
},
}
function xml.functions.remapmmlcsymbol(e)
local at = e.at
local cd = at.cd
if cd then
cd = csymbols[cd]
if cd then
local tx = e.dt[1]
if tx and tx ~= "" then
local tg = cd[tx]
if tg then
at.cd = nil
at.cdbase = nil
e.dt = { }
if type(tg) == "table" then
for k, v in next, tg do
if k == "tag" then
e.tg = v
else
at[k] = v
end
end
else
e.tg = tg
end
end
end
end
end
end
function xml.functions.remapmmlbind(e)
e.tg = "apply"
end
function xml.functions.remapopenmath(e)
local tg = e.tg
if tg == "OMOBJ" then
e.tg = "math"
elseif tg == "OMA" then
e.tg = "apply"
elseif tg == "OMB" then
e.tg = "apply"
elseif tg == "OMS" then
local at = e.at
e.tg = "csymbol"
e.dt = { at.name or "unknown" }
at.name = nil
elseif tg == "OMV" then
local at = e.at
e.tg = "ci"
e.dt = { at.name or "unknown" }
at.name = nil
elseif tg == "OMI" then
e.tg = "ci"
end
e.rn = "mml"
end
function mathml.checked_operator(str)
context(simpleoperatorremapper(str))
end
function mathml.stripped(str)
context(strip(str))
end
function mathml.mn(id,pattern)
-- maybe at some point we need to interpret the number, but
-- currently we assume an upright font
local str = xmlcontent(getid(id)) or ""
local rep = gsub(str,"&.-;","")
local rep = gsub(rep,"(%s+)",utfchar(0x205F)) -- medspace e.g.: twenty one (nbsp is not seen)
local rep = gsub(rep,".",n_replacements)
context.mn(rep)
end
function mathml.mo(id)
local str = xmlcontent(getid(id)) or ""
local rep = gsub(str,"&.-;","") -- todo
context(simpleoperatorremapper(rep) or rep)
end
function mathml.mi(id)
-- we need to strip comments etc .. todo when reading in tree
local e = getid(id)
local str = e.dt
if type(str) == "table" then
local n = #str
if n == 0 then
-- nothing to do
elseif n == 1 then
local first = str[1]
if type(first) == "string" then
local str = gsub(first,"&.-;","") -- bah
local rep = i_replacements[str]
if not rep then
rep = gsub(str,".",i_replacements)
end
context(rep)
-- context.mi(rep)
else
context.xmlflush(id) -- xmlsprint or so
end
else
context.xmlflush(id) -- xmlsprint or so
end
else
context.xmlflush(id) -- xmlsprint or so
end
end
function mathml.mfenced(id) -- multiple separators
id = getid(id)
local left, right, separators = id.at.open or "(", id.at.close or ")", id.at.separators or ","
local l, r = l_replacements[left], r_replacements[right]
context.enabledelimiter()
if l then
context(l_replacements[left] or o_replacements[left] or "")
else
context(o_replacements["@l"])
context(left)
end
context.disabledelimiter()
local collected = lxml.filter(id,"/*") -- check the *
if collected then
local n = #collected
if n == 0 then
-- skip
elseif n == 1 then
xmlsprint(collected[1]) -- to be checked
else
local t = utf.split(separators,true)
for i=1,n do
xmlsprint(collected[i]) -- to be checked
if i < n then
local m = t[i] or t[#t] or ""
if m == "|" then
m = "\\enabledelimiter\\middle|\\relax\\disabledelimiter"
elseif m == doublebar then
m = "\\enabledelimiter\\middle|\\relax\\disabledelimiter"
elseif m == "{" then
m = "\\{"
elseif m == "}" then
m = "\\}"
end
context(m)
end
end
end
end
context.enabledelimiter()
if r then
context(r_replacements[right] or o_replacements[right] or "")
else
context(right)
context(o_replacements["@r"])
end
context.disabledelimiter()
end
--~ local function flush(e,tag,toggle)
--~ if toggle then
--~ context("^{")
--~ else
--~ context("_{")
--~ end
--~ if tag == "none" then
--~ context("{}")
--~ else
--~ xmlsprint(e.dt)
--~ end
--~ if not toggle then
--~ context("}")
--~ else
--~ context("}{}")
--~ end
--~ return not toggle
--~ end
local function flush(e,tag,toggle)
if tag == "none" then
-- if not toggle then
context("{}") -- {} starts a new ^_ set
-- end
elseif toggle then
context("^{")
xmlsprint(e.dt)
context("}{}") -- {} starts a new ^_ set
else
context("_{")
xmlsprint(e.dt)
context("}")
end
return not toggle
end
function mathml.mmultiscripts(id)
local done, toggle = false, false
for e in lxml.collected(id,"/*") do
local tag = e.tg
if tag == "mprescripts" then
context("{}")
done = true
elseif done then
toggle = flush(e,tag,toggle)
end
end
local done, toggle = false, false
for e in lxml.collected(id,"/*") do
local tag = e.tg
if tag == "mprescripts" then
break
elseif done then
toggle = flush(e,tag,toggle)
else
xmlsprint(e.dt)
done = true
end
end
end
local columnalignments = {
left = "flushleft",
right = "flushright",
center = "middle",
}
local rowalignments = {
top = "high",
bottom = "low",
center = "lohi",
baseline = "top",
axis = "lohi",
}
local frametypes = {
none = "off",
solid = "on",
dashed = "on",
}
-- crazy element ... should be a proper structure instead of such a mess
function mathml.mcolumn(root)
root = getid(root)
local matrix, numbers = { }, 0
local function collect(m,e)
local tag = e.tg
if tag == "mi" or tag == "mn" or tag == "mo" or tag == "mtext" then
local str = xmltext(e)
str = gsub(str,"&.-;","")
for s in utfcharacters(str) do
m[#m+1] = { tag, s }
end
if tag == "mn" then
local n = utf.len(str)
if n > numbers then
numbers = n
end
end
elseif tag == "mspace" or tag == "mline" then
local str = e.at.spacing or ""
for s in utfcharacters(str) do
m[#m+1] = { tag, s }
end
-- elseif tag == "mline" then
-- m[#m+1] = { tag, e }
end
end
for e in lxml.collected(root,"/*") do
local m = { }
matrix[#matrix+1] = m
if e.tg == "mrow" then
-- only one level
for e in lxml.collected(e,"/*") do
collect(m,e)
end
else
collect(m,e)
end
end
context.halign()
context.bgroup()
context([[\hss\startimath\alignmark\stopimath\aligntab\startimath\alignmark\stopimath\cr]])
for i=1,#matrix do
local m = matrix[i]
local mline = true
for j=1,#m do
if m[j][1] ~= "mline" then
mline = false
break
end
end
if mline then
context.noalign([[\obeydepth\nointerlineskip]])
end
for j=1,#m do
local mm = m[j]
local tag, chr = mm[1], mm[2]
if tag == "mline" then
-- This code is under construction ... I need some real motivation
-- to deal with this kind of crap.
--~ local n, p = true, true
--~ for c=1,#matrix do
--~ local mc = matrix[c][j]
--~ if mc then
--~ mc = mc[2]
--~ if type(mc) ~= "string" then
--~ n, p = false, false
--~ break
--~ elseif find(mc,"^[%d ]$") then -- rangecheck is faster
--~ -- digit
--~ elseif not find(mc,"^[%.%,]$") then -- rangecheck is faster
--~ -- punctuation
--~ else
--~ n = false
--~ break
--~ end
--~ end
--~ end
--~ if n then
--~ chr = "\\mmlmcolumndigitrule"
--~ elseif p then
--~ chr = "\\mmlmcolumnpunctuationrule"
--~ else
--~ chr = "\\mmlmcolumnsymbolrule" -- should be widest char
--~ end
chr = "\\hrulefill"
elseif tag == "mspace" then
chr = "\\mmlmcolumndigitspace" -- utfchar(0x2007)
end
if j == numbers + 1 then
context("\\aligntab")
end
local nchr = n_replacements[chr]
context(nchr or chr)
end
context.crcr()
end
context.egroup()
end
local spacesplitter = lpeg.tsplitat(" ")
function mathml.mtable(root)
-- todo: align, rowspacing, columnspacing, rowlines, columnlines
root = getid(root)
local at = root.at
local rowalign = at.rowalign
local columnalign = at.columnalign
local frame = at.frame
local rowaligns = rowalign and lpegmatch(spacesplitter,rowalign)
local columnaligns = columnalign and lpegmatch(spacesplitter,columnalign)
local frames = frame and lpegmatch(spacesplitter,frame)
local framespacing = at.framespacing or "0pt"
local framespacing = at.framespacing or "-\\ruledlinewidth" -- make this an option
context.bTABLE { frame = frametypes[frame or "none"] or "off", offset = framespacing, background = "" } -- todo: use xtables and definextable
for e in lxml.collected(root,"/(mml:mtr|mml:mlabeledtr)") do
context.bTR()
local at = e.at
local col = 0
local rfr = at.frame or (frames and frames [#frames])
local rra = at.rowalign or (rowaligns and rowaligns [#rowaligns])
local rca = at.columnalign or (columnaligns and columnaligns[#columnaligns])
local ignorelabel = e.tg == "mlabeledtr"
for e in lxml.collected(e,"/mml:mtd") do -- nested we can use xml.collected
col = col + 1
if ignorelabel and col == 1 then
-- get rid of label, should happen at the document level
else
local at = e.at
local rowspan, columnspan = at.rowspan or 1, at.columnspan or 1
local cra = rowalignments [at.rowalign or (rowaligns and rowaligns [col]) or rra or "center"] or "lohi"
local cca = columnalignments[at.columnalign or (columnaligns and columnaligns[col]) or rca or "center"] or "middle"
local cfr = frametypes [at.frame or (frames and frames [col]) or rfr or "none" ] or "off"
context.bTD { align = format("{%s,%s}",cra,cca), frame = cfr, nx = columnspan, ny = rowspan }
context.startimath()
context.ignorespaces()
xmlcprint(e)
context.stopimath()
context.removeunwantedspaces()
context.eTD()
end
end
-- if e.tg == "mlabeledtr" then
-- context.bTD()
-- xmlcprint(xml.first(e,"/!mml:mtd"))
-- context.eTD()
-- end
context.eTR()
end
context.eTABLE()
end
function mathml.csymbol(root)
root = getid(root)
local at = root.at
local encoding = at.encoding or ""
local hash = url.hashed(lower(at.definitionUrl or ""))
local full = hash.original or ""
local base = hash.path or ""
local text = strip(xmltext(root) or "")
context.mmlapplycsymbol(full,base,encoding,text)
end
function mathml.menclosepattern(root)
root = getid(root)
local a = root.at.notation
if a and a ~= "" then
context("mml:enclose:",(gsub(a," +",",mml:enclose:")))
end
end
function xml.is_element(e,name)
return type(e) == "table" and (not name or e.tg == name)
end
function mathml.cpolar_a(root)
root = getid(root)
local dt = root.dt
context.mathopnolimits("Polar")
context.left(false,"(")
for k=1,#dt do
local dk = dt[k]
if xml.is_element(dk,"sep") then
context(",")
else
xmlsprint(dk)
end
end
context.right(false,")")
end
-- crap .. maybe in char-def a mathml overload
local mathmleq = {
[utfchar(0x00AF)] = utfchar(0x203E),
}
function mathml.extensible(chr)
context(mathmleq[chr] or chr)
end
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