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if not modules then modules = { } end modules ['math-ali'] = {
version = 1.001,
comment = "companion to math-ali.mkiv",
author = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
copyright = "PRAGMA ADE / ConTeXt Development Team",
license = "see context related readme files"
}
local unpack = unpack
local gsub = string.gsub
local sort, keys = table.sort, table.keys
local settings_to_array = utilities.parsers.settings_to_array
local P, R, S, C, Cc, Ct, Cs = lpeg.P, lpeg.R, lpeg.S, lpeg.C, lpeg.Cc, lpeg.Ct, lpeg.Cs
local lpegmatch = lpeg.match
local context = context
do
local rows = utilities.parsers.groupedsplitat(";")
local cols = utilities.parsers.groupedsplitat(",")
local actions = {
transpose = function(m)
local t = { }
for j=1,#m[1] do
local r = { }
for i=1,#m do
r[i] = m[i][j]
end
t[j] = r
end
return t
end,
negate = function(m)
for i=1,#m do
local mi = m[i]
for j=1,#mi do
mi[j] = - mi[j]
end
end
return m
end,
scale = function(m,s)
s = tonumber(s)
if s then
for i=1,#m do
local mi = m[i]
for j=1,#mi do
mi[j] = s*mi[j]
end
end
end
return m
end,
}
local useractions = {
}
interfaces.implement {
name = "simplematrix",
arguments = "2 strings",
actions = function(method,data)
local m = lpegmatch(rows,(gsub(data,"%s+"," ")))
for i=1,#m do
m[i] = lpegmatch(cols,m[i])
end
local methods = settings_to_array(method)
for i=1,#methods do
local detail = settings_to_array(methods[i])
local method = detail[1]
local action = actions[method] or useractions[method]
if action then
m = action(m,unpack(detail,2)) or m
end
end
for i=1,#m do
context("\\NC %{ \\NC }t \\NR",m[i])
end
end
}
function mathematics.registersimplematrix(name,action)
if type(action) == "function" then
useractions[name] = action
end
end
-- \cases{1, x>0 ; -1, x<0 }
interfaces.implement {
name = "simplecases",
arguments = "2 strings",
actions = function(method,data)
-- no methods yet
local m = lpegmatch(rows,(gsub(data,"%s+"," ")))
for i=1,#m do
m[i] = lpegmatch(cols,m[i])
end
for i=1,#m do
context("\\NC %{ \\NC }t \\NR",m[i])
end
end
}
end
do
local relations = {
["<"] = "<", [">"] = ">",
["!<"] = "≮", ["!>"] = "≯",
["<<"] = "≪", [">>"] = "≫",
["="] = "=", ["=="] = "=",
["<>"] = "≠", ["!="] = "≠",
["<="] = "≤", [">="] = "≥",
["=<"] = "≦", ["=>"] = "≧",
["!=<"] = "≰", ["!=>"] = "≱",
["~"] = "≈", ["~~"] = "≈",
}
for k, v in next, table.copy(relations) do relations[v] = v end
-- local binaries = {
-- ["+"] = "+",
-- ["-"] = "-",
-- ["/"] = "/",
-- ["*"] = "",
-- }
local separators = {
[","] = true,
[";"] = true,
}
local alternatives = {
-- not that many
}
local p_sign = S("-+")
local p_script = S("^")^1
local p_number = R("09","..")^1 + lpeg.patterns.nestedbraces
local p_alpha = R("az","AZ")^1
local p_variable = p_alpha * (P("_") * (p_number + p_alpha))^-1
local spacing = P(" ")^0
local script = Cs(p_script * Cc("{") * p_sign^0 * (p_number + p_variable) * Cc("}"))
local sign = C(p_sign) + Cc("+")
local number = C(p_number)
local variable = C(p_variable)
-- local binary = lpeg.utfchartabletopattern(binaries) / binaries
local relation = lpeg.utfchartabletopattern(relations) / relations
local separator = lpeg.utfchartabletopattern(separators)
local snippet = Ct (
(
spacing * sign * spacing * number * spacing * variable
+ spacing * sign * spacing * number * spacing * Cc(false)
+ spacing * sign * spacing * Cc(false) * spacing * variable
) * (script + Cc(false))
)
local parser = Ct ( Ct (
( Ct ( snippet^1 ) * spacing * relation )^1
* ( Ct ( snippet^1 ) * spacing * separator^0 )
)^1 )
local num = "!"
local ctx_NC, ctx_NR = context.NC, context.NR
local ctx_typ = context.typ
local ctx_ord, ctx_rel = context.mathord, context.mathrel
local clean = table.setmetatableindex(function(t,k)
local v = gsub(k,"[{}]","")
t[k] = v
return v
end)
alternatives.equationsystem = function(action,str)
local rows = lpegmatch(parser,str)
if not rows then
ctx_typ("bad system, case 1: %s",1,str)
return
end
local nrow = #rows
local all = table.setmetatableindex("table")
for r=1,nrow do
local row = rows[r]
for s=1,#row,2 do
local set = row[s]
for v=1,#set do
local vvv = set[v]
local var = vvv[3]
if not var then
var = num
end
if set[var] then
print("bad system, two constants")
end
set[var] = set[v]
all[s][var] = true
set[v] = nil
end
end
end
--
local cnt = #rows[1]
for r=1,nrow do
if #rows[r] ~= cnt then
ctx_typ("bad system, case %i: %s",2,str)
return
end
end
for r=1,#rows[1] do
local a = keys(all[r])
sort(a,function(a,b)
return clean[a] < clean[b]
end)
all[r] = a
end
--
for r=1,nrow do
local row = rows[r]
for r=1,#row do
local set = row[r]
local how = all[r]
if #how > 0 then
-- local done = false
for i=1,#how do
local k = how[i]
local e = set[k]
if e then
ctx_NC()
-- if not done and e[1] == "+" then
if i == 1 and e[1] == "+" then
-- ctx_ord("")
-- ctx_hphantom(e[1])
-- ctx_ord("")
else
ctx_ord("")
context(e[1])
ctx_ord("")
-- done = true
end
ctx_NC()
if e[2] then
context(e[2])
-- done = true
end
if e[3] then
context(e[3])
-- done = true
end
if e[4] then
context(e[4])
-- done = true
end
else
ctx_NC()
-- ctx_mathord("")
ctx_NC()
end
end
else
ctx_NC()
ctx_ord("")
context(set)
ctx_ord("")
end
end
ctx_NR()
end
end
interfaces.implement {
name = "simplealign",
-- public = true,
protected = true,
arguments = "3 strings",
actions = function(alternative,action,str)
local a = alternatives[alternative]
if a then
a(action,str)
else
context(str)
end
end
}
end
|
