diff options
Diffstat (limited to 'tex/context/modules/mkiv/x-calcmath.lua')
| -rw-r--r-- | tex/context/modules/mkiv/x-calcmath.lua | 363 |
1 files changed, 363 insertions, 0 deletions
diff --git a/tex/context/modules/mkiv/x-calcmath.lua b/tex/context/modules/mkiv/x-calcmath.lua new file mode 100644 index 000000000..c96d8d0ac --- /dev/null +++ b/tex/context/modules/mkiv/x-calcmath.lua @@ -0,0 +1,363 @@ +if not modules then modules = { } end modules ['x-calcmath'] = { + version = 1.001, + comment = "companion to x-calcmath.mkiv", + author = "Hans Hagen, PRAGMA-ADE, Hasselt NL", + copyright = "PRAGMA ADE / ConTeXt Development Team", + license = "see context related readme files" +} + +-- this really needs to be redone + +local format, lower, upper, gsub, sub = string.format, string.lower, string.upper, string.gsub, string.sub +local concat = table.concat +local lpegmatch = lpeg.match + +local calcmath = { } +local moduledata = moduledata or { } +moduledata.calcmath = calcmath + +local context = context + +local list_1 = { + "median", "min", "max", "round", "ln", "log", + "sin", "cos", "tan", "sinh", "cosh", "tanh" +} +local list_2 = { + "int", "sum", "prod" +} +local list_3 = { + "f", "g" +} +local list_4 = { + "pi", "inf" +} + +local list_1_1 = { } +local list_2_1 = { } +local list_2_2 = { } +local list_2_3 = { } +local list_4_1 = { } + +local frozen = false + +local function freeze() + for k=1,#list_1 do + local v = list_1[k] + list_1_1[v] = "\\".. upper(v) .." " + end + for k=1,#list_2 do + local v = list_2[k] + list_2_1[v .. "%((.-),(.-),(.-)%)"] = "\\" .. upper(v) .. "^{%1}_{%2}{%3}" + list_2_2[v .. "%((.-),(.-)%)"] = "\\" .. upper(v) .. "^{%1}{%2}" + list_2_3[v .. "%((.-)%)"] = "\\" .. upper(v) .. "{%1}" + end + for k=1,#list_4 do + local v = list_4[k] + list_4_1[v] = "\\" .. upper(v) + end + frozen = true +end + +local entities = { + ['gt'] = '>', + ['lt'] = '<', +} + +local symbols = { + ["<="] = "\\LE ", + [">="] = "\\GE ", + ["=<"] = "\\LE ", + ["=>"] = "\\GE ", + ["=="] = "\\EQ ", + ["<" ] = "\\LT ", + [">" ] = "\\GT ", + ["="] = "\\EQ ", +} + +local function nsub(str,tag,pre,post) + return (gsub(str,tag .. "(%b())", function(body) + return pre .. nsub(sub(body,2,-2),tag,pre,post) .. post + end)) +end + +local function totex(str,mode) + if not frozen then freeze() end + local n = 0 + -- crap + str = gsub(str,"%s+",' ') + -- xml + str = gsub(str,"&(.-);",entities) + -- ...E... + str = gsub(str,"([%-%+]?[%d%.%+%-]+)E([%-%+]?[%d%.]+)", "{\\SCINOT{%1}{%2}}") + -- ^-.. + str = gsub(str,"%^([%-%+]*%d+)", "^{%1}") + -- ^(...) + str = nsub(str,"%^", "^{", "}") + -- 1/x^2 + repeat + str, n = gsub(str,"([%d%w%.]+)/([%d%w%.]+%^{[%d%w%.]+})", "\\frac{%1}{%2}") + until n == 0 + -- todo: autoparenthesis + -- int(a,b,c) + for k, v in next, list_2_1 do + repeat str, n = gsub(str,k,v) until n == 0 + end + -- int(a,b) + for k, v in next, list_2_2 do + repeat str, n = gsub(str,k,v) until n == 0 + end + -- int(a) + for k, v in next, list_2_3 do + repeat str, n = gsub(str,k,v) until n == 0 + end + -- sin(x) => {\\sin(x)} + for k, v in next, list_1_1 do + repeat str, n = gsub(str,k,v) until n == 0 + end + -- mean + str = nsub(str, "mean", "\\OVERLINE{", "}") + -- (1+x)/(1+x) => \\FRAC{1+x}{1+x} + repeat + str, n = gsub(str,"(%b())/(%b())", function(a,b) + return "\\FRAC{" .. sub(a,2,-2) .. "}{" .. sub(b,2,-2) .. "}" + end ) + until n == 0 + -- (1+x)/x => \\FRAC{1+x}{x} + repeat + str, n = gsub(str,"(%b())/([%+%-]?[%.%d%w]+)", function(a,b) + return "\\FRAC{" .. sub(a,2,-2) .. "}{" .. b .. "}" + end ) + until n == 0 + -- 1/(1+x) => \\FRAC{1}{1+x} + repeat + str, n = gsub(str,"([%.%d%w]+)/(%b())", function(a,b) + return "\\FRAC{" .. a .. "}{" .. sub(b,2,-2) .. "}" + end ) + until n == 0 + -- 1/x => \\FRAC{1}{x} + repeat + str, n = gsub(str,"([%.%d%w]+)/([%+%-]?[%.%d%w]+)", "\\FRAC{%1}{%2}") + until n == 0 + -- times + str = gsub(str,"%*", " ") + -- symbols -- we can use a table substitution here + str = gsub(str,"([<>=][<>=]*)", symbols) + -- functions + str = nsub(str,"sqrt", "\\SQRT{", "}") + str = nsub(str,"exp", "e^{", "}") + str = nsub(str,"abs", "\\left|", "\\right|") + -- d/D + str = nsub(str,"D", "{\\FRAC{\\MBOX{d}}{\\MBOX{d}x}{(", ")}}") + str = gsub(str,"D([xy])", "\\FRAC{{\\RM d}%1}{{\\RM d}x}") + -- f/g + for k,v in next, list_3 do -- todo : prepare k,v + str = nsub(str,"D"..v,"{\\RM "..v.."}^{\\PRIME}(",")") + str = nsub(str,v,"{\\RM "..v.."}(",")") + end + -- more symbols + for k,v in next, list_4_1 do + str = gsub(str,k,v) + end + -- parenthesis (optional) + if mode == 2 then + str = gsub(str,"%(", "\\left(") + str = gsub(str,"%)", "\\right)") + end + -- csnames + str = gsub(str,"(\\[A-Z]+)", lower) + -- report + return str +end + +calcmath.totex = totex + +function calcmath.tex(str,mode) + context(totex(str)) +end + +function calcmath.xml(id,mode) + context(totex(lxml.id(id).dt[1],mode)) +end + +-- work in progress ... lpeg variant + +if false then + + -- todo: + + -- maybe rewrite to current lpeg, i.e. string replacement and no Cc's + + -- table approach we have now is less efficient but more flexible + + -- D \frac {\rm d} {{\rm d}x} + -- Dx Dy \frac {{\rm d}y} {{\rm d}x} + -- Df Dg {\rm f}^{\prime} + -- f() g() {\rm f}() + + -- valid utf8 + + local S, P, R, C, V, Cc, Ct = lpeg.S, lpeg.P, lpeg.R, lpeg.C, lpeg.V, lpeg.Cc, lpeg.Ct + + local space = S(" \n\r\t")^0 + local integer = P("-")^-1 * R("09")^1 + local realpart = P("-")^-1 * R("09")^1 * S(".")^1 * R("09")^1 + local number = Cc("number") * C(integer) * space + local real = Cc("real") * C(realpart) * space + local float = Cc("float") * C(realpart) * lpeg.P("E") * lpeg.C(integer) * space + local identifier = Cc("identifier") * C(R("az","AZ")) * space + local compareop = Cc("compare") * C(P("<") + P("=") + P(">") + P(">=") + P("<=") + P(">") + P("<")) * space + local factorop = Cc("factor") * C(S("+-^_,")) * space + local termop = Cc("term") * C(S("*/")) * space + local constant = Cc("constant") * C(P("pi") + lpeg.P("inf")) * space + local functionop = Cc("function") * C(R("az")^1) * space + local open = P("(") * space + local close = P(")") * space + + local grammar = P { + "expression", + expression = Ct(V("factor") * ((factorop+compareop) * V("factor"))^0), + factor = Ct(V("term") * (termop * V("term"))^0), + term = Ct( + float + real + number + + (open * V("expression") * close) + + (functionop * open * (V("expression") * (P(",") * V("expression"))^0) * close) + + (functionop * V("term")) + + constant + identifier + ), + } + + local parser = space * grammar * -1 + + local function has_factor(t) + for i=1,#t do + if t[i] == "factor" then + return true + end + end + end + + -- can be sped up if needed ... + + function totex(t) + if t then + local one = t[1] + if type(one) == "string" then + local two, three = t[2], t[3] + if one == "number" then + context(two) + elseif one == "real" then + context(two) + elseif one == "float" then + context("\\scinot{",two,"}{",three,"}") + elseif one == "identifier" then + context(two) + elseif one == "constant" then + context("\\"..two) + elseif one == "function" then + if two == "sqrt" then + context("\\sqrt{") + totex(three) + context("}") + elseif two == "exp" then + context(" e^{") + totex(three) + context("}") + elseif two == "abs" then + context("\\left|") + totex(three) + context("\\right|") + elseif two == "mean" then + context("\\overline{") + totex(three) + context("}") + elseif two == "int" or two == "prod" or two == "sum" then + local four, five = t[4], t[5] + if five then + context("\\"..two.."^{") -- context[two]("{") + totex(three) + context("}_{") + totex(four) + context("}") + totex(five) + elseif four then + context("\\"..two.."^{") + totex(three) + context("}") + totex(four) + elseif three then + context("\\"..two.." ") -- " " not needed + totex(three) + else + context("\\"..two) + end + else + context("\\"..two.."(") + totex(three) + context(")") + end + end + else + local nt = #t + local hasfactor = has_factor(t) + if hasfactor then + context("\\left(") + end + totex(one) + for i=2,nt,3 do + local what, how, rest = t[i], t[i+1], t[i+2] + if what == "factor" then + if how == '^' or how == "_" then + context(how) + context("{") + totex(rest) + context("}") + else + context(how) + totex(rest) + end + elseif what == "term" then + if how == '/' then + context("\\frac{") + totex(rest) + context("}{") + totex(t[i+3] or "") + context("}") + elseif how == '*' then + context("\\times") + totex(rest) + else + context(how) + totex(three) + end + elseif what == "compare" then + if two == ">=" then + context("\\ge") + elseif two == "<=" then + context("\\le") + elseif two == ">" then + context(">") + elseif two == "<" then + context("<") + end + totex(three) + end + end + if hasfactor then + context("\\right)") + end + end + end + end + + calcmath = { } + + function calcmath.parse(str) + return lpegmatch(parser,str) + end + + function calcmath.tex(str) + str = totex(lpegmatch(parser,str)) + return (str == "" and "[error]") or str + end + +end |