diff options
Diffstat (limited to 'macros/luatex')
26 files changed, 5820 insertions, 2066 deletions
diff --git a/macros/luatex/generic/lualibs/NEWS b/macros/luatex/generic/lualibs/NEWS index cf8a853b6c..889232dc47 100644 --- a/macros/luatex/generic/lualibs/NEWS +++ b/macros/luatex/generic/lualibs/NEWS @@ -1,6 +1,12 @@ History of the lualibs package +2022/10/04 v2.75/ + * sync with Context current as of 2022/10/04. + * add util-sac + * Replace l-gzip with util-zip + 2021/05/20 v2.74/ * sync with Context current as of 2021/05/20. + 2020/12/30 v2.73/ * sync with Context current as of 2020/12/30. diff --git a/macros/luatex/generic/lualibs/README.md b/macros/luatex/generic/lualibs/README.md index e2cd6be9bd..09194115ce 100644 --- a/macros/luatex/generic/lualibs/README.md +++ b/macros/luatex/generic/lualibs/README.md @@ -1,10 +1,10 @@ # The Lualibs Package -VERSION: 2.74 +VERSION: 2.75 -DATE: 2021-05-20 +DATE: 2022-10-04 -FONTLOADERDATE: 2021-05-20 +FONTLOADERDATE: 2022-10-04 Lualibs is a collection of Lua modules useful for general programming. @@ -47,7 +47,6 @@ See the 'NEWS' file for version history. | lualibs-compat.lua |tex/luatex/lualibs/lualibs-compat.lua | lualibs-dir.lua |tex/luatex/lualibs/lualibs-dir.lua | lualibs-file.lua | tex/luatex/lualibs/lualibs-file.lua -| lualibs-gzip.lua | tex/luatex/lualibs/lualibs-gzip.lua | lualibs-function.lua | tex/luatex/lualibs/lualibs-function.lua | lualibs-io.lua | tex/luatex/lualibs/lualibs-io.lua | lualibs-lpeg.lua | tex/luatex/lualibs/lualibs-lpeg.lua @@ -68,11 +67,13 @@ See the 'NEWS' file for version history. | lualibs-util-jsn.lua | tex/luatex/lualibs/lualibs-util-jsn.lua | lualibs-util-lua.lua | tex/luatex/lualibs/lualibs-util-lua.lua | lualibs-util-prs.lua | tex/luatex/lualibs/lualibs-util-prs.lua +| lualibs-util-sac.lua | tex/luatex/lualibs/lualibs-util-sac.lua | lualibs-util-sta.lua | tex/luatex/lualibs/lualibs-util-sta.lua | lualibs-util-sto.lua | tex/luatex/lualibs/lualibs-util-sto.lua | lualibs-util-str.lua | tex/luatex/lualibs/lualibs-util-str.lua | lualibs-util-tab.lua | tex/luatex/lualibs/lualibs-util-tab.lua | lualibs-util-tpl.lua | tex/luatex/lualibs/lualibs-util-tpl.lua +| lualibs-util-zip.lua | tex/luatex/lualibs/lualibs-util-zip.lua | LICENSE | doc/luatex/lualibs/LICENSE | NEWS | doc/luatex/lualibs/NEWS | README | doc/luatex/lualibs/README diff --git a/macros/luatex/generic/lualibs/lualibs-basic-merged.lua b/macros/luatex/generic/lualibs/lualibs-basic-merged.lua index ac98df379a..690a3160ac 100644 --- a/macros/luatex/generic/lualibs/lualibs-basic-merged.lua +++ b/macros/luatex/generic/lualibs/lualibs-basic-merged.lua @@ -1,6 +1,6 @@ -- merged file : lualibs-basic-merged.lua -- parent file : lualibs-basic.lua --- merge date : 2021-05-20 23:14 +-- merge date : 2022-10-04 17:16 do -- begin closure to overcome local limits and interference @@ -2737,8 +2737,14 @@ if not math.ceiling then math.ceiling=math.ceil end if not math.round then - local floor=math.floor - function math.round(x) return floor(x+0.5) end + if xmath then + math.round=xmath.round + else + local floor=math.floor + function math.round(x) + return x<0 and -floor(-x+0.5) or floor(x+0.5) + end + end end if not math.div then local floor=math.floor @@ -2808,7 +2814,7 @@ if not math.tointeger then end if not math.ult then local floor=math.floor - function math.tointeger(m,n) + function math.ult(m,n) return floor(m)<floor(n) end end @@ -2882,9 +2888,12 @@ function io.copydata(source,target,action) flush() end end -function io.savedata(filename,data,joiner) - local f=open(filename,"wb") +function io.savedata(filename,data,joiner,append) + local f=open(filename,append and "ab" or "wb") if f then + if append and joiner and f:seek("end")>0 then + f:write(joiner) + end if type(data)=="table" then f:write(concat(data,joiner or "")) elseif type(data)=="function" then @@ -3172,10 +3181,10 @@ if not modules then modules={} end modules ['l-os']={ license="see context related readme files" } local os=os -local date,time=os.date,os.time +local date,time,difftime=os.date,os.time,os.difftime local find,format,gsub,upper,gmatch=string.find,string.format,string.gsub,string.upper,string.gmatch local concat=table.concat -local random,ceil,randomseed=math.random,math.ceil,math.randomseed +local random,ceil,randomseed,modf=math.random,math.ceil,math.randomseed,math.modf local type,setmetatable,tonumber,tostring=type,setmetatable,tonumber,tostring do local selfdir=os.selfdir @@ -3273,7 +3282,7 @@ if not os.__getenv__ then osenv[K]=v end function os.getenv(k) - local K=upper(k) + local K=upper(k) local v=osenv[K] or osgetenv(K) or osgetenv(k) if v=="" then return nil @@ -3291,22 +3300,6 @@ if not os.__getenv__ then setmetatable(os.env,{ __index=__index,__newindex=__newindex } ) end end -local execute=os.execute -local iopopen=io.popen -local function resultof(command) - local handle=iopopen(command,"r") - if handle then - local result=handle:read("*all") or "" - handle:close() - return result - else - return "" - end -end -os.resultof=resultof -function os.pipeto(command) - return iopopen(command,"w") -end if not io.fileseparator then if find(os.getenv("PATH"),";",1,true) then io.fileseparator,io.pathseparator,os.type="\\",";",os.type or "windows" @@ -3321,228 +3314,231 @@ if os.type=="windows" then else os.libsuffix,os.binsuffix,os.binsuffixes='so','',{ '' } end -local launchers={ - windows="start %s", - macosx="open %s", - unix="xdg-open %s &> /dev/null &", -} -function os.launch(str) - local command=format(launchers[os.name] or launchers.unix,str) - execute(command) -end -local gettimeofday=os.gettimeofday or os.clock -os.gettimeofday=gettimeofday -local startuptime=gettimeofday() -function os.runtime() - return gettimeofday()-startuptime -end -local resolvers=os.resolvers or {} -os.resolvers=resolvers -setmetatable(os,{ __index=function(t,k) - local r=resolvers[k] - return r and r(t,k) or nil -end }) -local name,platform=os.name or "linux",os.getenv("MTX_PLATFORM") or "" -if platform~="" then - os.platform=platform -elseif os.type=="windows" then - function resolvers.platform(t,k) - local architecture=os.getenv("PROCESSOR_ARCHITECTURE") or "" - local platform="" - if find(architecture,"AMD64",1,true) then - platform="win64" +do + local execute=os.execute + local iopopen=io.popen + local ostype=os.type + local function resultof(command) + local handle=iopopen(command,ostype=="windows" and "rb" or "r") + if handle then + local result=handle:read("*all") or "" + handle:close() + return result else - platform="mswin" + return "" end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform end -elseif name=="linux" then - function resolvers.platform(t,k) - local architecture=os.getenv("HOSTTYPE") or resultof("uname -m") or "" - local platform=os.getenv("MTX_PLATFORM") or "" + os.resultof=resultof + function os.pipeto(command) + return iopopen(command,"w") + end + local launchers={ + windows="start %s", + macosx="open %s", + unix="xdg-open %s &> /dev/null &", + } + function os.launch(str) + local command=format(launchers[os.name] or launchers.unix,str) + execute(command) + end +end +do + local gettimeofday=os.gettimeofday or os.clock + os.gettimeofday=gettimeofday + local startuptime=gettimeofday() + function os.runtime() + return gettimeofday()-startuptime + end +end +do + local name=os.name or "linux" + local platform=os.getenv("MTX_PLATFORM") or "" + local architecture=os.uname and os.uname().machine + local bits=os.getenv("MTX_BITS") or find(platform,"64") and 64 or 32 + if platform~="" then + elseif os.type=="windows" then + architecture=string.lower(architecture or os.getenv("PROCESSOR_ARCHITECTURE") or "") + if architecture=="x86_64" then + bits,platform=64,"win64" + elseif find(architecture,"amd64") then + bits,platform=64,"win64" + elseif find(architecture,"arm64") then + bits,platform=64,"windows-arm64" + elseif find(architecture,"arm32") then + bits,platform=32,"windows-arm32" + else + bits,platform=32,"mswin" + end + elseif name=="linux" then + architecture=architecture or os.getenv("HOSTTYPE") or resultof("uname -m") or "" local musl=find(os.selfdir or "","linuxmusl") - if platform~="" then - elseif find(architecture,"x86_64",1,true) then - platform=musl and "linuxmusl" or "linux-64" - elseif find(architecture,"ppc",1,true) then - platform="linux-ppc" + if find(architecture,"x86_64") then + bits,platform=64,musl and "linuxmusl" or "linux-64" + elseif find(architecture,"ppc") then + bits,platform=32,"linux-ppc" else - platform=musl and "linuxmusl" or "linux" + bits,platform=32,musl and "linuxmusl" or "linux" end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform - end -elseif name=="macosx" then - function resolvers.platform(t,k) - local architecture=resultof("echo $HOSTTYPE") or "" - local platform="" + elseif name=="macosx" then + architecture=architecture or resultof("echo $HOSTTYPE") or "" if architecture=="" then - platform="osx-intel" - elseif find(architecture,"i386",1,true) then - platform="osx-intel" - elseif find(architecture,"x86_64",1,true) then - platform="osx-64" - elseif find(architecture,"arm64",1,true) then - platform="osx-arm" + bits,platform=64,"osx-intel" + elseif find(architecture,"i386") then + bits,platform=64,"osx-intel" + elseif find(architecture,"x86_64") then + bits,platform=64,"osx-64" + elseif find(architecture,"arm64") then + bits,platform=64,"osx-arm" else - platform="osx-ppc" - end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform - end -elseif name=="sunos" then - function resolvers.platform(t,k) - local architecture=resultof("uname -m") or "" - local platform="" - if find(architecture,"sparc",1,true) then - platform="solaris-sparc" + bits,platform=32,"osx-ppc" + end + elseif name=="sunos" then + architecture=architecture or resultof("uname -m") or "" + if find(architecture,"sparc") then + bits,platform=32,"solaris-sparc" else - platform="solaris-intel" - end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform - end -elseif name=="freebsd" then - function resolvers.platform(t,k) - local architecture=resultof("uname -m") or "" - local platform="" - if find(architecture,"amd64",1,true) then - platform="freebsd-amd64" + bits,platform=32,"solaris-intel" + end + elseif name=="freebsd" then + architecture=architecture or os.getenv("MACHTYPE") or resultof("uname -m") or "" + if find(architecture,"amd64") or find(architecture,"AMD64") then + bits,platform=64,"freebsd-amd64" else - platform="freebsd" - end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform - end -elseif name=="kfreebsd" then - function resolvers.platform(t,k) - local architecture=os.getenv("HOSTTYPE") or resultof("uname -m") or "" - local platform="" - if find(architecture,"x86_64",1,true) then - platform="kfreebsd-amd64" + bits,platform=32,"freebsd" + end + elseif name=="kfreebsd" then + architecture=architecture or os.getenv("HOSTTYPE") or resultof("uname -m") or "" + if architecture=="x86_64" then + bits,platform=64,"kfreebsd-amd64" + else + bits,platform=32,"kfreebsd-i386" + end + else + architecture=architecture or resultof("uname -m") or "" + if find(architecture,"aarch64") then + bits,platform="linux-aarch64" + elseif find(architecture,"armv7l") then + bits,platform=32,"linux-armhf" + elseif find(architecture,"mips64") or find(architecture,"mips64el") then + bits,platform=64,"linux-mipsel" + elseif find(architecture,"mipsel") or find(architecture,"mips") then + bits,platform=32,"linux-mipsel" else - platform="kfreebsd-i386" + bits,platform=64,"linux-64" end - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform end -else - function resolvers.platform(t,k) - local platform="linux" - os.setenv("MTX_PLATFORM",platform) - os.platform=platform - return platform + os.setenv("MTX_PLATFORM",platform) + os.setenv("MTX_BITS",bits) + os.platform=platform + os.bits=bits + os.newline=name=="windows" and "\013\010" or "\010" +end +do + local t={ 8,9,"a","b" } + function os.uuid() + return format("%04x%04x-4%03x-%s%03x-%04x-%04x%04x%04x", + random(0xFFFF),random(0xFFFF), + random(0x0FFF), + t[ceil(random(4))] or 8,random(0x0FFF), + random(0xFFFF), + random(0xFFFF),random(0xFFFF),random(0xFFFF) + ) end end -os.newline=name=="windows" and "\013\010" or "\010" -function resolvers.bits(t,k) - local bits=find(os.platform,"64",1,true) and 64 or 32 - os.bits=bits - return bits -end -local t={ 8,9,"a","b" } -function os.uuid() - return format("%04x%04x-4%03x-%s%03x-%04x-%04x%04x%04x", - random(0xFFFF),random(0xFFFF), - random(0x0FFF), - t[ceil(random(4))] or 8,random(0x0FFF), - random(0xFFFF), - random(0xFFFF),random(0xFFFF),random(0xFFFF) - ) -end -local d -function os.timezone(delta) - d=d or ((tonumber(date("%H")) or 0)-(tonumber(date("!%H")) or 0)) - if delta then - if d>0 then - return format("+%02i:00",d) +do + local hour,min + function os.timezone(difference) + if not hour then + local current=time() + local utcdate=date("!*t",current) + local localdate=date("*t",current) + localdate.isdst=false + local timediff=difftime(time(localdate),time(utcdate)) + hour,min=modf(timediff/3600) + min=min*60 + end + if difference then + return hour,min else - return format("-%02i:00",-d) + return format("%+03d:%02d",hour,min) end - else - return 1 - end -end -local timeformat=format("%%s%s",os.timezone(true)) -local dateformat="!%Y-%m-%d %H:%M:%S" -local lasttime=nil -local lastdate=nil -function os.fulltime(t,default) - t=t and tonumber(t) or 0 - if t>0 then - elseif default then - return default - else - t=time() - end - if t~=lasttime then - lasttime=t - lastdate=format(timeformat,date(dateformat)) - end - return lastdate -end -local dateformat="%Y-%m-%d %H:%M:%S" -local lasttime=nil -local lastdate=nil -function os.localtime(t,default) - t=t and tonumber(t) or 0 - if t>0 then - elseif default then - return default - else - t=time() end - if t~=lasttime then - lasttime=t - lastdate=date(dateformat,t) + local timeformat=format("%%s%s",os.timezone()) + local dateformat="%Y-%m-%d %H:%M:%S" + local lasttime=nil + local lastdate=nil + function os.fulltime(t,default) + t=t and tonumber(t) or 0 + if t>0 then + elseif default then + return default + else + t=time() + end + if t~=lasttime then + lasttime=t + lastdate=format(timeformat,date(dateformat)) + end + return lastdate + end + local dateformat="%Y-%m-%d %H:%M:%S" + local lasttime=nil + local lastdate=nil + function os.localtime(t,default) + t=t and tonumber(t) or 0 + if t>0 then + elseif default then + return default + else + t=time() + end + if t~=lasttime then + lasttime=t + lastdate=date(dateformat,t) + end + return lastdate + end + function os.converttime(t,default) + local t=tonumber(t) + if t and t>0 then + return date(dateformat,t) + else + return default or "-" + end + end + function os.today() + return date("!*t") + end + function os.now() + return date("!%Y-%m-%d %H:%M:%S") end - return lastdate end -function os.converttime(t,default) - local t=tonumber(t) - if t and t>0 then - return date(dateformat,t) - else - return default or "-" - end -end -local memory={} -local function which(filename) - local fullname=memory[filename] - if fullname==nil then - local suffix=file.suffix(filename) - local suffixes=suffix=="" and os.binsuffixes or { suffix } - for directory in gmatch(os.getenv("PATH"),"[^"..io.pathseparator.."]+") do - local df=file.join(directory,filename) - for i=1,#suffixes do - local dfs=file.addsuffix(df,suffixes[i]) - if io.exists(dfs) then - fullname=dfs - break +do + local cache={} + local function which(filename) + local fullname=cache[filename] + if fullname==nil then + local suffix=file.suffix(filename) + local suffixes=suffix=="" and os.binsuffixes or { suffix } + for directory in gmatch(os.getenv("PATH"),"[^"..io.pathseparator.."]+") do + local df=file.join(directory,filename) + for i=1,#suffixes do + local dfs=file.addsuffix(df,suffixes[i]) + if io.exists(dfs) then + fullname=dfs + break + end end end + if not fullname then + fullname=false + end + cache[filename]=fullname end - if not fullname then - fullname=false - end - memory[filename]=fullname + return fullname end - return fullname -end -os.which=which -os.where=which -function os.today() - return date("!*t") -end -function os.now() - return date("!%Y-%m-%d %H:%M:%S") + os.which=which + os.where=which end if not os.sleep then local socket=socket @@ -3553,65 +3549,69 @@ if not os.sleep then socket.sleep(n) end end -local function isleapyear(year) - return (year%4==0) and (year%100~=0 or year%400==0) -end -os.isleapyear=isleapyear -local days={ 31,28,31,30,31,30,31,31,30,31,30,31 } -local function nofdays(year,month,day) - if not month then - return isleapyear(year) and 365 or 364 - elseif not day then - return month==2 and isleapyear(year) and 29 or days[month] - else - for i=1,month-1 do - day=day+days[i] - end - if month>2 and isleapyear(year) then - day=day+1 +do + local function isleapyear(year) + return (year%4==0) and (year%100~=0 or year%400==0) + end + os.isleapyear=isleapyear + local days={ 31,28,31,30,31,30,31,31,30,31,30,31 } + local function nofdays(year,month,day) + if not month then + return isleapyear(year) and 365 or 364 + elseif not day then + return month==2 and isleapyear(year) and 29 or days[month] + else + for i=1,month-1 do + day=day+days[i] + end + if month>2 and isleapyear(year) then + day=day+1 + end + return day end - return day end -end -os.nofdays=nofdays -function os.weekday(day,month,year) - return date("%w",time { year=year,month=month,day=day })+1 -end -function os.validdate(year,month,day) - if month<1 then - month=1 - elseif month>12 then - month=12 + os.nofdays=nofdays + function os.weekday(day,month,year) + return date("%w",time { year=year,month=month,day=day })+1 end - if day<1 then - day=1 - else - local max=nofdays(year,month) - if day>max then - day=max + function os.validdate(year,month,day) + if month<1 then + month=1 + elseif month>12 then + month=12 + end + if day<1 then + day=1 + else + local max=nofdays(year,month) + if day>max then + day=max + end end + return year,month,day end - return year,month,day -end -function os.date(fmt,...) - if not fmt then - fmt="%Y-%m-%d %H:%M" + function os.date(fmt,...) + if not fmt then + fmt="%Y-%m-%d %H:%M" + end + return date(fmt,...) end - return date(fmt,...) end -local osexit=os.exit -local exitcode=nil -function os.setexitcode(code) - exitcode=code -end -function os.exit(c) - if exitcode~=nil then - return osexit(exitcode) +do + local osexit=os.exit + local exitcode=nil + function os.setexitcode(code) + exitcode=code end - if c~=nil then - return osexit(c) + function os.exit(c) + if exitcode~=nil then + return osexit(exitcode) + end + if c~=nil then + return osexit(c) + end + return osexit() end - return osexit() end end -- closure @@ -3872,7 +3872,7 @@ function file.join(one,two,three,...) if not two then return one=="" and one or lpegmatch(reslasher,one) end - if one=="" then + if not one or one=="" then return lpegmatch(stripper,three and concat({ two,three,... },"/") or two) end if lpegmatch(isnetwork,one) then @@ -4031,87 +4031,6 @@ end -- closure do -- begin closure to overcome local limits and interference -if not modules then modules={} end modules ['l-gzip']={ - version=1.001, - author="Hans Hagen, PRAGMA-ADE, Hasselt NL", - copyright="PRAGMA ADE / ConTeXt Development Team", - license="see context related readme files" -} -gzip=gzip or {} -if not zlib then - zlib=xzip -elseif not xzip then - xzip=zlib -end -if zlib then - local suffix=file.suffix - local suffixes=file.suffixes - local find=string.find - local openfile=io.open - local gzipwindow=15+16 - local gziplevel=3 - local identifier="^\x1F\x8B\x08" - local compress=zlib.compress - local decompress=zlib.decompress - function gzip.load(filename) - local f=openfile(filename,"rb") - if not f then - else - local data=f:read("*all") - f:close() - if data and data~="" then - if suffix(filename)=="gz" then - data=decompress(data,gzipwindow) - end - return data - end - end - end - function gzip.save(filename,data,level) - if suffix(filename)~="gz" then - filename=filename..".gz" - end - local f=openfile(filename,"wb") - if f then - data=compress(data or "",level or gziplevel,nil,gzipwindow) - f:write(data) - f:close() - return #data - end - end - function gzip.suffix(filename) - local suffix,extra=suffixes(filename) - local gzipped=extra=="gz" - return suffix,gzipped - end - function gzip.compressed(s) - return s and find(s,identifier) - end - function gzip.compress(s,level) - if s and not find(s,identifier) then - if not level then - level=gziplevel - elseif level<=0 then - return s - elseif level>9 then - level=9 - end - return compress(s,level or gziplevel,nil,gzipwindow) or s - end - end - function gzip.decompress(s) - if s and find(s,identifier) then - return decompress(s,gzipwindow) - else - return s - end - end -end - -end -- closure - -do -- begin closure to overcome local limits and interference - if not modules then modules={} end modules ['l-md5']={ version=1.001, author="Hans Hagen, PRAGMA-ADE, Hasselt NL", @@ -4389,15 +4308,15 @@ local separator,pattern if onwindows then local slash=S("/\\")/"/" pattern={ - [1]=(Cs(P(".")+slash^1)+Cs(R("az","AZ")*P(":")*slash^0)+Cc("./"))*V(2)*V(3), - [2]=Cs(((1-S("*?/\\"))^0*slash)^0), - [3]=Cs(P(1)^0) + (Cs(P(".")+slash^1)+Cs(R("az","AZ")*P(":")*slash^0)+Cc("./"))*V(2)*V(3), + Cs(((1-S("*?/\\"))^0*slash)^0), + Cs(P(1)^0) } else pattern={ - [1]=(C(P(".")+P("/")^1)+Cc("./"))*V(2)*V(3), - [2]=C(((1-S("*?/"))^0*P("/"))^0), - [3]=C(P(1)^0) + (C(P(".")+P("/")^1)+Cc("./"))*V(2)*V(3), + C(((1-S("*?/"))^0*P("/"))^0), + C(P(1)^0) } end local filter=Cs (( diff --git a/macros/luatex/generic/lualibs/lualibs-dir.lua b/macros/luatex/generic/lualibs/lualibs-dir.lua index 325039cb1e..ac8e2f4e8e 100644 --- a/macros/luatex/generic/lualibs/lualibs-dir.lua +++ b/macros/luatex/generic/lualibs/lualibs-dir.lua @@ -230,18 +230,18 @@ if onwindows then -- we could sanitize here -- pattern = Ct { pattern = { - [1] = (Cs(P(".") + slash^1) + Cs(R("az","AZ") * P(":") * slash^0) + Cc("./")) * V(2) * V(3), - [2] = Cs(((1-S("*?/\\"))^0 * slash)^0), - [3] = Cs(P(1)^0) + (Cs(P(".") + slash^1) + Cs(R("az","AZ") * P(":") * slash^0) + Cc("./")) * V(2) * V(3), + Cs(((1-S("*?/\\"))^0 * slash)^0), + Cs(P(1)^0) } else -- assume unix -- pattern = Ct { pattern = { - [1] = (C(P(".") + P("/")^1) + Cc("./")) * V(2) * V(3), - [2] = C(((1-S("*?/"))^0 * P("/"))^0), - [3] = C(P(1)^0) + (C(P(".") + P("/")^1) + Cc("./")) * V(2) * V(3), + C(((1-S("*?/"))^0 * P("/"))^0), + C(P(1)^0) } end diff --git a/macros/luatex/generic/lualibs/lualibs-extended-merged.lua b/macros/luatex/generic/lualibs/lualibs-extended-merged.lua index 9cd4487bf2..08428c51ac 100644 --- a/macros/luatex/generic/lualibs/lualibs-extended-merged.lua +++ b/macros/luatex/generic/lualibs/lualibs-extended-merged.lua @@ -1,6 +1,511 @@ -- merged file : lualibs-extended-merged.lua -- parent file : lualibs-extended.lua --- merge date : 2021-05-20 23:14 +-- merge date : 2022-10-04 17:16 + +do -- begin closure to overcome local limits and interference + +if not modules then modules={} end modules ['util-sac']={ + version=1.001, + optimize=true, + comment="companion to luat-lib.mkiv", + author="Hans Hagen, PRAGMA-ADE, Hasselt NL", + copyright="PRAGMA ADE / ConTeXt Development Team", + license="see context related readme files" +} +local byte,sub=string.byte,string.sub +local tonumber=tonumber +utilities=utilities or {} +local streams={} +utilities.streams=streams +function streams.open(filename,zerobased) + local f=filename and io.loaddata(filename) + if f then + return { f,1,#f,zerobased or false } + end +end +function streams.openstring(f,zerobased) + if f then + return { f,1,#f,zerobased or false } + end +end +function streams.getstring(f) + if f then + return f[1] + end +end +function streams.close() +end +function streams.size(f) + return f and f[3] or 0 +end +streams.getsize=streams.size +function streams.setposition(f,i) + if f[4] then + if i<=0 then + f[2]=1 + else + f[2]=i+1 + end + else + if i<=1 then + f[2]=1 + else + f[2]=i + end + end +end +function streams.getposition(f) + if f[4] then + return f[2]-1 + else + return f[2] + end +end +function streams.look(f,n,chars) + local b=f[2] + local e=b+n-1 + if chars then + return sub(f[1],b,e) + else + return byte(f[1],b,e) + end +end +function streams.skip(f,n) + f[2]=f[2]+n +end +function streams.readbyte(f) + local i=f[2] + f[2]=i+1 + return byte(f[1],i) +end +function streams.readbytes(f,n) + local i=f[2] + local j=i+n + f[2]=j + return byte(f[1],i,j-1) +end +function streams.readbytetable(f,n) + local i=f[2] + local j=i+n + f[2]=j + return { byte(f[1],i,j-1) } +end +function streams.skipbytes(f,n) + f[2]=f[2]+n +end +function streams.readchar(f) + local i=f[2] + f[2]=i+1 + return sub(f[1],i,i) +end +function streams.readstring(f,n) + local i=f[2] + local j=i+n + f[2]=j + return sub(f[1],i,j-1) +end +function streams.readinteger1(f) + local i=f[2] + f[2]=i+1 + local n=byte(f[1],i) + if n>=0x80 then + return n-0x100 + else + return n + end +end +streams.readcardinal1=streams.readbyte +streams.readcardinal=streams.readcardinal1 +streams.readinteger=streams.readinteger1 +function streams.readcardinal2(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local a,b=byte(f[1],i,j) + return 0x100*a+b +end +function streams.readcardinal2le(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local b,a=byte(f[1],i,j) + return 0x100*a+b +end +function streams.readinteger2(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local a,b=byte(f[1],i,j) + if a>=0x80 then + return 0x100*a+b-0x10000 + else + return 0x100*a+b + end +end +function streams.readinteger2le(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local b,a=byte(f[1],i,j) + if a>=0x80 then + return 0x100*a+b-0x10000 + else + return 0x100*a+b + end +end +function streams.readcardinal3(f) + local i=f[2] + local j=i+2 + f[2]=j+1 + local a,b,c=byte(f[1],i,j) + return 0x10000*a+0x100*b+c +end +function streams.readcardinal3le(f) + local i=f[2] + local j=i+2 + f[2]=j+1 + local c,b,a=byte(f[1],i,j) + return 0x10000*a+0x100*b+c +end +function streams.readinteger3(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local a,b,c=byte(f[1],i,j) + if a>=0x80 then + return 0x10000*a+0x100*b+c-0x1000000 + else + return 0x10000*a+0x100*b+c + end +end +function streams.readinteger3le(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local c,b,a=byte(f[1],i,j) + if a>=0x80 then + return 0x10000*a+0x100*b+c-0x1000000 + else + return 0x10000*a+0x100*b+c + end +end +function streams.readcardinal4(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local a,b,c,d=byte(f[1],i,j) + return 0x1000000*a+0x10000*b+0x100*c+d +end +function streams.readcardinal4le(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local d,c,b,a=byte(f[1],i,j) + return 0x1000000*a+0x10000*b+0x100*c+d +end +function streams.readinteger4(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local a,b,c,d=byte(f[1],i,j) + if a>=0x80 then + return 0x1000000*a+0x10000*b+0x100*c+d-0x100000000 + else + return 0x1000000*a+0x10000*b+0x100*c+d + end +end +function streams.readinteger4le(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local d,c,b,a=byte(f[1],i,j) + if a>=0x80 then + return 0x1000000*a+0x10000*b+0x100*c+d-0x100000000 + else + return 0x1000000*a+0x10000*b+0x100*c+d + end +end +function streams.readfixed2(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local n1,n2=byte(f[1],i,j) + if n1>=0x80 then + n1=n1-0x100 + end + return n1+n2/0xFF +end +function streams.readfixed4(f) + local i=f[2] + local j=i+3 + f[2]=j+1 + local a,b,c,d=byte(f[1],i,j) + local n1=0x100*a+b + local n2=0x100*c+d + if n1>=0x8000 then + n1=n1-0x10000 + end + return n1+n2/0xFFFF +end +if bit32 then + local extract=bit32.extract + local band=bit32.band + function streams.read2dot14(f) + local i=f[2] + local j=i+1 + f[2]=j+1 + local a,b=byte(f[1],i,j) + if a>=0x80 then + local n=-(0x100*a+b) + return-(extract(n,14,2)+(band(n,0x3FFF)/16384.0)) + else + local n=0x100*a+b + return (extract(n,14,2)+(band(n,0x3FFF)/16384.0)) + end + end +end +function streams.skipshort(f,n) + f[2]=f[2]+2*(n or 1) +end +function streams.skiplong(f,n) + f[2]=f[2]+4*(n or 1) +end +if sio and sio.readcardinal2 then + local readcardinal1=sio.readcardinal1 + local readcardinal2=sio.readcardinal2 + local readcardinal3=sio.readcardinal3 + local readcardinal4=sio.readcardinal4 + local readinteger1=sio.readinteger1 + local readinteger2=sio.readinteger2 + local readinteger3=sio.readinteger3 + local readinteger4=sio.readinteger4 + local readfixed2=sio.readfixed2 + local readfixed4=sio.readfixed4 + local read2dot14=sio.read2dot14 + local readbytes=sio.readbytes + local readbytetable=sio.readbytetable + function streams.readcardinal1(f) + local i=f[2] + f[2]=i+1 + return readcardinal1(f[1],i) + end + function streams.readcardinal2(f) + local i=f[2] + f[2]=i+2 + return readcardinal2(f[1],i) + end + function streams.readcardinal3(f) + local i=f[2] + f[2]=i+3 + return readcardinal3(f[1],i) + end + function streams.readcardinal4(f) + local i=f[2] + f[2]=i+4 + return readcardinal4(f[1],i) + end + function streams.readinteger1(f) + local i=f[2] + f[2]=i+1 + return readinteger1(f[1],i) + end + function streams.readinteger2(f) + local i=f[2] + f[2]=i+2 + return readinteger2(f[1],i) + end + function streams.readinteger3(f) + local i=f[2] + f[2]=i+3 + return readinteger3(f[1],i) + end + function streams.readinteger4(f) + local i=f[2] + f[2]=i+4 + return readinteger4(f[1],i) + end + function streams.readfixed2(f) + local i=f[2] + f[2]=i+2 + return readfixed2(f[1],i) + end + function streams.readfixed4(f) + local i=f[2] + f[2]=i+4 + return readfixed4(f[1],i) + end + function streams.read2dot14(f) + local i=f[2] + f[2]=i+2 + return read2dot14(f[1],i) + end + function streams.readbytes(f,n) + local i=f[2] + local s=f[3] + local p=i+n + if p>s then + f[2]=s+1 + else + f[2]=p + end + return readbytes(f[1],i,n) + end + function streams.readbytetable(f,n) + local i=f[2] + local s=f[3] + local p=i+n + if p>s then + f[2]=s+1 + else + f[2]=p + end + return readbytetable(f[1],i,n) + end + streams.readbyte=streams.readcardinal1 + streams.readsignedbyte=streams.readinteger1 + streams.readcardinal=streams.readcardinal1 + streams.readinteger=streams.readinteger1 +end +if sio and sio.readcardinaltable then + local readcardinaltable=sio.readcardinaltable + local readintegertable=sio.readintegertable + function utilities.streams.readcardinaltable(f,n,b) + local i=f[2] + local s=f[3] + local p=i+n*b + if p>s then + f[2]=s+1 + else + f[2]=p + end + return readcardinaltable(f[1],i,n,b) + end + function utilities.streams.readintegertable(f,n,b) + local i=f[2] + local s=f[3] + local p=i+n*b + if p>s then + f[2]=s+1 + else + f[2]=p + end + return readintegertable(f[1],i,n,b) + end +else + local readcardinal1=streams.readcardinal1 + local readcardinal2=streams.readcardinal2 + local readcardinal3=streams.readcardinal3 + local readcardinal4=streams.readcardinal4 + function streams.readcardinaltable(f,n,b) + local i=f[2] + local s=f[3] + local p=i+n*b + if p>s then + f[2]=s+1 + else + f[2]=p + end + local t={} + if b==1 then for i=1,n do t[i]=readcardinal1(f[1],i) end + elseif b==2 then for i=1,n do t[i]=readcardinal2(f[1],i) end + elseif b==3 then for i=1,n do t[i]=readcardinal3(f[1],i) end + elseif b==4 then for i=1,n do t[i]=readcardinal4(f[1],i) end end + return t + end + local readinteger1=streams.readinteger1 + local readinteger2=streams.readinteger2 + local readinteger3=streams.readinteger3 + local readinteger4=streams.readinteger4 + function streams.readintegertable(f,n,b) + local i=f[2] + local s=f[3] + local p=i+n*b + if p>s then + f[2]=s+1 + else + f[2]=p + end + local t={} + if b==1 then for i=1,n do t[i]=readinteger1(f[1],i) end + elseif b==2 then for i=1,n do t[i]=readinteger2(f[1],i) end + elseif b==3 then for i=1,n do t[i]=readinteger3(f[1],i) end + elseif b==4 then for i=1,n do t[i]=readinteger4(f[1],i) end end + return t + end +end +do + local files=utilities.files + if files then + local openfile=files.open + local openstream=streams.open + local openstring=streams.openstring + local setmetatable=setmetatable + function io.newreader(str,method) + local f,m + if method=="string" then + f=openstring(str,true) + m=streams + elseif method=="stream" then + f=openstream(str,true) + m=streams + else + f=openfile(str,"rb") + m=files + end + if f then + local t={} + setmetatable(t,{ + __index=function(t,k) + local r=m[k] + if k=="close" then + if f then + m.close(f) + f=nil + end + return function() end + elseif r then + local v=function(_,a,b) return r(f,a,b) end + t[k]=v + return v + else + print("unknown key",k) + end + end + } ) + return t + end + end + end +end +if bit32 and not streams.tocardinal1 then + local extract=bit32.extract + local char=string.char + streams.tocardinal1=char + function streams.tocardinal2(n) return char(extract(8,8),extract(0,8)) end + function streams.tocardinal3(n) return char(extract(16,8),extract(8,8),extract(0,8)) end + function streams.tocardinal4(n) return char(extract(24,8),extract(16,8),extract(8,8),extract(0,8)) end + streams.tocardinal1le=char + function streams.tocardinal2le(n) return char(extract(0,8),extract(8,8)) end + function streams.tocardinal3le(n) return char(extract(0,8),extract(8,8),extract(16,8)) end + function streams.tocardinal4le(n) return char(extract(0,8),extract(8,8),extract(16,8),extract(24,8)) end +end +if not streams.readcstring then + local readchar=streams.readchar + local concat=table.concat + function streams.readcstring(f) + local t={} + while true do + local c=readchar(f) + if c and c~="\0" then + t[#t+1]=c + else + return concat(t) + end + end + end +end + +end -- closure do -- begin closure to overcome local limits and interference @@ -14,12 +519,13 @@ if not modules then modules={} end modules ['util-str']={ utilities=utilities or {} utilities.strings=utilities.strings or {} local strings=utilities.strings -local format,gsub,rep,sub,find=string.format,string.gsub,string.rep,string.sub,string.find +local format,gsub,rep,sub,find,char=string.format,string.gsub,string.rep,string.sub,string.find,string.char local load,dump=load,string.dump local tonumber,type,tostring,next,setmetatable=tonumber,type,tostring,next,setmetatable local unpack,concat=table.unpack,table.concat local P,V,C,S,R,Ct,Cs,Cp,Carg,Cc=lpeg.P,lpeg.V,lpeg.C,lpeg.S,lpeg.R,lpeg.Ct,lpeg.Cs,lpeg.Cp,lpeg.Carg,lpeg.Cc local patterns,lpegmatch=lpeg.patterns,lpeg.match +local tsplitat=lpeg.tsplitat local utfchar,utfbyte,utflen=utf.char,utf.byte,utf.len local loadstripped=function(str,shortcuts) if shortcuts then @@ -373,6 +879,14 @@ patterns.escapedquotes=pattern function string.escapedquotes(s) return lpegmatch(pattern,s) end +local pattern=(1-P("\\"))^1;pattern=Cs ( + pattern*((P("\\")/""*(digit^-3/function(s) return char(tonumber(s)) end))+pattern )^1 +) +patterns.unescapedquotes=pattern +function string.unescapedquotes(s) + return lpegmatch(pattern,s) or s +end +string.texnewlines=lpeg.replacer(patterns.newline,"\r",true) local preamble="" local environment={ global=global or _G, @@ -908,7 +1422,6 @@ function number.to16dot16(n) return f_16_16(n/65536.0) end if not string.explode then - local tsplitat=lpeg.tsplitat local p_utf=patterns.utf8character local p_check=C(p_utf)*(P("+")*Cc(true))^0 local p_split=Ct(C(p_utf)^0) @@ -928,6 +1441,20 @@ if not string.explode then end end end +do + local p_whitespace=patterns.whitespace^1 + local cache=setmetatable({},{ __index=function(t,k) + local p=tsplitat(p_whitespace*P(k)*p_whitespace) + local v=function(s) + return lpegmatch(p,s) + end + t[k]=v + return v + end }) + function string.wordsplitter(s) + return cache[s] + end +end end -- closure @@ -1552,9 +2079,6 @@ if JITSUPPORTED then return concat(fastserialize(t,true)) end else - local f_v=formatters["[%q]=%q,"] - local f_t=formatters["[%q]="] - local f_q=formatters["%q,"] function table.fastserialize(t,prefix) local r={ type(prefix)=="string" and prefix or "return" } local m=1 @@ -1963,6 +2487,21 @@ function table.ordered(t) return function() end end end +function combine(target,source) + if target then + for k,v in next,source do + if type(v)=="table" then + target[k]=combine(target[k],source[k]) + else + target[k]=v + end + end + return target + else + return source + end +end +table.combine=combine end -- closure @@ -2181,8 +2720,8 @@ local noparent=1-(lparent+rparent) local nobracket=1-(lbracket+rbracket) local escape,left,right=P("\\"),P('{'),P('}') lpegpatterns.balanced=P { - [1]=((escape*(left+right))+(1-(left+right))+V(2))^0, - [2]=left*V(1)*right + ((escape*(left+right))+(1-(left+right))+V(2))^0, + left*V(1)*right } local nestedbraces=P { lbrace*(nobrace+V(1))^0*rbrace } local nestedparents=P { lparent*(noparent+V(1))^0*rparent } @@ -2190,11 +2729,12 @@ local nestedbrackets=P { lbracket*(nobracket+V(1))^0*rbracket } local spaces=space^0 local argument=Cs((lbrace/"")*((nobrace+nestedbraces)^0)*(rbrace/"")) local content=(1-endofstring)^0 -lpegpatterns.nestedbraces=nestedbraces -lpegpatterns.nestedparents=nestedparents -lpegpatterns.nested=nestedbraces -lpegpatterns.argument=argument -lpegpatterns.content=content +lpegpatterns.nestedbraces=nestedbraces +lpegpatterns.nestedparents=nestedparents +lpegpatterns.nestedbrackets=nestedbrackets +lpegpatterns.nested=nestedbraces +lpegpatterns.argument=argument +lpegpatterns.content=content local value=lbrace*C((nobrace+nestedbraces)^0)*rbrace+C((nestedbraces+(1-comma))^0) local key=C((1-equal-comma)^1) local pattern_a=(space+comma)^0*(key*equal*value+key*C("")) @@ -2600,15 +3140,24 @@ local function ranger(first,last,n,action) action(first) end end -local cardinal=lpegpatterns.cardinal/tonumber +local cardinal=(lpegpatterns.hexadecimal+lpegpatterns.cardinal)/tonumber local spacers=lpegpatterns.spacer^0 local endofstring=lpegpatterns.endofstring local stepper=spacers*(cardinal*(spacers*S(":-")*spacers*(cardinal+Cc(true) )+Cc(false) )*Carg(1)*Carg(2)/ranger*S(", ")^0 )^1 local stepper=spacers*(cardinal*(spacers*S(":-")*spacers*(cardinal+(P("*")+endofstring)*Cc(true) )+Cc(false) )*Carg(1)*Carg(2)/ranger*S(", ")^0 )^1*endofstring function parsers.stepper(str,n,action) + local ts=type(str) if type(n)=="function" then - lpegmatch(stepper,str,1,false,n or print) - else + if ts=="number" then + n(str) + elseif ts=="table" then + for i=1,#str do + n(str[i]) + end + else + lpegmatch(stepper,str,1,false,n or print) + end + elseif ts=="string" then lpegmatch(stepper,str,1,n,action or print) end end @@ -2626,7 +3175,7 @@ local cache={} local spaces=lpegpatterns.space^0 local dummy=function() end setmetatableindex(cache,function(t,k) - local separator=P(k) + local separator=S(k) local value=(1-separator)^0 local pattern=spaces*C(value)*separator^0*Cp() t[k]=pattern @@ -2706,8 +3255,11 @@ local p_year=lpegpatterns.digit^4/tonumber local pattern=Cf(Ct("")*( (Cg(Cc("year")*p_year)*S("-/")*Cg(Cc("month")*cardinal)*S("-/")*Cg(Cc("day")*cardinal) )+(Cg(Cc("day")*cardinal)*S("-/")*Cg(Cc("month")*cardinal)*S("-/")*Cg(Cc("year")*p_year) + )+(Cg(Cc("year")*p_year)*S("-/")*Cg(Cc("month")*cardinal) + )+(Cg(Cc("month")*cardinal)*S("-/")*Cg(Cc("year")*p_year) ) - )*P(" ")*Cg(Cc("hour")*cardinal)*P(":")*Cg(Cc("min")*cardinal)*(P(":")*Cg(Cc("sec")*cardinal))^-1 + )*( + P(" ")*Cg(Cc("hour")*cardinal)*P(":")*Cg(Cc("min")*cardinal)*(P(":")*Cg(Cc("sec")*cardinal))^-1+P(-1) ) ,rawset) lpegpatterns.splittime=pattern function parsers.totime(str) @@ -2914,6 +3466,9 @@ if not modules then modules={} end modules ['util-jsn']={ copyright="PRAGMA ADE / ConTeXt Development Team", license="see context related readme files" } +if utilities and utilities.json then + return json +end local P,V,R,S,C,Cc,Cs,Ct,Cf,Cg=lpeg.P,lpeg.V,lpeg.R,lpeg.S,lpeg.C,lpeg.Cc,lpeg.Cs,lpeg.Ct,lpeg.Cf,lpeg.Cg local lpegmatch=lpeg.match local format,gsub=string.format,string.gsub @@ -3118,6 +3673,8 @@ do k=lpegmatch(escaper,k) or k v=lpegmatch(escaper,v) or v n=n+1 t[n]=f_key_val_str(depth,k,v) + elseif i>1 then + n=n-1 end elseif tv=="table" then local l=#v @@ -3133,6 +3690,8 @@ do end elseif next(v) then tojsonpp(v,k,depth,level+1,0) + elseif i>1 then + n=n-1 end elseif tv=="boolean" then if tk=="number" then @@ -3150,6 +3709,8 @@ do else t[n]=f_key_val_nop(depth,k) end + elseif i>1 then + n=n-1 end else if tk=="number" then @@ -3159,6 +3720,8 @@ do k=lpegmatch(escaper,k) or k n=n+1 t[n]=f_key_val_null(depth,k) + elseif i>1 then + n=n-1 end end end @@ -3260,7 +3823,6 @@ do return jsontostring(value,true) end end -return json end -- closure @@ -3990,6 +4552,22 @@ local function showtraceback(rep) end end debugger.showtraceback=showtraceback +if luac then + local show,dump=luac.print,string.dump + function luac.inspect(v) + if type(v)=="function" then + local ok,str=xpcall(dump,function() end,v) + if ok then + v=str + end + end + if type(v)=="string" then + show(v,true) + else + print(v) + end + end +end end -- closure @@ -4379,3 +4957,560 @@ function stacker.new(name) end end -- closure + +do -- begin closure to overcome local limits and interference + +if not modules then modules={} end modules ['util-zip']={ + version=1.001, + author="Hans Hagen, PRAGMA-ADE, Hasselt NL", + copyright="PRAGMA ADE / ConTeXt Development Team", + license="see context related readme files" +} +local type,tostring,tonumber=type,tostring,tonumber +local sort,concat=table.sort,table.concat +local find,format,sub,gsub=string.find,string.format,string.sub,string.gsub +local osdate,ostime,osclock=os.date,os.time,os.clock +local ioopen=io.open +local loaddata,savedata=io.loaddata,io.savedata +local filejoin,isdir,dirname,mkdirs=file.join,lfs.isdir,file.dirname,dir.mkdirs +local suffix,suffixes=file.suffix,file.suffixes +local openfile=io.open +gzip=gzip or {} +if not zlib then + zlib=xzip +elseif not xzip then + xzip=zlib +end +local files=utilities.files +local openfile=files.open +local closefile=files.close +local readstring=files.readstring +local readcardinal2=files.readcardinal2le +local readcardinal4=files.readcardinal4le +local setposition=files.setposition +local getposition=files.getposition +local band=bit32.band +local rshift=bit32.rshift +local lshift=bit32.lshift +local zlibdecompress=zlib.decompress +local zlibdecompresssize=zlib.decompresssize +local zlibchecksum=zlib.crc32 +if not CONTEXTLMTXMODE or CONTEXTLMTXMODE==0 then + local cs=zlibchecksum + zlibchecksum=function(str,n) return cs(n or 0,str) end +end +local decompress=function(source) return zlibdecompress (source,-15) end +local decompresssize=function(source,targetsize) return zlibdecompresssize(source,targetsize,-15) end +local calculatecrc=function(buffer,initial) return zlibchecksum (initial or 0,buffer) end +local zipfiles={} +utilities.zipfiles=zipfiles +local openzipfile,closezipfile,unzipfile,foundzipfile,getziphash,getziplist do + function openzipfile(name) + return { + name=name, + handle=openfile(name,0), + } + end + local function collect(z) + if not z.list then + local list={} + local hash={} + local position=0 + local index=0 + local handle=z.handle + while true do + setposition(handle,position) + local signature=readstring(handle,4) + if signature=="PK\3\4" then + local version=readcardinal2(handle) + local flag=readcardinal2(handle) + local method=readcardinal2(handle) + local filetime=readcardinal2(handle) + local filedate=readcardinal2(handle) + local crc32=readcardinal4(handle) + local compressed=readcardinal4(handle) + local uncompressed=readcardinal4(handle) + local namelength=readcardinal2(handle) + local extralength=readcardinal2(handle) + local filename=readstring(handle,namelength) + local descriptor=band(flag,8)~=0 + local encrypted=band(flag,1)~=0 + local acceptable=method==0 or method==8 + local skipped=0 + local size=0 + if encrypted then + size=readcardinal2(handle) + skipbytes(size) + skipped=skipped+size+2 + skipbytes(8) + skipped=skipped+8 + size=readcardinal2(handle) + skipbytes(size) + skipped=skipped+size+2 + size=readcardinal4(handle) + skipbytes(size) + skipped=skipped+size+4 + size=readcardinal2(handle) + skipbytes(size) + skipped=skipped+size+2 + end + position=position+30+namelength+extralength+skipped + if descriptor then + setposition(handle,position+compressed) + crc32=readcardinal4(handle) + compressed=readcardinal4(handle) + uncompressed=readcardinal4(handle) + end + if acceptable then + index=index+1 + local data={ + filename=filename, + index=index, + position=position, + method=method, + compressed=compressed, + uncompressed=uncompressed, + crc32=crc32, + encrypted=encrypted, + } + hash[filename]=data + list[index]=data + else + end + position=position+compressed + else + break + end + z.list=list + z.hash=hash + end + end + end + function getziplist(z) + local list=z.list + if not list then + collect(z) + end + return z.list + end + function getziphash(z) + local hash=z.hash + if not hash then + collect(z) + end + return z.hash + end + function foundzipfile(z,name) + return getziphash(z)[name] + end + function closezipfile(z) + local f=z.handle + if f then + closefile(f) + z.handle=nil + end + end + function unzipfile(z,filename,check) + local hash=z.hash + if not hash then + hash=zipfiles.hash(z) + end + local data=hash[filename] + if not data then + end + if data then + local handle=z.handle + local position=data.position + local compressed=data.compressed + if compressed>0 then + setposition(handle,position) + local result=readstring(handle,compressed) + if data.method==8 then + if decompresssize then + result=decompresssize(result,data.uncompressed) + else + result=decompress(result) + end + end + if check and data.crc32~=calculatecrc(result) then + print("checksum mismatch") + return "" + end + return result + else + return "" + end + end + end + zipfiles.open=openzipfile + zipfiles.close=closezipfile + zipfiles.unzip=unzipfile + zipfiles.hash=getziphash + zipfiles.list=getziplist + zipfiles.found=foundzipfile +end +if xzip then + local writecardinal1=files.writebyte + local writecardinal2=files.writecardinal2le + local writecardinal4=files.writecardinal4le + local logwriter=logs.writer + local globpattern=dir.globpattern + local compress=xzip.compress + local checksum=xzip.crc32 + local function fromdostime(dostime,dosdate) + return ostime { + year=rshift(dosdate,9)+1980, + month=band(rshift(dosdate,5),0x0F), + day=band((dosdate ),0x1F), + hour=band(rshift(dostime,11) ), + min=band(rshift(dostime,5),0x3F), + sec=band((dostime ),0x1F), + } + end + local function todostime(time) + local t=osdate("*t",time) + return + lshift(t.year-1980,9)+lshift(t.month,5)+t.day, + lshift(t.hour,11)+lshift(t.min,5)+rshift(t.sec,1) + end + local function openzip(filename,level,comment,verbose) + local f=ioopen(filename,"wb") + if f then + return { + filename=filename, + handle=f, + list={}, + level=tonumber(level) or 3, + comment=tostring(comment), + verbose=verbose, + uncompressed=0, + compressed=0, + } + end + end + local function writezip(z,name,data,level,time) + local f=z.handle + local list=z.list + local level=tonumber(level) or z.level or 3 + local method=8 + local zipped=compress(data,level) + local checksum=checksum(data) + local verbose=z.verbose + if not zipped then + method=0 + zipped=data + end + local start=f:seek() + local compressed=#zipped + local uncompressed=#data + z.compressed=z.compressed+compressed + z.uncompressed=z.uncompressed+uncompressed + if verbose then + local pct=100*compressed/uncompressed + if pct>=100 then + logwriter(format("%10i %s",uncompressed,name)) + else + logwriter(format("%10i %02.1f %s",uncompressed,pct,name)) + end + end + f:write("\x50\x4b\x03\x04") + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,method) + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal4(f,checksum) + writecardinal4(f,compressed) + writecardinal4(f,uncompressed) + writecardinal2(f,#name) + writecardinal2(f,0) + f:write(name) + f:write(zipped) + list[#list+1]={ #zipped,#data,name,checksum,start,time or 0 } + end + local function closezip(z) + local f=z.handle + local list=z.list + local comment=z.comment + local verbose=z.verbose + local count=#list + local start=f:seek() + for i=1,count do + local l=list[i] + local compressed=l[1] + local uncompressed=l[2] + local name=l[3] + local checksum=l[4] + local start=l[5] + local time=l[6] + local date,time=todostime(time) + f:write('\x50\x4b\x01\x02') + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,8) + writecardinal2(f,time) + writecardinal2(f,date) + writecardinal4(f,checksum) + writecardinal4(f,compressed) + writecardinal4(f,uncompressed) + writecardinal2(f,#name) + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal4(f,0) + writecardinal4(f,start) + f:write(name) + end + local stop=f:seek() + local size=stop-start + f:write('\x50\x4b\x05\x06') + writecardinal2(f,0) + writecardinal2(f,0) + writecardinal2(f,count) + writecardinal2(f,count) + writecardinal4(f,size) + writecardinal4(f,start) + if type(comment)=="string" and comment~="" then + writecardinal2(f,#comment) + f:write(comment) + else + writecardinal2(f,0) + end + if verbose then + local compressed=z.compressed + local uncompressed=z.uncompressed + local filename=z.filename + local pct=100*compressed/uncompressed + logwriter("") + if pct>=100 then + logwriter(format("%10i %s",uncompressed,filename)) + else + logwriter(format("%10i %02.1f %s",uncompressed,pct,filename)) + end + end + f:close() + end + local function zipdir(zipname,path,level,verbose) + if type(zipname)=="table" then + verbose=zipname.verbose + level=zipname.level + path=zipname.path + zipname=zipname.zipname + end + if not zipname or zipname=="" then + return + end + if not path or path=="" then + path="." + end + if not isdir(path) then + return + end + path=gsub(path,"\\+","/") + path=gsub(path,"/+","/") + local list={} + local count=0 + globpattern(path,"",true,function(name,size,time) + count=count+1 + list[count]={ name,time } + end) + sort(list,function(a,b) + return a[1]<b[1] + end) + local zipf=openzip(zipname,level,comment,verbose) + if zipf then + local p=#path+2 + for i=1,count do + local li=list[i] + local name=li[1] + local time=li[2] + local data=loaddata(name) + local name=sub(name,p,#name) + writezip(zipf,name,data,level,time,verbose) + end + closezip(zipf) + end + end + local function unzipdir(zipname,path,verbose) + if type(zipname)=="table" then + verbose=zipname.verbose + path=zipname.path + zipname=zipname.zipname + end + if not zipname or zipname=="" then + return + end + if not path or path=="" then + path="." + end + local z=openzipfile(zipname) + if z then + local list=getziplist(z) + if list then + local total=0 + local count=#list + local step=number.idiv(count,10) + local done=0 + local steps=verbose=="steps" + local time=steps and osclock() + for i=1,count do + local l=list[i] + local n=l.filename + local d=unzipfile(z,n) + if d then + local p=filejoin(path,n) + if mkdirs(dirname(p)) then + if steps then + total=total+#d + done=done+1 + if done>=step then + done=0 + logwriter(format("%4i files of %4i done, %10i bytes, %0.3f seconds",i,count,total,osclock()-time)) + end + elseif verbose then + logwriter(n) + end + savedata(p,d) + end + else + logwriter(format("problem with file %s",n)) + end + end + if steps then + logwriter(format("%4i files of %4i done, %10i bytes, %0.3f seconds",count,count,total,osclock()-time)) + end + closezipfile(z) + return true + else + closezipfile(z) + end + end + end + zipfiles.zipdir=zipdir + zipfiles.unzipdir=unzipdir +end +local pattern="^\x1F\x8B\x08" +local gziplevel=3 +function gzip.suffix(filename) + local suffix,extra=suffixes(filename) + local gzipped=extra=="gz" + return suffix,gzipped +end +function gzip.compressed(s) + return s and find(s,pattern) +end +local getdecompressed +local putcompressed +if gzip.compress then + local gzipwindow=15+16 + local compress=zlib.compress + local decompress=zlib.decompress + getdecompressed=function(str) + return decompress(str,gzipwindow) + end + putcompressed=function(str,level) + return compress(str,level or gziplevel,nil,gzipwindow) + end +else + local gzipwindow=-15 + local identifier="\x1F\x8B" + local compress=zlib.compress + local decompress=zlib.decompress + local zlibchecksum=zlib.crc32 + if not CONTEXTLMTXMODE or CONTEXTLMTXMODE==0 then + local cs=zlibchecksum + zlibchecksum=function(str,n) return cs(n or 0,str) end + end + local streams=utilities.streams + local openstream=streams.openstring + local closestream=streams.close + local getposition=streams.getposition + local readbyte=streams.readbyte + local readcardinal4=streams.readcardinal4le + local readcardinal2=streams.readcardinal2le + local readstring=streams.readstring + local readcstring=streams.readcstring + local skipbytes=streams.skip + local tocardinal1=streams.tocardinal1 + local tocardinal4=streams.tocardinal4le + getdecompressed=function(str) + local s=openstream(str) + local identifier=readstring(s,2) + local method=readbyte(s,1) + local flags=readbyte(s,1) + local timestamp=readcardinal4(s) + local compression=readbyte(s,1) + local operating=readbyte(s,1) + local isjusttext=band(flags,0x01)~=0 and true or false + local extrasize=band(flags,0x04)~=0 and readcardinal2(s) or 0 + local filename=band(flags,0x08)~=0 and readcstring(s) or "" + local comment=band(flags,0x10)~=0 and readcstring(s) or "" + local checksum=band(flags,0x02)~=0 and readcardinal2(s) or 0 + local compressed=readstring(s,#str) + local data=decompress(compressed,gzipwindow) + return data + end + putcompressed=function(str,level,originalname) + return concat { + identifier, + tocardinal1(0x08), + tocardinal1(0x08), + tocardinal4(os.time()), + tocardinal1(0x02), + tocardinal1(0xFF), + (originalname or "unknownname").."\0", + compress(str,level,nil,gzipwindow), + tocardinal4(zlibchecksum(str)), + tocardinal4(#str), + } + end +end +function gzip.load(filename) + local f=openfile(filename,"rb") + if not f then + else + local data=f:read("*all") + f:close() + if data and data~="" then + if suffix(filename)=="gz" then + data=getdecompressed(data) + end + return data + end + end +end +function gzip.save(filename,data,level,originalname) + if suffix(filename)~="gz" then + filename=filename..".gz" + end + local f=openfile(filename,"wb") + if f then + data=putcompressed(data or "",level or gziplevel,originalname) + f:write(data) + f:close() + return #data + end +end +function gzip.compress(s,level) + if s and not find(s,pattern) then + if not level then + level=gziplevel + elseif level<=0 then + return s + elseif level>9 then + level=9 + end + return putcompressed(s,level or gziplevel) or s + end +end +function gzip.decompress(s) + if s and find(s,pattern) then + return getdecompressed(s) + else + return s + end +end + +end -- closure diff --git a/macros/luatex/generic/lualibs/lualibs-file.lua b/macros/luatex/generic/lualibs/lualibs-file.lua index d0af94f09d..9f8fd65483 100644 --- a/macros/luatex/generic/lualibs/lualibs-file.lua +++ b/macros/luatex/generic/lualibs/lualibs-file.lua @@ -456,7 +456,7 @@ function file.join(one, two, three, ...) if not two then return one == "" and one or lpegmatch(reslasher,one) end - if one == "" then + if not one or one == "" then return lpegmatch(stripper,three and concat({ two, three, ... },"/") or two) end if lpegmatch(isnetwork,one) then diff --git a/macros/luatex/generic/lualibs/lualibs-gzip.lua b/macros/luatex/generic/lualibs/lualibs-gzip.lua deleted file mode 100644 index f141b5ebbb..0000000000 --- a/macros/luatex/generic/lualibs/lualibs-gzip.lua +++ /dev/null @@ -1,180 +0,0 @@ -if not modules then modules = { } end modules ['l-gzip'] = { - version = 1.001, - author = "Hans Hagen, PRAGMA-ADE, Hasselt NL", - copyright = "PRAGMA ADE / ConTeXt Development Team", - license = "see context related readme files" -} - --- We only have a few official methods here: --- --- local decompressed = gzip.load (filename) --- local resultsize = gzip.save (filename,compresslevel) --- local compressed = gzip.compress (str,compresslevel) --- local decompressed = gzip.decompress (str) --- local iscompressed = gzip.compressed (str) --- local suffix, okay = gzip.suffix (filename) --- --- In LuaMetaTeX we have only xzip which implements a very few methods: --- --- compress (str,level,method,window,memory,strategy) --- decompress (str,window) --- adler32 (str,checksum) --- crc32 (str,checksum) --- --- Special window values are: --- --- flate : - 15 --- zlib : 15 --- gzip : 15 | 16 --- auto : 15 | 32 - -gzip = gzip or { } -- so in luatex we keep the old ones too - -if not zlib then - zlib = xzip -- in luametatex we shadow the old one -elseif not xzip then - xzip = zlib -end - -if zlib then - - local suffix = file.suffix - local suffixes = file.suffixes - local find = string.find - local openfile = io.open - - local gzipwindow = 15 + 16 -- +16: gzip, +32: gzip|zlib - local gziplevel = 3 - local identifier = "^\x1F\x8B\x08" - - local compress = zlib.compress - local decompress = zlib.decompress - - function gzip.load(filename) - local f = openfile(filename,"rb") - if not f then - -- invalid file - else - local data = f:read("*all") - f:close() - if data and data ~= "" then - if suffix(filename) == "gz" then - data = decompress(data,gzipwindow) - end - return data - end - end - end - - function gzip.save(filename,data,level) - if suffix(filename) ~= "gz" then - filename = filename .. ".gz" - end - local f = openfile(filename,"wb") - if f then - data = compress(data or "",level or gziplevel,nil,gzipwindow) - f:write(data) - f:close() - return #data - end - end - - function gzip.suffix(filename) - local suffix, extra = suffixes(filename) - local gzipped = extra == "gz" - return suffix, gzipped - end - - function gzip.compressed(s) - return s and find(s,identifier) - end - - function gzip.compress(s,level) - if s and not find(s,identifier) then -- the find check might go away - if not level then - level = gziplevel - elseif level <= 0 then - return s - elseif level > 9 then - level = 9 - end - return compress(s,level or gziplevel,nil,gzipwindow) or s - end - end - - function gzip.decompress(s) - if s and find(s,identifier) then - return decompress(s,gzipwindow) - else - return s - end - end - -end - --- In luametatex we can use this one but it doesn't look like there wil be stream --- support so for now we still use zlib (the performance difference is not that --- spectacular in our usage. - --- if flate then --- --- local type = type --- local find = string.find --- --- local compress = flate.gz_compress --- local decompress = flate.gz_decompress --- --- local absmax = 128*1024*1024 --- local initial = 64*1024 --- local identifier = "^\x1F\x8B\x08" --- --- function gzip.compressed(s) --- return s and find(s,identifier) --- end --- --- function gzip.compress(s,level) --- if s and not find(s,identifier) then -- the find check might go away --- if not level then --- level = 3 --- elseif level <= 0 then --- return s --- elseif level > 9 then --- level = 9 --- end --- return compress(s,level) or s --- end --- end --- --- function gzip.decompress(s,size,iterate) --- if s and find(s,identifier) then --- if type(size) ~= "number" then --- size = initial --- end --- if size > absmax then --- size = absmax --- end --- if type(iterate) == "number" then --- max = size * iterate --- elseif iterate == nil or iterate == true then --- iterate = true --- max = absmax --- end --- if max > absmax then --- max = absmax --- end --- while true do --- local d = decompress(s,size) --- if d then --- return d --- end --- size = 2 * size --- if not iterate or size > max then --- return false --- end --- end --- else --- return s --- end --- end --- --- end diff --git a/macros/luatex/generic/lualibs/lualibs-io.lua b/macros/luatex/generic/lualibs/lualibs-io.lua index a955262a31..6bf7a97bda 100644 --- a/macros/luatex/generic/lualibs/lualibs-io.lua +++ b/macros/luatex/generic/lualibs/lualibs-io.lua @@ -147,9 +147,12 @@ function io.copydata(source,target,action) end end -function io.savedata(filename,data,joiner) - local f = open(filename,"wb") +function io.savedata(filename,data,joiner,append) + local f = open(filename,append and "ab" or "wb") if f then + if append and joiner and f:seek("end") > 0 then + f:write(joiner) + end if type(data) == "table" then f:write(concat(data,joiner or "")) elseif type(data) == "function" then @@ -288,7 +291,8 @@ end io.noflines = noflines --- inlined is faster ... beware, better use util-fil +-- inlined is faster ... beware, better use util-fil so these are obsolete +-- and will go local nextchar = { [ 4] = function(f) diff --git a/macros/luatex/generic/lualibs/lualibs-lpeg.lua b/macros/luatex/generic/lualibs/lualibs-lpeg.lua index 50306e4ab6..5f3bea08ca 100644 --- a/macros/luatex/generic/lualibs/lualibs-lpeg.lua +++ b/macros/luatex/generic/lualibs/lualibs-lpeg.lua @@ -665,12 +665,12 @@ end -- lpeg.print(lpeg.P("a","b","c")) -- lpeg.print(lpeg.S("a","b","c")) --- print(lpeg.count("äáàa",lpeg.P("á") + lpeg.P("à"))) --- print(lpeg.count("äáàa",lpeg.UP("áà"))) --- print(lpeg.count("äáàa",lpeg.US("àá"))) --- print(lpeg.count("äáàa",lpeg.UR("aá"))) --- print(lpeg.count("äáàa",lpeg.UR("àá"))) --- print(lpeg.count("äáàa",lpeg.UR(0x0000,0xFFFF))) +-- print(lpeg.counter(lpeg.P("á") + lpeg.P("à"))("äáàa")) +-- print(lpeg.counter(lpeg.UP("áà"))("äáàa")) +-- print(lpeg.counter(lpeg.US("àá"))("äáàa")) +-- print(lpeg.counter(lpeg.UR("aá"))("äáàa")) +-- print(lpeg.counter(lpeg.UR("àá"))("äáàa")) +-- print(lpeg.counter(lpeg.UR(0x0000,0xFFFF))) function lpeg.is_lpeg(p) return p and lpegtype(p) == "pattern" diff --git a/macros/luatex/generic/lualibs/lualibs-math.lua b/macros/luatex/generic/lualibs/lualibs-math.lua index e5668a5db0..6105bc3c2d 100644 --- a/macros/luatex/generic/lualibs/lualibs-math.lua +++ b/macros/luatex/generic/lualibs/lualibs-math.lua @@ -14,9 +14,19 @@ end if not math.round then - local floor = math.floor + if xmath then + + math.round = xmath.round + + else - function math.round(x) return floor(x + 0.5) end + local floor = math.floor + + function math.round(x) + return x < 0 and -floor(-x + 0.5) or floor(x + 0.5) + end + + end end @@ -141,7 +151,7 @@ if not math.ult then local floor = math.floor - function math.tointeger(m,n) + function math.ult(m,n) -- not ok but i'm not motivated to look into it now return floor(m) < floor(n) -- unsigned comparison needed end diff --git a/macros/luatex/generic/lualibs/lualibs-os.lua b/macros/luatex/generic/lualibs/lualibs-os.lua index c7584ccce9..faae76881a 100644 --- a/macros/luatex/generic/lualibs/lualibs-os.lua +++ b/macros/luatex/generic/lualibs/lualibs-os.lua @@ -26,22 +26,27 @@ if not modules then modules = { } end modules ['l-os'] = { -- math.randomseed(tonumber(string.sub(string.reverse(tostring(math.floor(socket.gettime()*10000))),1,6))) local os = os -local date, time = os.date, os.time +local date, time, difftime = os.date, os.time, os.difftime local find, format, gsub, upper, gmatch = string.find, string.format, string.gsub, string.upper, string.gmatch local concat = table.concat -local random, ceil, randomseed = math.random, math.ceil, math.randomseed +local random, ceil, randomseed, modf = math.random, math.ceil, math.randomseed, math.modf local type, setmetatable, tonumber, tostring = type, setmetatable, tonumber, tostring -- This check needs to happen real early on. Todo: we can pick it up from the commandline -- if we pass --binpath= (which is useful anyway) do + local selfdir = os.selfdir + if selfdir == "" then selfdir = nil end + if not selfdir then + -- We need a fallback plan so let's see what we get. + if arg then -- passed by mtx-context ... saves network access for i=1,#arg do @@ -52,6 +57,7 @@ do end end end + if not selfdir then selfdir = os.selfbin or "luatex" if find(selfdir,"[/\\]") then @@ -92,11 +98,16 @@ do end end end + -- let's hope we're okay now + os.selfdir = selfdir or "." + end + + -- print(os.selfdir) os.exit() + end --- print(os.selfdir) os.exit() -- The following code permits traversing the environment table, at least in luatex. Internally all -- environment names are uppercase. @@ -157,7 +168,7 @@ if not os.__getenv__ then end function os.getenv(k) - local K = upper(k) + local K = upper(k) -- hm utf local v = osenv[K] or osgetenv(K) or osgetenv(k) if v == "" then return nil @@ -183,32 +194,14 @@ end -- end of environment hack -local execute = os.execute -local iopopen = io.popen - -local function resultof(command) - local handle = iopopen(command,"r") -- already has flush - if handle then - local result = handle:read("*all") or "" - handle:close() - return result - else - return "" - end -end - -os.resultof = resultof - -function os.pipeto(command) - return iopopen(command,"w") -- already has flush -end - if not io.fileseparator then + if find(os.getenv("PATH"),";",1,true) then io.fileseparator, io.pathseparator, os.type = "\\", ";", os.type or "windows" else io.fileseparator, io.pathseparator, os.type = "/" , ":", os.type or "unix" end + end os.type = os.type or (io.pathseparator == ";" and "windows") or "unix" @@ -220,351 +213,370 @@ else os.libsuffix, os.binsuffix, os.binsuffixes = 'so', '', { '' } end -local launchers = { - windows = "start %s", - macosx = "open %s", - unix = "xdg-open %s &> /dev/null &", -} +do -function os.launch(str) - local command = format(launchers[os.name] or launchers.unix,str) - -- todo: pcall --- print(command) - execute(command) -end + local execute = os.execute + local iopopen = io.popen + local ostype = os.type + + local function resultof(command) + -- already has flush, b is new and we need it to pipe xz output + local handle = iopopen(command,ostype == "windows" and "rb" or "r") + if handle then + local result = handle:read("*all") or "" + handle:close() + return result + else + return "" + end + end -local gettimeofday = os.gettimeofday or os.clock -os.gettimeofday = gettimeofday + os.resultof = resultof -local startuptime = gettimeofday() + function os.pipeto(command) + return iopopen(command,"w") -- already has flush + end -function os.runtime() - return gettimeofday() - startuptime -end + local launchers = { + windows = "start %s", + macosx = "open %s", + unix = "xdg-open %s &> /dev/null &", + } + + function os.launch(str) + local command = format(launchers[os.name] or launchers.unix,str) + -- todo: pcall + -- print(command) + execute(command) + end --- print(os.gettimeofday()-os.time()) --- os.sleep(1.234) --- print (">>",os.runtime()) --- print(os.date("%H:%M:%S",os.gettimeofday())) --- print(os.date("%H:%M:%S",os.time())) +end --- no need for function anymore as we have more clever code and helpers now --- this metatable trickery might as well disappear +do -local resolvers = os.resolvers or { } -os.resolvers = resolvers + local gettimeofday = os.gettimeofday or os.clock + os.gettimeofday = gettimeofday -setmetatable(os, { __index = function(t,k) - local r = resolvers[k] - return r and r(t,k) or nil -- no memoize -end }) + local startuptime = gettimeofday() --- we can use HOSTTYPE on some platforms + function os.runtime() + return gettimeofday() - startuptime + end -local name, platform = os.name or "linux", os.getenv("MTX_PLATFORM") or "" + -- print(os.gettimeofday()-os.time()) + -- os.sleep(1.234) + -- print (">>",os.runtime()) + -- print(os.date("%H:%M:%S",os.gettimeofday())) + -- print(os.date("%H:%M:%S",os.time())) --- local function guess() --- local architecture = resultof("uname -m") or "" --- if architecture ~= "" then --- return architecture --- end --- architecture = os.getenv("HOSTTYPE") or "" --- if architecture ~= "" then --- return architecture --- end --- return resultof("echo $HOSTTYPE") or "" --- end +end +-- We can use HOSTTYPE on some platforms (but not consistently on e.g. Linux). +-- -- os.bits = 32 | 64 +-- +-- os.uname() : return { +-- machine = "x86_64", +-- nodename = "MYLAPTOP", +-- release = "build 9200", +-- sysname = "Windows", +-- version = "6.02", +-- } --- os.uname() --- sysname --- machine --- release --- version --- nodename - -if platform ~= "" then +do - os.platform = platform + local name = os.name or "linux" + local platform = os.getenv("MTX_PLATFORM") or "" + local architecture = os.uname and os.uname().machine -- lmtx + local bits = os.getenv("MTX_BITS") or find(platform,"64") and 64 or 32 -elseif os.type == "windows" then + if platform ~= "" then - -- we could set the variable directly, no function needed here + -- we're okay already - -- PROCESSOR_ARCHITECTURE : binary platform - -- PROCESSOR_ARCHITEW6432 : OS platform + elseif os.type == "windows" then - -- mswin-64 is now win64 + -- PROCESSOR_ARCHITECTURE : binary platform + -- PROCESSOR_ARCHITEW6432 : OS platform - function resolvers.platform(t,k) - local architecture = os.getenv("PROCESSOR_ARCHITECTURE") or "" - local platform = "" - if find(architecture,"AMD64",1,true) then - platform = "win64" + architecture = string.lower(architecture or os.getenv("PROCESSOR_ARCHITECTURE") or "") + if architecture == "x86_64" then + bits, platform = 64, "win64" + elseif find(architecture,"amd64") then + bits, platform = 64, "win64" + elseif find(architecture,"arm64") then + bits, platform = 64, "windows-arm64" + elseif find(architecture,"arm32") then + bits, platform = 32, "windows-arm32" else - platform = "mswin" + bits, platform = 32, "mswin" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -elseif name == "linux" then - - function resolvers.platform(t,k) - -- we sometimes have HOSTTYPE set so let's check that first - local architecture = os.getenv("HOSTTYPE") or resultof("uname -m") or "" - local platform = os.getenv("MTX_PLATFORM") or "" - local musl = find(os.selfdir or "","linuxmusl") - if platform ~= "" then - -- we're done - elseif find(architecture,"x86_64",1,true) then - platform = musl and "linuxmusl" or "linux-64" - elseif find(architecture,"ppc",1,true) then - platform = "linux-ppc" + elseif name == "linux" then + + -- There is no way to detect if musl is used because there is no __MUSL__ + -- and it looks like there never will be. Folks don't care about cases where + -- one ships multipe binaries (as with TeX distibutions) and want to select + -- the right one. So probably it expects users to compile locally in which + -- case we don't care to much as they can then sort it out. + + architecture = architecture or os.getenv("HOSTTYPE") or resultof("uname -m") or "" + local musl = find(os.selfdir or "","linuxmusl") + if find(architecture,"x86_64") then + bits, platform = 64, musl and "linuxmusl" or "linux-64" + elseif find(architecture,"ppc") then + bits, platform = 32, "linux-ppc" -- this will be dropped else - platform = musl and "linuxmusl" or "linux" + bits, platform = 32, musl and "linuxmusl" or "linux" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -elseif name == "macosx" then - - --[[ - Identifying the architecture of OSX is quite a mess and this - is the best we can come up with. For some reason $HOSTTYPE is - a kind of pseudo environment variable, not known to the current - environment. And yes, uname cannot be trusted either, so there - is a change that you end up with a 32 bit run on a 64 bit system. - Also, some proper 64 bit intel macs are too cheap (low-end) and - therefore not permitted to run the 64 bit kernel. - ]]-- - - function resolvers.platform(t,k) - -- local platform = "" - -- local architecture = os.getenv("HOSTTYPE") or "" - -- if architecture == "" then - -- architecture = resultof("echo $HOSTTYPE") or "" - -- end - local architecture = resultof("echo $HOSTTYPE") or "" - local platform = "" + elseif name == "macosx" then + + -- Identifying the architecture of OSX is quite a mess and this is the best + -- we can come up with. For some reason $HOSTTYPE is a kind of pseudo + -- environment variable, not known to the current environment. And yes, + -- uname cannot be trusted either, so there is a change that you end up with + -- a 32 bit run on a 64 bit system. Also, some proper 64 bit intel macs are + -- too cheap (low-end) and therefore not permitted to run the 64 bit kernel. + + architecture = architecture or resultof("echo $HOSTTYPE") or "" if architecture == "" then - -- print("\nI have no clue what kind of OSX you're running so let's assume an 32 bit intel.\n") - platform = "osx-intel" - elseif find(architecture,"i386",1,true) then - platform = "osx-intel" - elseif find(architecture,"x86_64",1,true) then - platform = "osx-64" - elseif find(architecture,"arm64",1,true) then - platform = "osx-arm" + bits, platform = 64, "osx-intel" + elseif find(architecture,"i386") then + bits, platform = 64, "osx-intel" + elseif find(architecture,"x86_64") then + bits, platform = 64, "osx-64" + elseif find(architecture,"arm64") then + bits, platform = 64, "osx-arm" else - platform = "osx-ppc" + bits, platform = 32, "osx-ppc" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -elseif name == "sunos" then + elseif name == "sunos" then - function resolvers.platform(t,k) - local architecture = resultof("uname -m") or "" - local platform = "" - if find(architecture,"sparc",1,true) then - platform = "solaris-sparc" + architecture = architecture or resultof("uname -m") or "" + if find(architecture,"sparc") then + bits, platform = 32, "solaris-sparc" else -- if architecture == 'i86pc' - platform = "solaris-intel" + bits, platform = 32, "solaris-intel" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -elseif name == "freebsd" then + elseif name == "freebsd" then - function resolvers.platform(t,k) - local architecture = resultof("uname -m") or "" - local platform = "" - if find(architecture,"amd64",1,true) then - platform = "freebsd-amd64" + architecture = architecture or os.getenv("MACHTYPE") or resultof("uname -m") or "" + if find(architecture,"amd64") or find(architecture,"AMD64") then + bits, platform = 64, "freebsd-amd64" else - platform = "freebsd" + bits, platform = 32, "freebsd" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -elseif name == "kfreebsd" then + elseif name == "kfreebsd" then - function resolvers.platform(t,k) - -- we sometimes have HOSTTYPE set so let's check that first - local architecture = os.getenv("HOSTTYPE") or resultof("uname -m") or "" - local platform = "" - if find(architecture,"x86_64",1,true) then - platform = "kfreebsd-amd64" + architecture = architecture or os.getenv("HOSTTYPE") or resultof("uname -m") or "" + if architecture == "x86_64" then + bits, platform = 64, "kfreebsd-amd64" else - platform = "kfreebsd-i386" + bits, platform = 32, "kfreebsd-i386" end - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform - end -else + else - -- platform = "linux" - -- os.setenv("MTX_PLATFORM",platform) - -- os.platform = platform + architecture = architecture or resultof("uname -m") or "" + + if find(architecture,"aarch64") then + bits, platform = "linux-aarch64" + elseif find(architecture,"armv7l") then + -- linux-armel + bits, platform = 32, "linux-armhf" + elseif find(architecture,"mips64") or find(architecture,"mips64el") then + bits, platform = 64, "linux-mipsel" + elseif find(architecture,"mipsel") or find(architecture,"mips") then + bits, platform = 32, "linux-mipsel" + else + bits, platform = 64, "linux-64" -- was 32, "linux" + end - function resolvers.platform(t,k) - local platform = "linux" - os.setenv("MTX_PLATFORM",platform) - os.platform = platform - return platform end -end + os.setenv("MTX_PLATFORM",platform) + os.setenv("MTX_BITS", bits) -os.newline = name == "windows" and "\013\010" or "\010" -- crlf or lf + os.platform = platform + os.bits = bits + os.newline = name == "windows" and "\013\010" or "\010" -- crlf or lf -function resolvers.bits(t,k) - local bits = find(os.platform,"64",1,true) and 64 or 32 - os.bits = bits - return bits end -- beware, we set the randomseed --- from wikipedia: Version 4 UUIDs use a scheme relying only on random numbers. This algorithm sets the --- version number as well as two reserved bits. All other bits are set using a random or pseudorandom --- data source. Version 4 UUIDs have the form xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx with hexadecimal --- digits x and hexadecimal digits 8, 9, A, or B for y. e.g. f47ac10b-58cc-4372-a567-0e02b2c3d479. --- --- as we don't call this function too often there is not so much risk on repetition - -local t = { 8, 9, "a", "b" } - -function os.uuid() - return format("%04x%04x-4%03x-%s%03x-%04x-%04x%04x%04x", - random(0xFFFF),random(0xFFFF), - random(0x0FFF), - t[ceil(random(4))] or 8,random(0x0FFF), - random(0xFFFF), - random(0xFFFF),random(0xFFFF),random(0xFFFF) - ) +-- From wikipedia: Version 4 UUIDs use a scheme relying only on random numbers. This +-- algorithm sets the version number as well as two reserved bits. All other bits +-- are set using a random or pseudorandom data source. Version 4 UUIDs have the form +-- xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx with hexadecimal digits x and hexadecimal +-- digits 8, 9, A, or B for y. e.g. f47ac10b-58cc-4372-a567-0e02b2c3d479. As we don't +-- call this function too often there is not so much risk on repetition. + +do + + local t = { 8, 9, "a", "b" } + + function os.uuid() + return format("%04x%04x-4%03x-%s%03x-%04x-%04x%04x%04x", + random(0xFFFF),random(0xFFFF), + random(0x0FFF), + t[ceil(random(4))] or 8,random(0x0FFF), + random(0xFFFF), + random(0xFFFF),random(0xFFFF),random(0xFFFF) + ) + end + end -local d +do -function os.timezone(delta) - d = d or ((tonumber(date("%H")) or 0) - (tonumber(date("!%H")) or 0)) - if delta then - if d > 0 then - return format("+%02i:00",d) + -- this is fragile because it depends on time and so we only check once during + -- a run (the computer doesn't move zones) .. Michal Vlasák made a better one + + -- local d + -- + -- function os.timezone() + -- d = d or ((tonumber(date("%H")) or 0) - (tonumber(date("!%H")) or 0)) + -- if d > 0 then + -- return format("+%02i:00",d) + -- else + -- return format("-%02i:00",-d) + -- end + -- end + + local hour, min + + function os.timezone(difference) + if not hour then + -- somehow looks too complex: + local current = time() + local utcdate = date("!*t", current) + local localdate = date("*t", current) + localdate.isdst = false + local timediff = difftime(time(localdate), time(utcdate)) + hour, min = modf(timediff / 3600) + min = min * 60 + end + if difference then + return hour, min else - return format("-%02i:00",-d) + return format("%+03d:%02d",hour,min) -- %+ means: always show sign end - else - return 1 end -end -local timeformat = format("%%s%s",os.timezone(true)) -local dateformat = "!%Y-%m-%d %H:%M:%S" -local lasttime = nil -local lastdate = nil - -function os.fulltime(t,default) - t = t and tonumber(t) or 0 - if t > 0 then - -- valid time - elseif default then - return default - else - t = time() - end - if t ~= lasttime then - lasttime = t - lastdate = format(timeformat,date(dateformat)) + -- localtime with timezone: 2021-10-22 10:22:54+02:00 + + local timeformat = format("%%s%s",os.timezone()) + local dateformat = "%Y-%m-%d %H:%M:%S" + local lasttime = nil + local lastdate = nil + + function os.fulltime(t,default) + t = t and tonumber(t) or 0 + if t > 0 then + -- valid time + elseif default then + return default + else + t = time() + end + if t ~= lasttime then + lasttime = t + lastdate = format(timeformat,date(dateformat)) + end + return lastdate end - return lastdate -end -local dateformat = "%Y-%m-%d %H:%M:%S" -local lasttime = nil -local lastdate = nil + -- localtime without timezone: 2021-10-22 10:22:54 -function os.localtime(t,default) - t = t and tonumber(t) or 0 - if t > 0 then - -- valid time - elseif default then - return default - else - t = time() + local dateformat = "%Y-%m-%d %H:%M:%S" + local lasttime = nil + local lastdate = nil + + function os.localtime(t,default) + t = t and tonumber(t) or 0 + if t > 0 then + -- valid time + elseif default then + return default + else + t = time() + end + if t ~= lasttime then + lasttime = t + lastdate = date(dateformat,t) + end + return lastdate end - if t ~= lasttime then - lasttime = t - lastdate = date(dateformat,t) + + function os.converttime(t,default) + local t = tonumber(t) + if t and t > 0 then + return date(dateformat,t) + else + return default or "-" + end end - return lastdate -end -function os.converttime(t,default) - local t = tonumber(t) - if t and t > 0 then - return date(dateformat,t) - else - return default or "-" + -- table with values + + function os.today() + return date("!*t") + end + + -- utc time without timezone: 2021-10-22 08:22:54 + + function os.now() + return date("!%Y-%m-%d %H:%M:%S") end + end -local memory = { } - -local function which(filename) - local fullname = memory[filename] - if fullname == nil then - local suffix = file.suffix(filename) - local suffixes = suffix == "" and os.binsuffixes or { suffix } - for directory in gmatch(os.getenv("PATH"),"[^" .. io.pathseparator .."]+") do - local df = file.join(directory,filename) - for i=1,#suffixes do - local dfs = file.addsuffix(df,suffixes[i]) - if io.exists(dfs) then - fullname = dfs - break +do + + local cache = { } + + local function which(filename) + local fullname = cache[filename] + if fullname == nil then + local suffix = file.suffix(filename) + local suffixes = suffix == "" and os.binsuffixes or { suffix } + for directory in gmatch(os.getenv("PATH"),"[^" .. io.pathseparator .."]+") do + local df = file.join(directory,filename) + for i=1,#suffixes do + local dfs = file.addsuffix(df,suffixes[i]) + if io.exists(dfs) then + fullname = dfs + break + end end end + if not fullname then + fullname = false + end + cache[filename] = fullname end - if not fullname then - fullname = false - end - memory[filename] = fullname + return fullname end - return fullname -end -os.which = which -os.where = which + os.which = which + os.where = which -function os.today() - return date("!*t") -- table with values -end + -- print(os.which("inkscape.exe")) + -- print(os.which("inkscape")) + -- print(os.which("gs.exe")) + -- print(os.which("ps2pdf")) -function os.now() - return date("!%Y-%m-%d %H:%M:%S") -- 2011-12-04 14:59:12 end --- if not os.sleep and socket then --- os.sleep = socket.sleep --- end - if not os.sleep then + local socket = socket + function os.sleep(n) if not socket then -- so we delay ... if os.sleep is really needed then one should also @@ -573,101 +585,105 @@ if not os.sleep then end socket.sleep(n) end -end - --- print(os.which("inkscape.exe")) --- print(os.which("inkscape")) --- print(os.which("gs.exe")) --- print(os.which("ps2pdf")) - --- These are moved from core-con.lua (as I needed them elsewhere). -local function isleapyear(year) -- timed for bram's cs practicum - -- return (year % 400 == 0) or (year % 100 ~= 0 and year % 4 == 0) -- 3:4:1600:1900 = 9.9 : 8.2 : 5.0 : 6.8 (29.9) - return (year % 4 == 0) and (year % 100 ~= 0 or year % 400 == 0) -- 3:4:1600:1900 = 5.1 : 6.5 : 8.1 : 10.2 (29.9) - -- return (year % 4 == 0) and (year % 400 == 0 or year % 100 ~= 0) -- 3:4:1600:1900 = 5.2 : 8.5 : 6.8 : 10.1 (30.6) end -os.isleapyear = isleapyear +-- These are moved from core-con.lua (as I needed them elsewhere). --- nicer: --- --- local days = { --- [false] = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }, --- [true] = { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 } --- } --- --- local function nofdays(year,month) --- return days[isleapyear(year)][month] --- return month == 2 and isleapyear(year) and 29 or days[month] --- end --- --- more efficient: +do -local days = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 } + local function isleapyear(year) -- timed for bram's cs practicum + -- return (year % 400 == 0) or (year % 100 ~= 0 and year % 4 == 0) -- 3:4:1600:1900 = 9.9 : 8.2 : 5.0 : 6.8 (29.9) + return (year % 4 == 0) and (year % 100 ~= 0 or year % 400 == 0) -- 3:4:1600:1900 = 5.1 : 6.5 : 8.1 : 10.2 (29.9) + -- return (year % 4 == 0) and (year % 400 == 0 or year % 100 ~= 0) -- 3:4:1600:1900 = 5.2 : 8.5 : 6.8 : 10.1 (30.6) + end -local function nofdays(year,month,day) - if not month then - return isleapyear(year) and 365 or 364 - elseif not day then - return month == 2 and isleapyear(year) and 29 or days[month] - else - for i=1,month-1 do - day = day + days[i] - end - if month > 2 and isleapyear(year) then - day = day + 1 + os.isleapyear = isleapyear + + -- nicer: + -- + -- local days = { + -- [false] = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }, + -- [true] = { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 } + -- } + -- + -- local function nofdays(year,month) + -- return days[isleapyear(year)][month] + -- return month == 2 and isleapyear(year) and 29 or days[month] + -- end + -- + -- more efficient: + + local days = { 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 } + + local function nofdays(year,month,day) + if not month then + return isleapyear(year) and 365 or 364 + elseif not day then + return month == 2 and isleapyear(year) and 29 or days[month] + else + for i=1,month-1 do + day = day + days[i] + end + if month > 2 and isleapyear(year) then + day = day + 1 + end + return day end - return day end -end - -os.nofdays = nofdays -function os.weekday(day,month,year) - return date("%w",time { year = year, month = month, day = day }) + 1 -end + os.nofdays = nofdays -function os.validdate(year,month,day) - -- we assume that all three values are set - -- year is always ok, even if lua has a 1970 time limit - if month < 1 then - month = 1 - elseif month > 12 then - month = 12 + function os.weekday(day,month,year) + return date("%w",time { year = year, month = month, day = day }) + 1 end - if day < 1 then - day = 1 - else - local max = nofdays(year,month) - if day > max then - day = max + + function os.validdate(year,month,day) + -- we assume that all three values are set + -- year is always ok, even if lua has a 1970 time limit + if month < 1 then + month = 1 + elseif month > 12 then + month = 12 end + if day < 1 then + day = 1 + else + local max = nofdays(year,month) + if day > max then + day = max + end + end + return year, month, day end - return year, month, day -end -function os.date(fmt,...) - if not fmt then - -- otherwise differences between unix, mingw and msvc - fmt = "%Y-%m-%d %H:%M" + function os.date(fmt,...) + if not fmt then + -- otherwise differences between unix, mingw and msvc + fmt = "%Y-%m-%d %H:%M" + end + return date(fmt,...) end - return date(fmt,...) + end -local osexit = os.exit -local exitcode = nil +do -function os.setexitcode(code) - exitcode = code -end + local osexit = os.exit + local exitcode = nil -function os.exit(c) - if exitcode ~= nil then - return osexit(exitcode) + function os.setexitcode(code) + exitcode = code end - if c ~= nil then - return osexit(c) + + function os.exit(c) + if exitcode ~= nil then + return osexit(exitcode) + end + if c ~= nil then + return osexit(c) + end + return osexit() end - return osexit() + end diff --git a/macros/luatex/generic/lualibs/lualibs-util-deb.lua b/macros/luatex/generic/lualibs/lualibs-util-deb.lua index bd94b6d01e..10e5731b03 100644 --- a/macros/luatex/generic/lualibs/lualibs-util-deb.lua +++ b/macros/luatex/generic/lualibs/lualibs-util-deb.lua @@ -346,3 +346,25 @@ debugger.showtraceback = showtraceback -- debug.showtraceback = showtraceback -- showtraceback() + +-- For now also here because we want it in mtxrun (taken from lmt file): + +if luac then + + local show, dump = luac.print, string.dump + + function luac.inspect(v) + if type(v) == "function" then + local ok, str = xpcall(dump,function() end,v) + if ok then + v = str + end + end + if type(v) == "string" then + show(v,true) + else + print(v) + end + end + +end diff --git a/macros/luatex/generic/lualibs/lualibs-util-jsn.lua b/macros/luatex/generic/lualibs/lualibs-util-jsn.lua index 8da3518979..2d78561971 100644 --- a/macros/luatex/generic/lualibs/lualibs-util-jsn.lua +++ b/macros/luatex/generic/lualibs/lualibs-util-jsn.lua @@ -17,6 +17,10 @@ if not modules then modules = { } end modules ['util-jsn'] = { -- -- Upgraded for handling the somewhat more fax server templates. +if utilities and utilities.json then + return json +end + local P, V, R, S, C, Cc, Cs, Ct, Cf, Cg = lpeg.P, lpeg.V, lpeg.R, lpeg.S, lpeg.C, lpeg.Cc, lpeg.Cs, lpeg.Ct, lpeg.Cf, lpeg.Cg local lpegmatch = lpeg.match local format, gsub = string.format, string.gsub @@ -265,6 +269,8 @@ do k = lpegmatch(escaper,k) or k v = lpegmatch(escaper,v) or v n = n + 1 t[n] = f_key_val_str(depth,k,v) + elseif i > 1 then + n = n - 1 end elseif tv == "table" then local l = #v @@ -280,6 +286,9 @@ do end elseif next(v) then tojsonpp(v,k,depth,level+1,0) + elseif i > 1 then + n = n - 1 + -- we don't know if we have a hash or string end elseif tv == "boolean" then if tk == "number" then @@ -297,6 +306,8 @@ do else t[n] = f_key_val_nop(depth,k) end + elseif i > 1 then + n = n - 1 end else if tk == "number" then @@ -306,6 +317,8 @@ do k = lpegmatch(escaper,k) or k n = n + 1 t[n] = f_key_val_null(depth,k) + elseif i > 1 then + n = n - 1 end end end @@ -440,4 +453,8 @@ end -- inspect(l) -- print(s==l.s) -return json +-- if not package.loaded.json then +-- package.loaded.json = json +-- end + +-- return json diff --git a/macros/luatex/generic/lualibs/lualibs-util-prs.lua b/macros/luatex/generic/lualibs/lualibs-util-prs.lua index 6d2f8c19e0..635b610e07 100644 --- a/macros/luatex/generic/lualibs/lualibs-util-prs.lua +++ b/macros/luatex/generic/lualibs/lualibs-util-prs.lua @@ -55,9 +55,13 @@ local nobracket = 1 - (lbracket + rbracket) local escape, left, right = P("\\"), P('{'), P('}') +-- lpegpatterns.balanced = P { +-- [1] = ((escape * (left+right)) + (1 - (left+right)) + V(2))^0, +-- [2] = left * V(1) * right +-- } lpegpatterns.balanced = P { - [1] = ((escape * (left+right)) + (1 - (left+right)) + V(2))^0, - [2] = left * V(1) * right + ((escape * (left+right)) + (1 - (left+right)) + V(2))^0, + left * V(1) * right } local nestedbraces = P { lbrace * (nobrace + V(1))^0 * rbrace } @@ -67,11 +71,12 @@ local spaces = space^0 local argument = Cs((lbrace/"") * ((nobrace + nestedbraces)^0) * (rbrace/"")) local content = (1-endofstring)^0 -lpegpatterns.nestedbraces = nestedbraces -- no capture -lpegpatterns.nestedparents = nestedparents -- no capture -lpegpatterns.nested = nestedbraces -- no capture -lpegpatterns.argument = argument -- argument after e.g. = -lpegpatterns.content = content -- rest after e.g = +lpegpatterns.nestedbraces = nestedbraces -- no capture +lpegpatterns.nestedparents = nestedparents -- no capture +lpegpatterns.nestedbrackets = nestedbrackets -- no capture +lpegpatterns.nested = nestedbraces -- no capture +lpegpatterns.argument = argument -- argument after e.g. = +lpegpatterns.content = content -- rest after e.g = local value = lbrace * C((nobrace + nestedbraces)^0) * rbrace + C((nestedbraces + (1-comma))^0) @@ -568,9 +573,9 @@ end -- "1","2","3","4" -- "5","6","7","8" -- ]] --- + -- local mycsvsplitter = parsers.csvsplitter { numbers = true } --- + -- local list = mycsvsplitter(crap) inspect(list) -- and this is a slightly patched version of a version posted by Philipp Gesang @@ -617,12 +622,6 @@ end -- local list, names = mycsvsplitter(crap,true) inspect(list) inspect(names) -- local list, names = mycsvsplitter(crap) inspect(list) inspect(names) --- parsers.stepper("1,7-",9,function(i) print(">>>",i) end) --- parsers.stepper("1-3,7,8,9") --- parsers.stepper("1-3,6,7",function(i) print(">>>",i) end) --- parsers.stepper(" 1 : 3, ,7 ") --- parsers.stepper("1:4,9:13,24:*",30) - local function ranger(first,last,n,action) if not first then -- forget about it @@ -639,7 +638,7 @@ local function ranger(first,last,n,action) end end -local cardinal = lpegpatterns.cardinal / tonumber +local cardinal = (lpegpatterns.hexadecimal + lpegpatterns.cardinal) / tonumber local spacers = lpegpatterns.spacer^0 local endofstring = lpegpatterns.endofstring @@ -650,14 +649,29 @@ local stepper = spacers * ( cardinal * ( spacers * S(":-") * spacers * ( cardin * Carg(1) * Carg(2) / ranger * S(", ")^0 )^1 * endofstring -- we're sort of strict (could do without endofstring) function parsers.stepper(str,n,action) + local ts = type(str) if type(n) == "function" then - lpegmatch(stepper,str,1,false,n or print) - else + if ts == "number" then + n(str) + elseif ts == "table" then + for i=1,#str do + n(str[i]) + end + else + lpegmatch(stepper,str,1,false,n or print) + end + elseif ts == "string" then lpegmatch(stepper,str,1,n,action or print) end end --- +-- parsers.stepper("1,7-",9,function(i) print(">>>",i) end) +-- parsers.stepper("1-3,7,8,9") +-- parsers.stepper("1-3,6,7",function(i) print(">>>",i) end) +-- parsers.stepper(" 1 : 3, ,7 ") +-- parsers.stepper("1:4,9:13,24:*",30) +-- parsers.stepper(1,print) +-- parsers.stepper({1,3,4},print) local pattern_math = Cs((P("%")/"\\percent " + P("^") * Cc("{") * lpegpatterns.integer * Cc("}") + anything)^0) local pattern_text = Cs((P("%")/"\\percent " + (P("^")/"\\high") * Cc("{") * lpegpatterns.integer * Cc("}") + anything)^0) @@ -681,7 +695,7 @@ local spaces = lpegpatterns.space^0 local dummy = function() end setmetatableindex(cache,function(t,k) - local separator = P(k) + local separator = S(k) -- was P local value = (1-separator)^0 local pattern = spaces * C(value) * separator^0 * Cp() t[k] = pattern @@ -801,11 +815,20 @@ local pattern = Cf( Ct("") * ( Cg(Cc("day") * cardinal) * S("-/") * Cg(Cc("month") * cardinal) * S("-/") * Cg(Cc("year") * p_year) + ) + + ( Cg(Cc("year") * p_year) + * S("-/") * Cg(Cc("month") * cardinal) + ) + + ( Cg(Cc("month") * cardinal) + * S("-/") * Cg(Cc("year") * p_year) ) ) - * P(" ") * Cg(Cc("hour") * cardinal) + * ( + P(" ") * Cg(Cc("hour") * cardinal) * P(":") * Cg(Cc("min") * cardinal) * (P(":") * Cg(Cc("sec") * cardinal))^-1 + + P(-1) ) + , rawset) lpegpatterns.splittime = pattern @@ -814,6 +837,8 @@ function parsers.totime(str) return lpegmatch(pattern,str) end +-- inspect(parsers.totime("2019-03-05")) +-- inspect(parsers.totime("2019-03-05 12:12:12")) -- print(os.time(parsers.totime("2019-03-05 12:12:12"))) -- print(os.time(parsers.totime("2019/03/05 12:12:12"))) -- print(os.time(parsers.totime("05-03-2019 12:12:12"))) diff --git a/macros/luatex/generic/lualibs/lualibs-util-sac.lua b/macros/luatex/generic/lualibs/lualibs-util-sac.lua new file mode 100644 index 0000000000..36daef8167 --- /dev/null +++ b/macros/luatex/generic/lualibs/lualibs-util-sac.lua @@ -0,0 +1,582 @@ +if not modules then modules = { } end modules ['util-sac'] = { + version = 1.001, + optimize = true, + comment = "companion to luat-lib.mkiv", + author = "Hans Hagen, PRAGMA-ADE, Hasselt NL", + copyright = "PRAGMA ADE / ConTeXt Development Team", + license = "see context related readme files" +} + +-- experimental string access (some 3 times faster than file access when messing +-- with bytes) + +local byte, sub = string.byte, string.sub +local tonumber = tonumber + +utilities = utilities or { } +local streams = { } +utilities.streams = streams + +function streams.open(filename,zerobased) + local f = filename and io.loaddata(filename) + if f then + return { f, 1, #f, zerobased or false } + end +end + +function streams.openstring(f,zerobased) + if f then + return { f, 1, #f, zerobased or false } + end +end + +function streams.getstring(f) + if f then + return f[1] + end +end + +function streams.close() + -- dummy +end + +function streams.size(f) + return f and f[3] or 0 +end + +streams.getsize = streams.size + +function streams.setposition(f,i) + if f[4] then + -- zerobased + if i <= 0 then + f[2] = 1 + else + f[2] = i + 1 + end + else + if i <= 1 then + f[2] = 1 + else + f[2] = i + end + end +end + +function streams.getposition(f) + if f[4] then + -- zerobased + return f[2] - 1 + else + return f[2] + end +end + +function streams.look(f,n,chars) + local b = f[2] + local e = b + n - 1 + if chars then + return sub(f[1],b,e) + else + return byte(f[1],b,e) + end +end + +function streams.skip(f,n) + f[2] = f[2] + n +end + +function streams.readbyte(f) + local i = f[2] + f[2] = i + 1 + return byte(f[1],i) +end + +function streams.readbytes(f,n) + local i = f[2] + local j = i + n + f[2] = j + return byte(f[1],i,j-1) +end + +function streams.readbytetable(f,n) + local i = f[2] + local j = i + n + f[2] = j + return { byte(f[1],i,j-1) } +end + +function streams.skipbytes(f,n) + f[2] = f[2] + n +end + +function streams.readchar(f) + local i = f[2] + f[2] = i + 1 + return sub(f[1],i,i) +end + +function streams.readstring(f,n) + local i = f[2] + local j = i + n + f[2] = j + return sub(f[1],i,j-1) +end + +function streams.readinteger1(f) -- one byte + local i = f[2] + f[2] = i + 1 + local n = byte(f[1],i) + if n >= 0x80 then + return n - 0x100 + else + return n + end +end + +streams.readcardinal1 = streams.readbyte -- one byte +streams.readcardinal = streams.readcardinal1 +streams.readinteger = streams.readinteger1 + +function streams.readcardinal2(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local a, b = byte(f[1],i,j) + return 0x100 * a + b +end + +function streams.readcardinal2le(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local b, a = byte(f[1],i,j) + return 0x100 * a + b +end + +function streams.readinteger2(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local a, b = byte(f[1],i,j) + if a >= 0x80 then + return 0x100 * a + b - 0x10000 + else + return 0x100 * a + b + end +end + +function streams.readinteger2le(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local b, a = byte(f[1],i,j) + if a >= 0x80 then + return 0x100 * a + b - 0x10000 + else + return 0x100 * a + b + end +end + +function streams.readcardinal3(f) + local i = f[2] + local j = i + 2 + f[2] = j + 1 + local a, b, c = byte(f[1],i,j) + return 0x10000 * a + 0x100 * b + c +end + +function streams.readcardinal3le(f) + local i = f[2] + local j = i + 2 + f[2] = j + 1 + local c, b, a = byte(f[1],i,j) + return 0x10000 * a + 0x100 * b + c +end + +function streams.readinteger3(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local a, b, c = byte(f[1],i,j) + if a >= 0x80 then + return 0x10000 * a + 0x100 * b + c - 0x1000000 + else + return 0x10000 * a + 0x100 * b + c + end +end + +function streams.readinteger3le(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local c, b, a = byte(f[1],i,j) + if a >= 0x80 then + return 0x10000 * a + 0x100 * b + c - 0x1000000 + else + return 0x10000 * a + 0x100 * b + c + end +end + +function streams.readcardinal4(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local a, b, c, d = byte(f[1],i,j) + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d +end + +function streams.readcardinal4le(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local d, c, b, a = byte(f[1],i,j) + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d +end + +function streams.readinteger4(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local a, b, c, d = byte(f[1],i,j) + if a >= 0x80 then + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d - 0x100000000 + else + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d + end +end + +function streams.readinteger4le(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local d, c, b, a = byte(f[1],i,j) + if a >= 0x80 then + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d - 0x100000000 + else + return 0x1000000 * a + 0x10000 * b + 0x100 * c + d + end +end + +function streams.readfixed2(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local n1, n2 = byte(f[1],i,j) + if n1 >= 0x80 then + n1 = n1 - 0x100 + end + return n1 + n2/0xFF +end + +function streams.readfixed4(f) + local i = f[2] + local j = i + 3 + f[2] = j + 1 + local a, b, c, d = byte(f[1],i,j) + local n1 = 0x100 * a + b + local n2 = 0x100 * c + d + if n1 >= 0x8000 then + n1 = n1 - 0x10000 + end + return n1 + n2/0xFFFF +end + +if bit32 then + + local extract = bit32.extract + local band = bit32.band + + function streams.read2dot14(f) + local i = f[2] + local j = i + 1 + f[2] = j + 1 + local a, b = byte(f[1],i,j) + if a >= 0x80 then + local n = -(0x100 * a + b) + return - (extract(n,14,2) + (band(n,0x3FFF) / 16384.0)) + else + local n = 0x100 * a + b + return (extract(n,14,2) + (band(n,0x3FFF) / 16384.0)) + end + end + +end + +function streams.skipshort(f,n) + f[2] = f[2] + 2*(n or 1) +end + +function streams.skiplong(f,n) + f[2] = f[2] + 4*(n or 1) +end + +if sio and sio.readcardinal2 then + + local readcardinal1 = sio.readcardinal1 + local readcardinal2 = sio.readcardinal2 + local readcardinal3 = sio.readcardinal3 + local readcardinal4 = sio.readcardinal4 + local readinteger1 = sio.readinteger1 + local readinteger2 = sio.readinteger2 + local readinteger3 = sio.readinteger3 + local readinteger4 = sio.readinteger4 + local readfixed2 = sio.readfixed2 + local readfixed4 = sio.readfixed4 + local read2dot14 = sio.read2dot14 + local readbytes = sio.readbytes + local readbytetable = sio.readbytetable + + function streams.readcardinal1(f) + local i = f[2] + f[2] = i + 1 + return readcardinal1(f[1],i) + end + function streams.readcardinal2(f) + local i = f[2] + f[2] = i + 2 + return readcardinal2(f[1],i) + end + function streams.readcardinal3(f) + local i = f[2] + f[2] = i + 3 + return readcardinal3(f[1],i) + end + function streams.readcardinal4(f) + local i = f[2] + f[2] = i + 4 + return readcardinal4(f[1],i) + end + function streams.readinteger1(f) + local i = f[2] + f[2] = i + 1 + return readinteger1(f[1],i) + end + function streams.readinteger2(f) + local i = f[2] + f[2] = i + 2 + return readinteger2(f[1],i) + end + function streams.readinteger3(f) + local i = f[2] + f[2] = i + 3 + return readinteger3(f[1],i) + end + function streams.readinteger4(f) + local i = f[2] + f[2] = i + 4 + return readinteger4(f[1],i) + end + function streams.readfixed2(f) -- needs recent luatex + local i = f[2] + f[2] = i + 2 + return readfixed2(f[1],i) + end + function streams.readfixed4(f) -- needs recent luatex + local i = f[2] + f[2] = i + 4 + return readfixed4(f[1],i) + end + function streams.read2dot14(f) + local i = f[2] + f[2] = i + 2 + return read2dot14(f[1],i) + end + function streams.readbytes(f,n) + local i = f[2] + local s = f[3] + local p = i + n + if p > s then + f[2] = s + 1 + else + f[2] = p + end + return readbytes(f[1],i,n) + end + function streams.readbytetable(f,n) + local i = f[2] + local s = f[3] + local p = i + n + if p > s then + f[2] = s + 1 + else + f[2] = p + end + return readbytetable(f[1],i,n) + end + + streams.readbyte = streams.readcardinal1 + streams.readsignedbyte = streams.readinteger1 + streams.readcardinal = streams.readcardinal1 + streams.readinteger = streams.readinteger1 + +end + +if sio and sio.readcardinaltable then + + local readcardinaltable = sio.readcardinaltable + local readintegertable = sio.readintegertable + + function utilities.streams.readcardinaltable(f,n,b) + local i = f[2] + local s = f[3] + local p = i + n * b + if p > s then + f[2] = s + 1 + else + f[2] = p + end + return readcardinaltable(f[1],i,n,b) + end + + function utilities.streams.readintegertable(f,n,b) + local i = f[2] + local s = f[3] + local p = i + n * b + if p > s then + f[2] = s + 1 + else + f[2] = p + end + return readintegertable(f[1],i,n,b) + end + +else + + local readcardinal1 = streams.readcardinal1 + local readcardinal2 = streams.readcardinal2 + local readcardinal3 = streams.readcardinal3 + local readcardinal4 = streams.readcardinal4 + + function streams.readcardinaltable(f,n,b) + local i = f[2] + local s = f[3] + local p = i + n * b + if p > s then + f[2] = s + 1 + else + f[2] = p + end + local t = { } + if b == 1 then for i=1,n do t[i] = readcardinal1(f[1],i) end + elseif b == 2 then for i=1,n do t[i] = readcardinal2(f[1],i) end + elseif b == 3 then for i=1,n do t[i] = readcardinal3(f[1],i) end + elseif b == 4 then for i=1,n do t[i] = readcardinal4(f[1],i) end end + return t + end + + local readinteger1 = streams.readinteger1 + local readinteger2 = streams.readinteger2 + local readinteger3 = streams.readinteger3 + local readinteger4 = streams.readinteger4 + + function streams.readintegertable(f,n,b) + local i = f[2] + local s = f[3] + local p = i + n * b + if p > s then + f[2] = s + 1 + else + f[2] = p + end + local t = { } + if b == 1 then for i=1,n do t[i] = readinteger1(f[1],i) end + elseif b == 2 then for i=1,n do t[i] = readinteger2(f[1],i) end + elseif b == 3 then for i=1,n do t[i] = readinteger3(f[1],i) end + elseif b == 4 then for i=1,n do t[i] = readinteger4(f[1],i) end end + return t + end + +end + +-- For practical reasons we put this here. It's less efficient but ok when we don't +-- have much access. + +do + + local files = utilities.files + + if files then + + local openfile = files.open + local openstream = streams.open + local openstring = streams.openstring + + local setmetatable = setmetatable + + function io.newreader(str,method) + local f, m + if method == "string" then + f = openstring(str,true) + m = streams + elseif method == "stream" then + f = openstream(str,true) + m = streams + else + f = openfile(str,"rb") + m = files + end + if f then + local t = { } + setmetatable(t, { + __index = function(t,k) + local r = m[k] + if k == "close" then + -- maybe use __toclose + if f then + m.close(f) + f = nil + end + return function() end + elseif r then + local v = function(_,a,b) return r(f,a,b) end + t[k] = v + return v + else + print("unknown key",k) + end + end + } ) + return t + end + end + + end + +end + +if bit32 and not streams.tocardinal1 then + + local extract = bit32.extract + local char = string.char + + streams.tocardinal1 = char + function streams.tocardinal2(n) return char(extract( 8,8),extract( 0,8)) end + function streams.tocardinal3(n) return char(extract(16,8),extract( 8,8),extract(0,8)) end + function streams.tocardinal4(n) return char(extract(24,8),extract(16,8),extract(8,8),extract(0,8)) end + + streams.tocardinal1le = char + function streams.tocardinal2le(n) return char(extract(0,8),extract(8,8)) end + function streams.tocardinal3le(n) return char(extract(0,8),extract(8,8),extract(16,8)) end + function streams.tocardinal4le(n) return char(extract(0,8),extract(8,8),extract(16,8),extract(24,8)) end + +end + +if not streams.readcstring then + + local readchar = streams.readchar + local concat = table.concat + + function streams.readcstring(f) + local t = { } + while true do + local c = readchar(f) + if c and c ~= "\0" then + t[#t+1] = c + else + return concat(t) + end + end + end + +end diff --git a/macros/luatex/generic/lualibs/lualibs-util-str.lua b/macros/luatex/generic/lualibs/lualibs-util-str.lua index 0d1f39de9d..b5c721a41d 100644 --- a/macros/luatex/generic/lualibs/lualibs-util-str.lua +++ b/macros/luatex/generic/lualibs/lualibs-util-str.lua @@ -10,12 +10,13 @@ utilities = utilities or { } utilities.strings = utilities.strings or { } local strings = utilities.strings -local format, gsub, rep, sub, find = string.format, string.gsub, string.rep, string.sub, string.find +local format, gsub, rep, sub, find, char = string.format, string.gsub, string.rep, string.sub, string.find, string.char local load, dump = load, string.dump local tonumber, type, tostring, next, setmetatable = tonumber, type, tostring, next, setmetatable local unpack, concat = table.unpack, table.concat local P, V, C, S, R, Ct, Cs, Cp, Carg, Cc = lpeg.P, lpeg.V, lpeg.C, lpeg.S, lpeg.R, lpeg.Ct, lpeg.Cs, lpeg.Cp, lpeg.Carg, lpeg.Cc local patterns, lpegmatch = lpeg.patterns, lpeg.match +local tsplitat = lpeg.tsplitat local utfchar, utfbyte, utflen = utf.char, utf.byte, utf.len ----- loadstripped = utilities.lua.loadstripped @@ -622,7 +623,7 @@ local template = [[ return function(%s) return %s end ]] --- this might move +-- We only use fast serialize in controlled cases. local pattern = Cs(Cc('"') * ( (1-S('"\\\n\r'))^1 @@ -632,12 +633,43 @@ local pattern = Cs(Cc('"') * ( + P('\r') / '\\r' )^0 * Cc('"')) +-- -- I need to do more experiments with this: +-- +-- local pattern = Cs(Cc('"') * ( +-- (1-S('"\\\n\r'))^1 +-- + P('"') / '\\034' +-- + P('\\') / '\\092' +-- + P('\n') / '\\013' +-- + P('\r') / '\\010' +-- )^0 * Cc('"')) + patterns.escapedquotes = pattern function string.escapedquotes(s) return lpegmatch(pattern,s) end +local pattern = (1 - P("\\"))^1 ; pattern = Cs ( + pattern + * ( (P("\\") / "" * (digit^-3 / function(s) return char(tonumber(s)) end)) + pattern )^1 +) + +patterns.unescapedquotes = pattern + +function string.unescapedquotes(s) + return lpegmatch(pattern,s) or s +end + +-- function string.longifneeded(s) +-- if find(s,'["\\\n\r]') then +-- return "[===[" .. s .. "]===]" +-- else +-- return '"' .. s ..'"' +-- end +-- end + +string.texnewlines = lpeg.replacer(patterns.newline,"\r",true) + -- print(string.escapedquotes('1\\23\n"')) -- but for now here @@ -1476,7 +1508,7 @@ end if not string.explode then - local tsplitat = lpeg.tsplitat + -- local tsplitat = lpeg.tsplitat local p_utf = patterns.utf8character local p_check = C(p_utf) * (P("+") * Cc(true))^0 @@ -1499,3 +1531,24 @@ if not string.explode then end end + + +do + + local p_whitespace = patterns.whitespace^1 + + local cache = setmetatable({ }, { __index = function(t,k) + local p = tsplitat(p_whitespace * P(k) * p_whitespace) + local v = function(s) + return lpegmatch(p,s) + end + t[k] = v + return v + end }) + + function string.wordsplitter(s) + return cache[s] + end + +end + diff --git a/macros/luatex/generic/lualibs/lualibs-util-tab.lua b/macros/luatex/generic/lualibs/lualibs-util-tab.lua index 9f7112eb91..64fa1af4fb 100644 --- a/macros/luatex/generic/lualibs/lualibs-util-tab.lua +++ b/macros/luatex/generic/lualibs/lualibs-util-tab.lua @@ -417,9 +417,9 @@ if JITSUPPORTED then else - local f_v = formatters["[%q]=%q,"] - local f_t = formatters["[%q]="] - local f_q = formatters["%q,"] + -- local f_v = formatters["[%q]=%q,"] + -- local f_t = formatters["[%q]="] + -- local f_q = formatters["%q,"] function table.fastserialize(t,prefix) -- todo, move local function out local r = { type(prefix) == "string" and prefix or "return" } @@ -720,6 +720,7 @@ local function serialize(root,name,specification) local t -- = { } local n = 1 + -- local m = 0 -- no gain local unknown = false local function do_serialize(root,name,depth,level,indexed) @@ -850,6 +851,12 @@ local function serialize(root,name,specification) n = n + 1 t[n] = f_key_str_value_str(depth,tostring(k),tostring(v)) end end + -- if n > 100000 then -- no gain + -- local k = m + 1 + -- t[k] = concat(t,"\n",k,n) + -- n = k + -- m = k + -- end end end if level > 0 then @@ -898,6 +905,7 @@ local function serialize(root,name,specification) n = n + 1 t[n] = f_table_finish() return concat(t,"\n") + -- return concat(t,"\n",1,n) -- no gain end table.serialize = serialize @@ -970,3 +978,43 @@ end -- return remove(t,random(1,n)) -- end -- end + +function combine(target,source) + -- no copy so if that is needed one needs to deepcopy source first + if target then + for k, v in next, source do + if type(v) == "table" then + target[k] = combine(target[k],source[k]) + else + target[k] = v + end + end + return target + else + return source + end +end + +table.combine = combine + +-- If needed we can add something (some discussion on the list but I'm not sure if +-- it makes sense because merging such mixed tables is quite unusual. +-- +-- function table.himerged(...) +-- local result = { } +-- local r = 0 +-- for i=1,select("#",...) do +-- local s = select(i,...) +-- if s then +-- for k, v in next, s do +-- if type(k) == "number" then +-- r = r + 1 +-- result[r] = v +-- else +-- result[k] = v +-- end +-- end +-- end +-- end +-- return result +-- end diff --git a/macros/luatex/generic/lualibs/lualibs-util-zip.lua b/macros/luatex/generic/lualibs/lualibs-util-zip.lua new file mode 100644 index 0000000000..bd8fdf287f --- /dev/null +++ b/macros/luatex/generic/lualibs/lualibs-util-zip.lua @@ -0,0 +1,684 @@ +if not modules then modules = { } end modules ['util-zip'] = { + version = 1.001, + author = "Hans Hagen, PRAGMA-ADE, Hasselt NL", + copyright = "PRAGMA ADE / ConTeXt Development Team", + license = "see context related readme files" +} + +-- This module is mostly meant for relative simple zip and unzip tasks. We can read +-- and write zip files but with limitations. Performance is quite good and it makes +-- us independent of zip tools, which (for some reason) are not always installed. +-- +-- This is an lmtx module and at some point will be lmtx only but for a while we +-- keep some hybrid functionality. + +local type, tostring, tonumber = type, tostring, tonumber +local sort, concat = table.sort, table.concat + +local find, format, sub, gsub = string.find, string.format, string.sub, string.gsub +local osdate, ostime, osclock = os.date, os.time, os.clock +local ioopen = io.open +local loaddata, savedata = io.loaddata, io.savedata +local filejoin, isdir, dirname, mkdirs = file.join, lfs.isdir, file.dirname, dir.mkdirs +local suffix, suffixes = file.suffix, file.suffixes +local openfile = io.open + +gzip = gzip or { } -- so in luatex we keep the old ones too + +if not zlib then + zlib = xzip -- in luametatex we shadow the old one +elseif not xzip then + xzip = zlib +end + +local files = utilities.files +local openfile = files.open +local closefile = files.close +local readstring = files.readstring +local readcardinal2 = files.readcardinal2le +local readcardinal4 = files.readcardinal4le +local setposition = files.setposition +local getposition = files.getposition + +local band = bit32.band +local rshift = bit32.rshift +local lshift = bit32.lshift + +local zlibdecompress = zlib.decompress +local zlibdecompresssize = zlib.decompresssize +local zlibchecksum = zlib.crc32 + +if not CONTEXTLMTXMODE or CONTEXTLMTXMODE == 0 then + local cs = zlibchecksum + zlibchecksum = function(str,n) return cs(n or 0, str) end +end + +local decompress = function(source) return zlibdecompress (source,-15) end -- auto +local decompresssize = function(source,targetsize) return zlibdecompresssize(source,targetsize,-15) end -- auto +local calculatecrc = function(buffer,initial) return zlibchecksum (initial or 0,buffer) end + +local zipfiles = { } +utilities.zipfiles = zipfiles + +local openzipfile, closezipfile, unzipfile, foundzipfile, getziphash, getziplist do + + function openzipfile(name) + return { + name = name, + handle = openfile(name,0), + } + end + + local function collect(z) + if not z.list then + local list = { } + local hash = { } + local position = 0 + local index = 0 + local handle = z.handle + while true do + setposition(handle,position) + local signature = readstring(handle,4) + if signature == "PK\3\4" then + -- [local file header 1] + -- [encryption header 1] + -- [file data 1] + -- [data descriptor 1] + local version = readcardinal2(handle) + local flag = readcardinal2(handle) + local method = readcardinal2(handle) + local filetime = readcardinal2(handle) + local filedate = readcardinal2(handle) + local crc32 = readcardinal4(handle) + local compressed = readcardinal4(handle) + local uncompressed = readcardinal4(handle) + local namelength = readcardinal2(handle) + local extralength = readcardinal2(handle) + local filename = readstring(handle,namelength) + local descriptor = band(flag,8) ~= 0 + local encrypted = band(flag,1) ~= 0 + local acceptable = method == 0 or method == 8 + -- 30 bytes of header including the signature + local skipped = 0 + local size = 0 + if encrypted then + size = readcardinal2(handle) + skipbytes(size) + skipped = skipped + size + 2 + skipbytes(8) + skipped = skipped + 8 + size = readcardinal2(handle) + skipbytes(size) + skipped = skipped + size + 2 + size = readcardinal4(handle) + skipbytes(size) + skipped = skipped + size + 4 + size = readcardinal2(handle) + skipbytes(size) + skipped = skipped + size + 2 + end + position = position + 30 + namelength + extralength + skipped + if descriptor then + setposition(handle,position + compressed) + crc32 = readcardinal4(handle) + compressed = readcardinal4(handle) + uncompressed = readcardinal4(handle) + end + if acceptable then + index = index + 1 + local data = { + filename = filename, + index = index, + position = position, + method = method, + compressed = compressed, + uncompressed = uncompressed, + crc32 = crc32, + encrypted = encrypted, + } + hash[filename] = data + list[index] = data + else + -- maybe a warning when encrypted + end + position = position + compressed + else + break + end + z.list = list + z.hash = hash + end + end + end + + function getziplist(z) + local list = z.list + if not list then + collect(z) + end + return z.list + end + + function getziphash(z) + local hash = z.hash + if not hash then + collect(z) + end + return z.hash + end + + function foundzipfile(z,name) + return getziphash(z)[name] + end + + function closezipfile(z) + local f = z.handle + if f then + closefile(f) + z.handle = nil + end + end + + function unzipfile(z,filename,check) + local hash = z.hash + if not hash then + hash = zipfiles.hash(z) + end + local data = hash[filename] -- normalize + if not data then + -- lower and cleanup + -- only name + end + if data then + local handle = z.handle + local position = data.position + local compressed = data.compressed + if compressed > 0 then + setposition(handle,position) + local result = readstring(handle,compressed) + if data.method == 8 then + if decompresssize then + result = decompresssize(result,data.uncompressed) + else + result = decompress(result) + end + end + if check and data.crc32 ~= calculatecrc(result) then + print("checksum mismatch") + return "" + end + return result + else + return "" + end + end + end + + zipfiles.open = openzipfile + zipfiles.close = closezipfile + zipfiles.unzip = unzipfile + zipfiles.hash = getziphash + zipfiles.list = getziplist + zipfiles.found = foundzipfile + +end + +if xzip then -- flate then do + + local writecardinal1 = files.writebyte + local writecardinal2 = files.writecardinal2le + local writecardinal4 = files.writecardinal4le + + local logwriter = logs.writer + + local globpattern = dir.globpattern +-- local compress = flate.flate_compress +-- local checksum = flate.update_crc32 + local compress = xzip.compress + local checksum = xzip.crc32 + + -- local function fromdostime(dostime,dosdate) + -- return ostime { + -- year = (dosdate >> 9) + 1980, -- 25 .. 31 + -- month = (dosdate >> 5) & 0x0F, -- 21 .. 24 + -- day = (dosdate ) & 0x1F, -- 16 .. 20 + -- hour = (dostime >> 11) , -- 11 .. 15 + -- min = (dostime >> 5) & 0x3F, -- 5 .. 10 + -- sec = (dostime ) & 0x1F, -- 0 .. 4 + -- } + -- end + -- + -- local function todostime(time) + -- local t = osdate("*t",time) + -- return + -- ((t.year - 1980) << 9) + (t.month << 5) + t.day, + -- (t.hour << 11) + (t.min << 5) + (t.sec >> 1) + -- end + + local function fromdostime(dostime,dosdate) + return ostime { + year = rshift(dosdate, 9) + 1980, -- 25 .. 31 + month = band(rshift(dosdate, 5), 0x0F), -- 21 .. 24 + day = band( (dosdate ), 0x1F), -- 16 .. 20 + hour = band(rshift(dostime,11) ), -- 11 .. 15 + min = band(rshift(dostime, 5), 0x3F), -- 5 .. 10 + sec = band( (dostime ), 0x1F), -- 0 .. 4 + } + end + + local function todostime(time) + local t = osdate("*t",time) + return + lshift(t.year - 1980, 9) + lshift(t.month,5) + t.day, + lshift(t.hour ,11) + lshift(t.min ,5) + rshift(t.sec,1) + end + + local function openzip(filename,level,comment,verbose) + local f = ioopen(filename,"wb") + if f then + return { + filename = filename, + handle = f, + list = { }, + level = tonumber(level) or 3, + comment = tostring(comment), + verbose = verbose, + uncompressed = 0, + compressed = 0, + } + end + end + + local function writezip(z,name,data,level,time) + local f = z.handle + local list = z.list + local level = tonumber(level) or z.level or 3 + local method = 8 + local zipped = compress(data,level) + local checksum = checksum(data) + local verbose = z.verbose + -- + if not zipped then + method = 0 + zipped = data + end + -- + local start = f:seek() + local compressed = #zipped + local uncompressed = #data + -- + z.compressed = z.compressed + compressed + z.uncompressed = z.uncompressed + uncompressed + -- + if verbose then + local pct = 100 * compressed/uncompressed + if pct >= 100 then + logwriter(format("%10i %s",uncompressed,name)) + else + logwriter(format("%10i %02.1f %s",uncompressed,pct,name)) + end + end + -- + f:write("\x50\x4b\x03\x04") -- PK.. 0x04034b50 + -- + writecardinal2(f,0) -- minimum version + writecardinal2(f,0) -- flag + writecardinal2(f,method) -- method + writecardinal2(f,0) -- time + writecardinal2(f,0) -- date + writecardinal4(f,checksum) -- crc32 + writecardinal4(f,compressed) -- compressed + writecardinal4(f,uncompressed) -- uncompressed + writecardinal2(f,#name) -- namelength + writecardinal2(f,0) -- extralength + -- + f:write(name) -- name + f:write(zipped) + -- + list[#list+1] = { #zipped, #data, name, checksum, start, time or 0 } + end + + local function closezip(z) + local f = z.handle + local list = z.list + local comment = z.comment + local verbose = z.verbose + local count = #list + local start = f:seek() + -- + for i=1,count do + local l = list[i] + local compressed = l[1] + local uncompressed = l[2] + local name = l[3] + local checksum = l[4] + local start = l[5] + local time = l[6] + local date, time = todostime(time) + f:write('\x50\x4b\x01\x02') + writecardinal2(f,0) -- version made by + writecardinal2(f,0) -- version needed to extract + writecardinal2(f,0) -- flags + writecardinal2(f,8) -- method + writecardinal2(f,time) -- time + writecardinal2(f,date) -- date + writecardinal4(f,checksum) -- crc32 + writecardinal4(f,compressed) -- compressed + writecardinal4(f,uncompressed) -- uncompressed + writecardinal2(f,#name) -- namelength + writecardinal2(f,0) -- extralength + writecardinal2(f,0) -- commentlength + writecardinal2(f,0) -- nofdisks -- ? + writecardinal2(f,0) -- internal attr (type) + writecardinal4(f,0) -- external attr (mode) + writecardinal4(f,start) -- local offset + f:write(name) -- name + end + -- + local stop = f:seek() + local size = stop - start + -- + f:write('\x50\x4b\x05\x06') + writecardinal2(f,0) -- disk + writecardinal2(f,0) -- disks + writecardinal2(f,count) -- entries + writecardinal2(f,count) -- entries + writecardinal4(f,size) -- dir size + writecardinal4(f,start) -- dir offset + if type(comment) == "string" and comment ~= "" then + writecardinal2(f,#comment) -- comment length + f:write(comment) -- comemnt + else + writecardinal2(f,0) + end + -- + if verbose then + local compressed = z.compressed + local uncompressed = z.uncompressed + local filename = z.filename + -- + local pct = 100 * compressed/uncompressed + logwriter("") + if pct >= 100 then + logwriter(format("%10i %s",uncompressed,filename)) + else + logwriter(format("%10i %02.1f %s",uncompressed,pct,filename)) + end + end + -- + f:close() + end + + local function zipdir(zipname,path,level,verbose) + if type(zipname) == "table" then + verbose = zipname.verbose + level = zipname.level + path = zipname.path + zipname = zipname.zipname + end + if not zipname or zipname == "" then + return + end + if not path or path == "" then + path = "." + end + if not isdir(path) then + return + end + path = gsub(path,"\\+","/") + path = gsub(path,"/+","/") + local list = { } + local count = 0 + globpattern(path,"",true,function(name,size,time) + count = count + 1 + list[count] = { name, time } + end) + sort(list,function(a,b) + return a[1] < b[1] + end) + local zipf = openzip(zipname,level,comment,verbose) + if zipf then + local p = #path + 2 + for i=1,count do + local li = list[i] + local name = li[1] + local time = li[2] + local data = loaddata(name) + local name = sub(name,p,#name) + writezip(zipf,name,data,level,time,verbose) + end + closezip(zipf) + end + end + + local function unzipdir(zipname,path,verbose) + if type(zipname) == "table" then + verbose = zipname.verbose + path = zipname.path + zipname = zipname.zipname + end + if not zipname or zipname == "" then + return + end + if not path or path == "" then + path = "." + end + local z = openzipfile(zipname) + if z then + local list = getziplist(z) + if list then + local total = 0 + local count = #list + local step = number.idiv(count,10) + local done = 0 + local steps = verbose == "steps" + local time = steps and osclock() + for i=1,count do + local l = list[i] + local n = l.filename + local d = unzipfile(z,n) -- true for check + if d then + local p = filejoin(path,n) + if mkdirs(dirname(p)) then + if steps then + total = total + #d + done = done + 1 + if done >= step then + done = 0 + logwriter(format("%4i files of %4i done, %10i bytes, %0.3f seconds",i,count,total,osclock()-time)) + end + elseif verbose then + logwriter(n) + end + savedata(p,d) + end + else + logwriter(format("problem with file %s",n)) + end + end + if steps then + logwriter(format("%4i files of %4i done, %10i bytes, %0.3f seconds",count,count,total,osclock()-time)) + end + closezipfile(z) + return true + else + closezipfile(z) + end + end + end + + zipfiles.zipdir = zipdir + zipfiles.unzipdir = unzipdir + +end + +-- todo: compress/decompress that work with offset in string + +-- We only have a few official methods here: +-- +-- local decompressed = gzip.load (filename) +-- local resultsize = gzip.save (filename,compresslevel) +-- local compressed = gzip.compress (str,compresslevel) +-- local decompressed = gzip.decompress (str) +-- local iscompressed = gzip.compressed (str) +-- local suffix, okay = gzip.suffix (filename) +-- +-- In LuaMetaTeX we have only xzip which implements a very few methods: +-- +-- compress (str,level,method,window,memory,strategy) +-- decompress (str,window) +-- adler32 (str,checksum) +-- crc32 (str,checksum) + +local pattern = "^\x1F\x8B\x08" +local gziplevel = 3 + +function gzip.suffix(filename) + local suffix, extra = suffixes(filename) + local gzipped = extra == "gz" + return suffix, gzipped +end + +function gzip.compressed(s) + return s and find(s,pattern) +end + +local getdecompressed +local putcompressed + +if gzip.compress then + + local gzipwindow = 15 + 16 -- +16: gzip, +32: gzip|zlib + + local compress = zlib.compress + local decompress = zlib.decompress + + getdecompressed = function(str) + return decompress(str,gzipwindow) -- pass offset + end + + putcompressed = function(str,level) + return compress(str,level or gziplevel,nil,gzipwindow) + end + +else + + -- Special window values are: flate: -15, zlib: 15, gzip : -15 + + local gzipwindow = -15 -- miniz needs this + local identifier = "\x1F\x8B" + + local compress = zlib.compress + local decompress = zlib.decompress + local zlibchecksum = zlib.crc32 + + if not CONTEXTLMTXMODE or CONTEXTLMTXMODE == 0 then + local cs = zlibchecksum + zlibchecksum = function(str,n) return cs(n or 0, str) end + end + + local streams = utilities.streams + local openstream = streams.openstring + local closestream = streams.close + local getposition = streams.getposition + local readbyte = streams.readbyte + local readcardinal4 = streams.readcardinal4le + local readcardinal2 = streams.readcardinal2le + local readstring = streams.readstring + local readcstring = streams.readcstring + local skipbytes = streams.skip + + local tocardinal1 = streams.tocardinal1 + local tocardinal4 = streams.tocardinal4le + + getdecompressed = function(str) + local s = openstream(str) + local identifier = readstring(s,2) + local method = readbyte(s,1) + local flags = readbyte(s,1) + local timestamp = readcardinal4(s) + local compression = readbyte(s,1) + local operating = readbyte(s,1) + -- local isjusttext = (flags & 0x01 ~= 0) and true or false + -- local extrasize = (flags & 0x04 ~= 0) and readcardinal2(s) or 0 + -- local filename = (flags & 0x08 ~= 0) and readcstring(s) or "" + -- local comment = (flags & 0x10 ~= 0) and readcstring(s) or "" + -- local checksum = (flags & 0x02 ~= 0) and readcardinal2(s) or 0 + local isjusttext = band(flags,0x01) ~= 0 and true or false + local extrasize = band(flags,0x04) ~= 0 and readcardinal2(s) or 0 + local filename = band(flags,0x08) ~= 0 and readcstring(s) or "" + local comment = band(flags,0x10) ~= 0 and readcstring(s) or "" + local checksum = band(flags,0x02) ~= 0 and readcardinal2(s) or 0 + local compressed = readstring(s,#str) + local data = decompress(compressed,gzipwindow) -- pass offset + return data + end + + putcompressed = function(str,level,originalname) + return concat { + identifier, -- 2 identifier + tocardinal1(0x08), -- 1 method + tocardinal1(0x08), -- 1 flags + tocardinal4(os.time()), -- 4 mtime + tocardinal1(0x02), -- 1 compression (2 or 4) + tocardinal1(0xFF), -- 1 operating + (originalname or "unknownname") .. "\0", + compress(str,level,nil,gzipwindow), + tocardinal4(zlibchecksum(str)), -- 4 + tocardinal4(#str), -- 4 + } + end + +end + +function gzip.load(filename) + local f = openfile(filename,"rb") + if not f then + -- invalid file + else + local data = f:read("*all") + f:close() + if data and data ~= "" then + if suffix(filename) == "gz" then + data = getdecompressed(data) + end + return data + end + end +end + +function gzip.save(filename,data,level,originalname) + if suffix(filename) ~= "gz" then + filename = filename .. ".gz" + end + local f = openfile(filename,"wb") + if f then + data = putcompressed(data or "",level or gziplevel,originalname) + f:write(data) + f:close() + return #data + end +end + +function gzip.compress(s,level) + if s and not find(s,pattern) then + if not level then + level = gziplevel + elseif level <= 0 then + return s + elseif level > 9 then + level = 9 + end + return putcompressed(s,level or gziplevel) or s + end +end + +function gzip.decompress(s) + if s and find(s,pattern) then + return getdecompressed(s) + else + return s + end +end + +-- return zipfiles diff --git a/macros/luatex/generic/lualibs/lualibs.dtx b/macros/luatex/generic/lualibs/lualibs.dtx index 73c5aafcc1..ebdba58424 100644 --- a/macros/luatex/generic/lualibs/lualibs.dtx +++ b/macros/luatex/generic/lualibs/lualibs.dtx @@ -37,7 +37,7 @@ \input docstrip.tex \Msg{************************************************************************} \Msg{* Installation} -\Msg{* Package: lualibs 2021-05-20 v2.74 Lua additional functions.} +\Msg{* Package: lualibs 2022-10-04 v2.75 Lua additional functions.} \Msg{************************************************************************} \keepsilent @@ -107,7 +107,7 @@ and lualibs-extended.lua. %<*driver> \NeedsTeXFormat{LaTeX2e} \ProvidesFile{lualibs.drv} - [2021/05/20 v2.74 Lua Libraries.] + [2022/10/04 v2.75 Lua Libraries.] \documentclass{ltxdoc} \usepackage{fancyvrb,xspace} \usepackage[x11names]{xcolor} @@ -115,6 +115,7 @@ and lualibs-extended.lua. \def\primarycolor{DodgerBlue4} %%-> rgb 16 78 139 | #104e8b \def\secondarycolor{Goldenrod4} %%-> rgb 139 105 200 | #8b6914 % +\AddToHook{package/hyperref/after}{% \hypersetup{ colorlinks=true, linkcolor=\primarycolor, @@ -123,7 +124,7 @@ and lualibs-extended.lua. pdftitle={The lualibs package}, pdfsubject={Port of the ConTeXt Lua libraries}, pdfauthor={Elie Roux & Philipp Gesang}, - pdfkeywords={luatex, lualatex, unicode, opentype}} + pdfkeywords={luatex, lualatex, unicode, opentype}}} \newcommand*\email[1]{\href{mailto:#1}{#1}} \usepackage{fontspec} @@ -207,7 +208,7 @@ and lualibs-extended.lua. % \GetFileInfo{lualibs.drv} % % \title{The \identifier{lualibs} package} -% \date{2021/05/20 v2.74} +% \date{2022/10/04 v2.75} % \author{Élie Roux · \email{elie.roux@telecom-bretagne.eu}\\ % Philipp Gesang · \email{phg@phi-gamma.net}\\ % The \LaTeX{} Project · \email{https://github.com/latex3/lualibs/}\\ @@ -322,12 +323,11 @@ and lualibs-extended.lua. % lualibs-io.lua & l-io.lua & reading and writing files \\ % lualibs-os.lua & l-os.lua & platform specific code \\ % lualibs-file.lua & l-file.lua & filesystem operations \\ -% lualibs-gzip.lua & l-gzip.lua & wrapper for \identifier{lgzip} \\ % lualibs-md5.lua & l-md5.lua & checksum functions \\ % lualibs-dir.lua & l-dir.lua & directory handling \\ % lualibs-unicode.lua & l-unicode.lua & utf and unicode \\ % lualibs-url.lua & l-url.lua & url handling \\ -% lualibs-set.lua & l-set.lua & sets \\[1ex] +% lualibs-set.lua & l-set.lua & sets \\ % \end{tabular} % \label{tab:basic} % \hrule @@ -346,6 +346,7 @@ and lualibs-extended.lua. % \vskip1em % \begin{tabular}{l l l} % \identifier{lualibs} name & \CONTEXT name & primary purpose \\[1ex] +% lualibs-util-sac.lua & util-sac.lua & string based file readers \\ % lualibs-util-str.lua & util-str.lua & extra |string| functions \\ % lualibs-util-fil.lua & util-fil.lua & extra |file| functions \\ % lualibs-util-tab.lua & util-tab.lua & extra |table| functions \\ @@ -357,7 +358,8 @@ and lualibs-extended.lua. % lualibs-util-deb.lua & util-deb.lua & extra |debug| functionality \\ % lualibs-util-tpl.lua & util-tpl.lua & templating \\ % lualibs-util-sta.lua & util-sta.lua & stacker (e.~g. for \abbrev{pdf}) \\ -% lualibs-util-jsn.lua & util-jsn.lua & conversion to and from json \\[1ex] +% lualibs-util-jsn.lua & util-jsn.lua & conversion to and from json \\ +% lualibs-util-zip.lua & util-zip.lua & compression and zip files \\[1ex] % \end{tabular} % \label{tab:extended} % \hrule @@ -428,8 +430,8 @@ lualibs = lualibs or { } lualibs.module_info = { name = "lualibs", - version = "2.74", --TAGVERSION - date = "2021-05-20", --TAGDATE + version = "2.75", --TAGVERSION + date = "2022-10-04", --TAGDATE description = "ConTeXt Lua standard libraries.", author = "Hans Hagen, PRAGMA-ADE, Hasselt NL & Elie Roux & Philipp Gesang", copyright = "PRAGMA ADE / ConTeXt Development Team", @@ -582,8 +584,8 @@ local loadmodule = lualibs.loadmodule local lualibs_basic_module = { name = "lualibs-basic", - version = "2.74", --TAGVERSION - date = "2021-05-20", --TAGDATE + version = "2.75", --TAGVERSION + date = "2022-10-04", --TAGDATE description = "ConTeXt Lua libraries -- basic collection.", author = "Hans Hagen, PRAGMA-ADE, Hasselt NL & Elie Roux & Philipp Gesang", copyright = "PRAGMA ADE / ConTeXt Development Team", @@ -621,7 +623,6 @@ if loaded == false then loadmodule("lualibs-io.lua") loadmodule("lualibs-os.lua") loadmodule("lualibs-file.lua") - loadmodule("lualibs-gzip.lua") loadmodule("lualibs-md5.lua") loadmodule("lualibs-dir.lua") loadmodule("lualibs-unicode.lua") @@ -664,8 +665,8 @@ lualibs = lualibs or { } local lualibs_extended_module = { name = "lualibs-extended", - version = "2.74", --TAGVERSION - date = "2021-05-20", --TAGDATE + version = "2.75", --TAGVERSION + date = "2022-10-04", --TAGDATE description = "ConTeXt Lua libraries -- extended collection.", author = "Hans Hagen, PRAGMA-ADE, Hasselt NL & Elie Roux & Philipp Gesang", copyright = "PRAGMA ADE / ConTeXt Development Team", @@ -776,6 +777,7 @@ else end if loaded == false then + loadmodule("lualibs-util-sac.lua")--- streams: string based file parsers loadmodule("lualibs-util-str.lua")--- string formatters (fast) loadmodule("lualibs-util-fil.lua")--- extra file helpers loadmodule("lualibs-util-tab.lua")--- extended table operations @@ -795,6 +797,7 @@ if loaded == false then loadmodule("lualibs-util-deb.lua")--- extra debugging loadmodule("lualibs-util-tpl.lua")--- templating loadmodule("lualibs-util-sta.lua")--- stacker (for writing pdf) + loadmodule("lualibs-util-zip.lua")--- compression and zip files end unfake_context() --- TODO check if this works at runtime diff --git a/macros/luatex/generic/lualibs/lualibs.pdf b/macros/luatex/generic/lualibs/lualibs.pdf Binary files differindex 23df3045e6..175e7e9f01 100644 --- a/macros/luatex/generic/lualibs/lualibs.pdf +++ b/macros/luatex/generic/lualibs/lualibs.pdf diff --git a/macros/luatex/latex/japanese-mathformulas/README.txt b/macros/luatex/latex/japanese-mathformulas/README.txt index b936573615..8f5c0199b8 100644 --- a/macros/luatex/latex/japanese-mathformulas/README.txt +++ b/macros/luatex/latex/japanese-mathformulas/README.txt @@ -1,5 +1,5 @@ japanese-mathformulas - mathematical formula using amsmath and tikz================================== -version 1.0.0 +version 1.0.1 Licence---------------------------------------------------------------------------------------------- lppl1.3c diff --git a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.pdf b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.pdf Binary files differindex 6657bbf2e4..a1af2c5b67 100644 --- a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.pdf +++ b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.pdf diff --git a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.tex b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.tex index 08786e5a34..4eb0ec70a2 100644 --- a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.tex +++ b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas-sample.tex @@ -2,7 +2,7 @@ \usepackage{iwona}% \usepackage{bookmark,xurl} -\usepackage{mathformula,ascolorbox,enumerate,environ,tcolorbox,color}% +\usepackage{japanese-mathformulas,ascolorbox,enumerate,environ,tcolorbox,color}% \usepackage[hiragino-pron,deluxe,expert,bold]{luatexja-preset}% \usepackage[usetype1]{uline--} \usepackage[margin=15mm]{geometry} diff --git a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.pdf b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.pdf Binary files differindex e0b9699357..8514e8de6a 100644 --- a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.pdf +++ b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.pdf diff --git a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.sty b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.sty index 201d70314e..5038049b59 100644 --- a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.sty +++ b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.sty @@ -1,6 +1,6 @@ \NeedsTeXFormat{LaTeX2e}% -\ProvidesPackage{mathformula}[2022/9/30,Version 1.0.0]% +\ProvidesPackage{japanese-mathformulas}[2022/10/3,Version 1.0.1]% \RequirePackage{luatexja}% \RequirePackage{luatexja-fontspec}% @@ -9,11 +9,36 @@ \RequirePackage{amsmath,amssymb,siunitx,ifthen,xparse,tikz,mathtools,graphics}% \usetikzlibrary{arrows,shapes,intersections,calc,angles,decorations.shapes,arrows.meta,quotes,through,decorations.text}% -\newcommand{\空行}{\vskip\baselineskip}% +\newcommand{\空行}{\vskip0.00001\baselineskip}% +%\def\空行{\br{.1}} +\newlength{\@tempdimf@math}% +\def\br{\@ifstar{\@br}{\@@br}}% +\def\@br#1{% +\allowbreak +\setlength{\@tempdimf@math}{\baselineskip * \real{#1}}% +\vspace*{\@tempdimf@math}% +}% +\def\@@br#1{% +\setlength{\@tempdimf@math}{\baselineskip * \real{#1}}% +\vspace{\@tempdimf@math}% +}% \newcommand{\半空行}{\vskip.5\baselineskip}% \newcommand{\証明開始}{\noindent\textgt{【証明】}\par}% -\newcommand{\証明終了}{\@rightalign{\ (Q.E.D.)}\par}% +\newcommand{\証明終了}{\@rightalign{\ （Q.E.D.）}\par}% \newcommand{\数式カンマスペース}{,\ }% +\NewDocumentCommand\根号{ O{} m }% + {\ifthenelse{\equal{#1}{}}{\sqrt{#2\,}}{\sqrt[#1]{#2\,}}}% +\newcommand{\ベクトル}[1]{\vec{\mathstrut #1}}% +\newcommand{\overrightarrowtext}[1]{\overrightarrow{\text{#1}}}% +\newcommand{\overarc}[1]% + {% + \tikz[baseline = (N.base),every node/.style={}]% + {% + \node[inner sep = 0pt](N){\text{#1}};% + \draw[line width = 0.4pt] plot [smooth, tension=1.3]coordinates% + {($(N.north west)+(0.1ex,0)$)($(N.north)+(0,0.5ex)$)($(N.north east)+(0,0)$)};% + }% + }% \newcommand*{\@rightalign}[1]% {% \hspace{\parfillskip}% @@ -23,7 +48,7 @@ \newcommand{\Ttyuukakko}[1]{\left(#1\right)}% \newcommand{\Ttyuubracket}[1]{\left[#1\right]}% \newcommand{\Tdaikakko}[1]{\left\{#1\right\}}% -\newcommand{\Tzettaiti}[1]{\left|#1\right|}% +\newcommand{\Tzettaiti}[1]{\left|\,#1\,\right|}% \def\shikimaru#1{\text{\quad$\cdots\cdots$\,\ajMaru{#1}}} \let\originalbigtriangleup\bigtriangleup \def\bigtriangleup#1{\originalbigtriangleup{\mathrm{#1}}} @@ -148,55 +173,55 @@ \NewDocumentCommand{\平方根}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {$a$は実数として，$\sqrt{a^2}=\Tzettaiti{a}$}% + {$a$は実数として，$\根号{a^2}=\Tzettaiti{a}$}% {\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% $a$は実数として，% - \[\sqrt{a^2}=\Tzettaiti{a}\]% + \[\根号{a^2}=\Tzettaiti{a}\]% }% {\relax}% \ifthenelse{\equal{#1}{性質A}\AND\equal{#2}{i}}% {% $a\geqq0$のとき，% - $\Ttyuukakko{\sqrt{a}}^2=\Ttyuukakko{-\sqrt{a}}^2=a\数式カンマスペース\sqrt{a}\leqq0$% + $\Ttyuukakko{\根号{a}}^2=\Ttyuukakko{-\根号{a}}^2=a\数式カンマスペース\根号{a}\leqq0$% }% {\relax}% \ifthenelse{\equal{#1}{性質A}\AND\equal{#2}{b}}% {% $a\leqq0$のとき，% - \[\Ttyuukakko{\sqrt{a}}^2=\Ttyuukakko{-\sqrt{a}}^2=a\数式カンマスペース\sqrt{a}\leqq0\]% + \[\Ttyuukakko{\根号{a}}^2=\Ttyuukakko{-\根号{a}}^2=a\数式カンマスペース\根号{a}\leqq0\]% }% {\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{i}}% - {$\sqrt{a}=\Tzettaiti{a}$}% + {$\根号{a}=\Tzettaiti{a}$}% {\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{b}}% - {\[\sqrt{a}=\Tzettaiti{a}\]}% + {\[\根号{a}=\Tzettaiti{a}\]}% {\relax}% \ifthenelse{\equal{#1}{性質C}\AND\equal{#2}{i}}% {% $a>0\数式カンマスペース b>0\数式カンマスペース a\neq b$のとき，% - $\sqrt{a}\sqrt{b}=\sqrt{ab}$% + $\根号{a}\根号{b}=\根号{ab}$% }% {\relax} \ifthenelse{\equal{#1}{性質C}\AND\equal{#2}{b}}% {% $a>0\数式カンマスペース b>0\数式カンマスペース a\neq b$のとき，% - \[\sqrt{a}\sqrt{b}=\sqrt{ab}\]% + \[\根号{a}\根号{b}=\根号{ab}\]% }% {\relax}% \ifthenelse{\equal{#1}{性質D}\AND\equal{#2}{i}}% - {$\bunsuu{\sqrt{a}}{\sqrt{b}}=\sqrt{\bunsuu{a}{b}}$}% + {$\bunsuu{\根号{a}}{\根号{b}}=\根号{\bunsuu{a}{b}}$}% {\relax}% \ifthenelse{\equal{#1}{性質D}\AND\equal{#2}{b}}% - {\[\bunsuu{\sqrt{a}}{\sqrt{b}}=\sqrt{\bunsuu{a}{b}}\]}% + {\[\bunsuu{\根号{a}}{\根号{b}}=\根号{\bunsuu{a}{b}}\]}% {\relax}% \ifthenelse{\equal{#1}{性質E}\AND\equal{#2}{i}}% - {$\sqrt{k^2a}=k\sqrt{a}$}% + {$\根号{k^2a}=k\根号{a}$}% {\relax}% \ifthenelse{\equal{#1}{性質E}\AND\equal{#2}{b}}% - {\[\sqrt{k^2a}=k\sqrt{a}\]}% + {\[\根号{k^2a}=k\根号{a}\]}% {\relax}% }% @@ -311,24 +336,24 @@ \NewDocumentCommand{\二次方程式の解の公式}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {$ax^2+bx+c=0 \Ttyuukakko{a\neq0}$に対して，$x=\bunsuu{-b\pm\sqrt{b^2-4ac}}{2a}$}{\relax}% + {$ax^2+bx+c=0 \Ttyuukakko{a\neq0}$に対して，$x=\bunsuu{-b\pm\根号{b^2-4ac}}{2a}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% $ax^2+bx+c=0 \Ttyuukakko{a\neq0}$に対して，% - \[x=\bunsuu{-b\pm\sqrt{b^2-4ac}}{2a}\]% + \[x=\bunsuu{-b\pm\根号{b^2-4ac}}{2a}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明A}}% {% \証明開始% - \vspace{-1\zw}% + \vspace{-2.5\zw}% \begin{align*}% ax^2+bx+c&=0&\\% a\Ttyuukakko{x^2+\bunsuu{b}{a}x}+c&=0&\\% a\Tdaikakko{\Ttyuukakko{x+\bunsuu{b}{2a}}^2-\bunsuu{b^2}{4a^2}}+c&=0&\\% a\Ttyuukakko{x+\bunsuu{b}{2a}}^2-\bunsuu{b^2}{4a}+c&=0&\\% \Ttyuukakko{x+\bunsuu{b}{2a}}^2&=\bunsuu{b^2-4ac}{4a^2}&\\% - x&=\bunsuu{-b\pm\sqrt{b^2-4ac}}{2a}% + x&=\bunsuu{-b\pm\根号{b^2-4ac}}{2a}% \end{align*}% \証明終了% }% @@ -336,13 +361,13 @@ \ifthenelse{\equal{#1}{証明B}}% {% \証明開始% - \vspace{-1\zw}% + \vspace{-2.5\zw}% \begin{align*}% ax^2+bx+c&=0&\\% 4a^2x^2+4abx+4ac&=0&\\% \Ttyuukakko{2ax+b}^2-b^2+4ac&=0&\\% - 2ax+b&=\pm\sqrt{b^2-4ac}&\\% - x&=\bunsuu{-b\pm\sqrt{b^2-4ac}}{2a}% + 2ax+b&=\pm\根号{b^2-4ac}&\\% + x&=\bunsuu{-b\pm\根号{b^2-4ac}}{2a}% \end{align*}% \証明終了% }% @@ -366,7 +391,7 @@ \draw pic["$\theta$",draw=black,->,thin,angle eccentricity=1.4,angle radius=0.4cm]{angle=B--A--C};% \end{tikzpicture}% \空行% - 図の様な直角三角形ABCにおいて$\angle\mathrm{CAB}=\theta$のとき，% + 図の様な直角$\triangle{\text{ABC}}$において$\angle\mathrm{CAB}=\theta$のとき，% \[% \sin\theta=\bunsuu{\text{BC}}{\text{AC}}\数式カンマスペース% \cos\theta=\bunsuu{\text{AB}}{\text{AC}}\数式カンマスペース% @@ -467,15 +492,15 @@ \newcommand{\直線}{両方向に限りなく伸びたまっすぐな線。}% -\newcommand{\線分}{直線ABのうち，二点A\数式カンマスペース Bを端とする部分。}% +\newcommand{\線分}{直線$\text{AB}$のうち，二点$\text{A}\数式カンマスペース\text{B}$を端とする部分。}% -\newcommand{\半直線}{直線ABのうち，一方の点を端とし，もう一方に限りなく伸びた部分。}% +\newcommand{\半直線}{直線$\text{AB}$のうち，一方の点を端とし，もう一方に限りなく伸びた部分。}% \newcommand{\距離} {% - 空でない集合Xの元$x\数式カンマスペース y$にたいして，実数値$d(x\数式カンマスペース y)$が定義され，% + 空でない集合Xの元$x\数式カンマスペース y$に対して，実数値$d(x\数式カンマスペース y)$が定義され，% \[d(x\数式カンマスペース y)=0\Leftrightarrow x=y\数式カンマスペース\quad(x\数式カンマスペース y)=d(y\数式カンマスペース x)\数式カンマスペース\quad(x\数式カンマスペース y)\leqq d(x\数式カンマスペース y)+d(y\数式カンマスペース x)\]% の三つの性質を満たす$d$をX上の距離といい，$(\text{X}\数式カンマスペース d)$を距離空間という。 % }% @@ -484,7 +509,7 @@ \newcommand{\円}{平面上の一点から等しい距離にある点の集合。}% -\newcommand{\弧}{円周上の二点A\数式カンマスペース Bに対して，A\数式カンマスペース Bによって分けられた円周の各々の部分を弧ABといい，$\overarc{AB}$と表す。}% +\newcommand{\弧}{円周上の二点$\text{A}\数式カンマスペース\text{B}$に対して，A\数式カンマスペース Bによって分けられた円周の各々の部分を弧$\text{AB}$といい，$\overarc{AB}$と表す。}% \newcommand{\弦}{弧の両端を結んだ線分。}% @@ -495,9 +520,9 @@ \NewDocumentCommand{\対頂角}{ m O{i} }% {% - \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{定義}}% {% - \begin{tikzpicture}% + \begin{tikzpicture}% \draw(0,0)--(2,2);% \draw(2,0)--(0,2);% \draw(0,0)coordinate(O);% @@ -512,23 +537,23 @@ 図において，$\angle\mathrm{A}$と$\angle\mathrm{B}$を対頂角という。% }% {\relax}% - \ifthenelse{\equal{#1}{性質}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{性質}}% {対頂角は等しい。}{\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% \begin{tikzpicture}% - \draw(0,0)--(2,2);% - \draw(2,0)--(0,2);% - \draw(0,0)coordinate(O);% - \draw(2,2)coordinate(A);% - \draw(2,0)coordinate(B);% - \draw(0,2)coordinate(C);% - \draw(1,1)coordinate(D);% - \draw pic["A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=A--D--C};% - \draw pic["\,C",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=B--D--A};% - \draw pic["B",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=O--D--B};% - \end{tikzpicture}% + \draw(0,0)--(2,2);% + \draw(2,0)--(0,2);% + \draw(0,0)coordinate(O);% + \draw(2,2)coordinate(A);% + \draw(2,0)coordinate(B);% + \draw(0,2)coordinate(C);% + \draw(1,1)coordinate(D);% + \draw pic["A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=A--D--C};% + \draw pic["\,C",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=B--D--A};% + \draw pic["B",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=O--D--B};% + \end{tikzpicture}% \空行% \[180^\circ =\angle\mathrm{A}+\angle\mathrm{C}\]% \[180^\circ=\angle\mathrm{B}+\angle\mathrm{C}\]% @@ -541,29 +566,29 @@ \NewDocumentCommand{\錯角}{ m O{i} }% {% - \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{定義}}% {% \begin{tikzpicture}% - \draw(-1,-0.5)--(2,1);% - \draw(-1,-1)--(2,-1);% - \draw(0,-2)--(2,2);% - \draw(2,2)coordinate(A);% - \draw(1.3333,0.66666)coordinate(B);% - \draw(2,1)coordinate(C);% - \draw(2,-1)coordinate(D);% - \draw(0.5,-1)coordinate(E);% - \draw(0,-2)coordinate(F);% - \draw(-1,-1)coordinate(G);% - \draw(-1,-0.5)coordinate(H);% - \draw pic["\,A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=E--B--C};% - \draw pic["B\,\,\,",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=B--E--G};% + \draw(-1,-0.5)--(2,1);% + \draw(-1,-1)--(2,-1);% + \draw(0,-2)--(2,2);% + \draw(2,2)coordinate(A);% + \draw(1.3333,0.66666)coordinate(B);% + \draw(2,1)coordinate(C);% + \draw(2,-1)coordinate(D);% + \draw(0.5,-1)coordinate(E);% + \draw(0,-2)coordinate(F);% + \draw(-1,-1)coordinate(G);% + \draw(-1,-0.5)coordinate(H);% + \draw pic["\,A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=E--B--C};% + \draw pic["B\,\,\,",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.3cm] {angle=B--E--G};% \end{tikzpicture} \空行% 図において，$\angle\mathrm{A}$と$\angle\mathrm{B}$を錯角という。% }% {\relax}% - \ifthenelse{\equal{#1}{性質}\AND\equal{#2}{i}}% - {直線$l\数式カンマスペース m$において，錯角が等しい$\Leftrightarrow$直線$l,m$は平行。}{\relax}% + \ifthenelse{\equal{#1}{性質}}% + {直線$l\数式カンマスペース m$において，錯角が等しい$\Leftrightarrow$直線$l\数式カンマスペース m$は平行。}{\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% @@ -607,28 +632,28 @@ \NewDocumentCommand{\同位角}{ m O{i} }% {% - \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{定義}}% {% \begin{tikzpicture}% - \draw(-1,-0.5)--(2,1);% - \draw(-1,-1)--(2,-1);% - \draw(0,-2)--(2,2);% - \draw(2,2)coordinate(A);% - \draw(1.3333,0.66666)coordinate(B);% - \draw(2,1)coordinate(C);% - \draw(2,-1)coordinate(D);% - \draw(0.5,-1)coordinate(E);% - \draw(0,-2)coordinate(F);% - \draw(-1,-1)coordinate(G);% - \draw(-1,-0.5)coordinate(H);% - \draw pic["\,\,A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=C--B--A};% - \draw pic["\,\,B",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=D--E--B};% + \draw(-1,-0.5)--(2,1);% + \draw(-1,-1)--(2,-1);% + \draw(0,-2)--(2,2);% + \draw(2,2)coordinate(A);% + \draw(1.3333,0.66666)coordinate(B);% + \draw(2,1)coordinate(C);% + \draw(2,-1)coordinate(D);% + \draw(0.5,-1)coordinate(E);% + \draw(0,-2)coordinate(F);% + \draw(-1,-1)coordinate(G);% + \draw(-1,-0.5)coordinate(H);% + \draw pic["\,\,A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=C--B--A};% + \draw pic["\,\,B",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=D--E--B};% \end{tikzpicture} \空行% 図において，$\angle\mathrm{A}$と$\angle\mathrm{B}$を同位角という。 }% {\relax}% - \ifthenelse{\equal{#1}{公理}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{公理}}% {直線$l,m$において，同位角が等しい$\Leftrightarrow$直線$l\数式カンマスペース m$は平行。}{\relax}% }% @@ -636,13 +661,12 @@ \NewDocumentCommand{\正弦定理}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {三角形ABCの外接円の半径をRとして，$\bunsuu{a}{\sin\text{A}}=2\text{R}\text{\ （}b\数式カンマスペース\text{B + {$\triangle{\text{ABC}}$の外接円の半径を$R$として，$\bunsuu{a}{\sin\text{A}}=2\text{R}\text{\ （}b\数式カンマスペース\text{B }\数式カンマスペース c\数式カンマスペース\text{Cについても同様に成立}）$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - 三角形ABCの外接円の半径をRとして，% - \[\bunsuu{a}{sin\text{A}}=2\text{R}\]% - ($b,B,c,C$についても同様に成立)% + $\triangle{\text{ABC}}$の外接円の半径を$R$として，% + \[\bunsuu{a}{sin\text{A}}=2R\text{\ （\,$b\数式カンマスペース\text{B}\数式カンマスペース c\数式カンマスペース\text{C}$についても同様に成立）}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明}}% @@ -651,9 +675,9 @@ \空行% \begin{tikzpicture}% \draw(0,1.25)coordinate(A)-- (1,-0.75)coordinate(C)-- (-1,-0.75)coordinate(B);% - \draw pic["A",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=B--A--C};% + \draw pic[draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=B--A--C};% \draw(-1,0.75)coordinate(D);% - \draw pic["D",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=B--D--C};% + \draw pic[draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=B--D--C};% \draw(0,1.25)--(1,-0.75)--(-1,-0.75)--cycle;% \draw(0,1.25)node[above]{A};% \draw(1,-0.75)node[below]{C};% @@ -681,10 +705,10 @@ \NewDocumentCommand{\余弦定理}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {三角形ABCにおいて，$a^2=b^2+c^2-2bc\cos\text{A}$}{\relax}% + {$\triangle{\text{ABC}}$において，$a^2=b^2+c^2-2bc\cos\text{A}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - 三角形ABCにおいて，% + $\triangle{\text{ABC}}$において，% \[a^2=b^2+c^2-2bc\cos\text{A}\]% }% {\relax}% @@ -703,12 +727,12 @@ \draw(1.5,2)coordinate(B);% \draw(1.5,0)--(1.5,2);% \draw pic[draw,black,thin,angle radius=0.3cm] {right angle=A--H--B};% - \draw pic["$A$",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=H--A--B};% + \draw pic[draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=H--A--B};% \end{tikzpicture}% \空行% 図において$\text{BC}=a,\text{CA}=b,\text{AC}=c$として，% \[\text{BH}=c\sin\text{A},\quad\text{AH}=c\cos\text{A}\]% - また，三角形BHCに三平方の定理を用いることにより% + また，$\triangle{\text{BHC}}$に三平方の定理を用いることにより% \[\text{CB}^2=\text{BH}^2+\text{HC}^2\]% ここで，$\text{HC}=\text{AC}-\text{AH}=b-c\cos\text{A},\quad\text{BH}=c\sin\text{A}$より% \begin{align*}% @@ -728,10 +752,10 @@ \NewDocumentCommand{\三角形の面積}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {三角形ABCの面積を$S$として，$S=\bunsuu{1}{2}bc\sin\text{A}$}{\relax}% + {$\triangle{\text{ABC}}$の面積を$S$として，$S=\bunsuu{1}{2}bc\sin\text{A}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - 三角形ABCの面積を$S$として，% + $\triangle{\text{ABC}}$の面積を$S$として，% \[S=\bunsuu{1}{2}bc\sin\text{A}\]% }% {\relax}% @@ -749,12 +773,12 @@ \draw(1.5,2)coordinate(B);% \draw(1.5,0)--(1.5,2);% \draw pic[draw,black,thin,angle radius=0.3cm] {right angle=A--H--B};% - \draw pic["$A$",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=H--A--B};% + \draw pic[draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=H--A--B};% \end{tikzpicture}% \空行% 図において% \[\text{BC}=a\数式カンマスペース\text{CA}=B\数式カンマスペース\text{AC}=c\]% - また，三角形ABCの面積を$S$として$S=\bunsuu{1}{2}\text{AC}\times\text{BH}$と，$AB\sin\text{A}=\text{BH}$から，% + また，$\triangle{\text{ABC}}$の面積を$S$として$S=\bunsuu{1}{2}\text{AC}\times\text{BH}$と，$\text{AB}\sin\text{A}=\text{BH}$から，% \[S=\bunsuu{1}{2}bc\sin\text{A}\]% \証明終了% }% @@ -773,13 +797,13 @@ \ifthenelse{\equal{#1}{補集合の要素の個数}\AND\equal{#2}{b}}% {全体集合を$U$として，\[n\Ttyuukakko{\overline{A}}=n\Ttyuukakko{U}-n\Ttyuukakko{A}\]}{\relax}% \ifthenelse{\equal{#1}{和の法則}\AND\equal{#2}{i}}% - {二つの事象A\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AまたはBの起こる場合の数は$a+b$通り}{\relax}% + {二つの事象$\text{A}$\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AまたはBの起こる場合の数は$a+b$通り}{\relax}% \ifthenelse{\equal{#1}{和の法則}\AND\equal{#2}{b}}% - {二つの事象A\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AまたはBの起こる場合の数は$a+b$通り}{\relax}% + {二つの事象$\text{A}$\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AまたはBの起こる場合の数は$a+b$通り}{\relax}% \ifthenelse{\equal{#1}{積の法則}\AND\equal{#2}{i}}% - {二つの事象A\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AかつBの起こる場合の数は$ab$通り}{\relax}% + {二つの事象$\text{A}$\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AかつBの起こる場合の数は$ab$通り}{\relax}% \ifthenelse{\equal{#1}{積の法則}\AND\equal{#2}{b}}% - {二つの事象A\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AかつBの起こる場合の数は$ab$通り}{\relax}% + {二つの事象$\text{A}$\数式カンマスペース Bにたいして，Aの起こりかたが$a$通り，Bの起こりかたが$b$通りのとき，AかつBの起こる場合の数は$ab$通り}{\relax}% \ifthenelse{\equal{#1}{順列}\AND\equal{#2}{i}}% {異なる$n$個のものから$r$個選んで並べる場合の数は${}_{n}P_{r}=\bunsuu{n!}{\Ttyuukakko{n-r}!}$}{\relax}% \ifthenelse{\equal{#1}{順列}\AND\equal{#2}{b}}% @@ -788,7 +812,7 @@ \[{}_{n}P_{r}=\bunsuu{n!}{\Ttyuukakko{n-r}!}\]% }% {\relax}% - \ifthenelse{\equal{#1}{順列の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{順列の証明}}% {% \証明開始% 異なる$n$個のものから$r$個選んで並べる場合の数は，% @@ -801,7 +825,7 @@ {異なる$n$個のものを円に並べる場合の数は$\Ttyuukakko{n-1}!$}{\relax}% \ifthenelse{\equal{#1}{円順列}\AND\equal{#2}{b}}% {異なる$n$個のものを円に並べる場合の数は\[\Ttyuukakko{n-1}!\]}{\relax}% - \ifthenelse{\equal{#1}{円順列の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{円順列の証明}}% {% \証明開始% $n$個のものを円形に並べるとき，1つを固定して考えると，残り$n-1$個を並べる順列の個数に等しい。よって$\Ttyuukakko{n-1}!$通りとなる。% @@ -819,7 +843,7 @@ \[{}_{n}C_{r}=\bunsuu{n!}{r!\Ttyuukakko{n-r}!}\]% }% {\relax}% - \ifthenelse{\equal{#1}{組み合わせの証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{組み合わせの証明}}% {% \証明開始% 異なる$n$個のものから$r$個選ぶ場合の数は，順列を重複度で割ったものなので% @@ -829,14 +853,14 @@ }% {\relax}% \ifthenelse{\equal{#1}{同じものを含む順列}\AND\equal{#2}{i}}% - {aが$p$個，bが$q$個，cが$r$個，とある時，それら全部を並べる場合の数は，$\bunsuu{n!}{p!q!r!}$（ただし，$p+q+r=n$）}{\relax}% + {$a$が$p$個，$b$が$q$個，$c$が$r$個，とあるとき，それら全部を並べる場合の数は，$\bunsuu{n!}{p!q!r!}$（ただし，$p+q+r=n$）}{\relax}% \ifthenelse{\equal{#1}{同じものを含む順列}\AND\equal{#2}{b}}% {% - aが$p$個，bが$q$個，cが$r$個，とある時，それら全部を並べる場合の数は，% + $a$が$p$個，$b$が$q$個，$c$が$r$個，とあるとき，それら全部を並べる場合の数は，% \[\bunsuu{n!}{p!q!r!}\text{\ （ただし，$p+q+r=n$）}\]% }% {\relax}% - \ifthenelse{\equal{#1}{同じものを含む順列の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{同じものを含む順列の証明}}% {% \証明開始% $n$個のものを並べる場合の数は$n!$通りだが，$n$個の中に同じものが含まれているので，重複度で割ることで$\bunsuu{n!}{p!q!r!}$を得る。% @@ -845,30 +869,30 @@ {\relax}% \ifthenelse{\equal{#1}{確率の定義}\AND\equal{#2}{i}}% - {全事象$U$のどの根元事象も同様に確からしいとき，事象Aの起こる確率は，$P\Ttyuukakko{A}=\bunsuu{n\Ttyuukakko{A}}{n\Ttyuukakko{U}}$}{\relax}% + {全事象$\text{U}$のどの根元事象も同様に確からしいとき，事象$\text{A}$の起こる確率は，$P\Ttyuukakko{A}=\bunsuu{n\Ttyuukakko{A}}{n\Ttyuukakko{U}}$}{\relax}% \ifthenelse{\equal{#1}{確率の定義}\AND\equal{#2}{b}}% {% - 全事象$U$のどの根元事象も同様に確からしいとき，事象Aの起こる確率は，% + 全事象$\text{U}$のどの根元事象も同様に確からしいとき，事象$\text{A}$の起こる確率は，% \[P\Ttyuukakko{A}=\bunsuu{n\Ttyuukakko{A}}{n\Ttyuukakko{U}}\]% }% {\relax}% \ifthenelse{\equal{#1}{排反の定義}\AND\equal{#2}{i}}% - {事象A\数式カンマスペース Bが同時に起こりえないとき}{\relax}% + {事象$\text{A}$\数式カンマスペース$\text{B}$が同時に起こりえないとき，AとBは互いに排反であるという。}{\relax}% \ifthenelse{\equal{#1}{排反の定義}\AND\equal{#2}{b}}% - {事象A\数式カンマスペース Bが同時に起こりえないとき}{\relax}% + {事象$\text{A}$\数式カンマスペース$\text{B}$が同時に起こりえないとき，AとBは互いに排反であるという。}{\relax}% \ifthenelse{\equal{#1}{確率の性質A}\AND\equal{#2}{i}}% - {任意の事象Aに対して，$0\leqq A\leqq1$}{\relax}% + {任意の事象$\text{A}$に対して，$0\leqq A\leqq1$}{\relax}% \ifthenelse{\equal{#1}{確率の性質A}\AND\equal{#2}{b}}% {% - 任意の事象Aに対して，% + 任意の事象$\text{A}$に対して，% \[0\leqq A\leqq1\]% }% {\relax}% \ifthenelse{\equal{#1}{確率の性質B}\AND\equal{#2}{i}}% - {全事象Uの確率$P\Ttyuukakko{U}=1$}{\relax}% + {全事象$\text{U}$の確率$P\Ttyuukakko{U}=1$}{\relax}% \ifthenelse{\equal{#1}{確率の性質B}\AND\equal{#2}{b}}% {% - 全事象Uの確率% + 全事象$\text{U}$の確率% \[P\Ttyuukakko{U}=1\]% }% {\relax}% @@ -881,35 +905,35 @@ \ifthenelse{\equal{#1}{余事象の確率}\AND\equal{#2}{b}}% {\[P\Ttyuukakko{\overline{A}}=1-P\Ttyuukakko{A}\]}{\relax}% \ifthenelse{\equal{#1}{独立な事象の確率}\AND\equal{#2}{i}}% - {事象AとBが独立のとき，事象Aが起こりかつ事象Bが起こる確率$p$は，$p=P\Ttyuukakko{A}P\Ttyuukakko{B}$}{\relax}% + {事象$\text{A}$とBが独立のとき，事象$\text{A}$が起こりかつ事象$\text{B}$が起こる確率$p$は，$p=P\Ttyuukakko{A}P\Ttyuukakko{B}$}{\relax}% \ifthenelse{\equal{#1}{独立な事象の確率}\AND\equal{#2}{b}}% {% - 事象AとBが独立のとき，事象Aが起こりかつ事象Bが起こる確率$p$は，% + 事象$\text{A}$とBが独立のとき，事象$\text{A}$が起こりかつ事象$\text{B}$が起こる確率$p$は，% \[p=P\Ttyuukakko{A}P\Ttyuukakko{B}\]% }% {\relax}% \ifthenelse{\equal{#1}{反復試行の確率}\AND\equal{#2}{i}}% - {一回の試行で事象Aの起こる確率を$p$として，この試行を$n$回行う反復試行でAが$r$回起こる確率は，${}_{n}C_{r}\Ttyuukakko{p}^r\Ttyuukakko{1-p}^{n-r}$}{\relax}% + {一回の試行で事象$\text{A}$の起こる確率を$p$として，この試行を$n$回行う反復試行でAが$r$回起こる確率は，${}_{n}C_{r}\Ttyuukakko{p}^r\Ttyuukakko{1-p}^{n-r}$}{\relax}% \ifthenelse{\equal{#1}{反復試行の確率}\AND\equal{#2}{b}}% {% - 一回の試行で事象Aの起こる確率を$p$として，この試行を$n$回行う反復試行でAが$r$回起こる確率は，% + 一回の試行で事象$\text{A}$の起こる確率を$p$として，この試行を$n$回行う反復試行でAが$r$回起こる確率は，% \[{}_{n}C_{r}\Ttyuukakko{p}^r\Ttyuukakko{1-p}^{n-r}\]% }% {\relax}% - \ifthenelse{\equal{#1}{反復試行の確率の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{反復試行の確率の証明}}% {% \証明開始% - $n$回の試行のうち事象Aが$r$回起こる順番の場合の数は${}_{n} C_{r}$通り。さらに，Aが起こる確率は$p$で$r$回起こり，Aの余事象が起こる確率は$p-1$で$n-r$回起こるので，% + $n$回の試行のうち事象$\text{A}$が$r$回起こる順番の場合の数は${}_{n} C_{r}$通り。さらに，Aが起こる確率は$p$で$r$回起こり，Aの余事象が起こる確率は$p-1$で$n-r$回起こるので，% \[{}_{n}C_{r}\Ttyuukakko{p}^r\Ttyuukakko{1-p}^{n-r}\]% となる。 \証明終了% }% {\relax}% \ifthenelse{\equal{#1}{条件付き確率}\AND\equal{#2}{i}}% - {事象Aが起こったときの事象Bの起こる確率は，$P_{A}\Ttyuukakko{B}=\bunsuu{P\Ttyuukakko{A\cap B}}{P\Ttyuukakko{A}}$}{\relax}% + {事象$\text{A}$が起こったときの事象$\text{B}$の起こる確率は，$P_{A}\Ttyuukakko{B}=\bunsuu{P\Ttyuukakko{A\cap B}}{P\Ttyuukakko{A}}$}{\relax}% \ifthenelse{\equal{#1}{条件付き確率}\AND\equal{#2}{b}}% {% - 事象Aが起こったときの事象Bの起こる確率は，% + 事象$\text{A}$が起こったときの事象$\text{B}$の起こる確率は，% \[P_{A}\Ttyuukakko{B}=\bunsuu{P\Ttyuukakko{A\cap B}}{P\Ttyuukakko{A}}\]% }% {\relax}% @@ -1128,9 +1152,9 @@ \draw(0,0)circle[radius=2];% \end{tikzpicture}% \空行% - 三角形AOP,BOPは二等辺三角形なので，% + $\triangle{\text{AOP}}$\数式カンマスペース$\triangle{\text{BOP}}$は二等辺三角形なので，% \[\angle\mathrm{APO}=\angle\mathrm{OAP}\数式カンマスペース\angle\mathrm{BPO}=\angle\mathrm{OBP}\]% - 三角形の外角より，% + 外角定理より，% \[\angle\mathrm{AOD}=2\angle\mathrm{APO}\数式カンマスペース\angle\mathrm{BOD}=2\angle\mathrm{BPO}\]% \[\Leftrightarrow\angle\mathrm{AOB}=2\angle\mathrm{APB}\]% \空行% @@ -1144,9 +1168,9 @@ \draw(0,0)circle[radius=2];% \end{tikzpicture}% \空行% - 三角形OPBは二等辺三角形なので，% + $\triangle{\text{OPB}}$は二等辺三角形なので，% \[\angle\mathrm{OPB}=\angle\mathrm{OBP}\]% - 三角形の外角より% + 外角定理より% \[\angle\mathrm{AOB}=2\angle\mathrm{OPB}\]% \空行% \begin{tikzpicture}% @@ -1161,15 +1185,13 @@ \draw(0,0)circle[radius=2];% \end{tikzpicture}% \空行% - 三角形QOA,OQBは二等辺三角形なので，% + $\triangle{\text{QOA}}\数式カンマスペース\triangle{\text{OQB}}$は二等辺三角形なので，% \[\angle\mathrm{OQA}=\angle\mathrm{OAQ}\数式カンマスペース\angle\mathrm{OQB}=\angle\mathrm{OBQ}\]% - となる，\par% - 三角形の外角より，% + 外角定理より，% \[\angle\mathrm{OQA}+\angle\mathrm{OAQ}=\angle\mathrm{DOA}\数式カンマスペース\angle\mathrm{OQB}+\angle\mathrm{OBQ}=\angle\mathrm{DOB}\]% \[\Leftrightarrow\angle\mathrm{DOA}-\angle\mathrm{DOB}=2\Ttyuukakko{\angle\mathrm{OQA}-\angle\mathrm{BQO}}\]% \[\Leftrightarrow\angle\mathrm{AOB}=2\angle\mathrm{AQB}\]% - \空行% - 従って，円に内接する三角形について，円周角の$2$倍が中心角である。\par% + 従って，円に内接する三角形について，円周角の$2$倍が中心角である。% \空行% \begin{tikzpicture}% \draw(-1.6,-1.2)--(1.2,-1.6)--(1.2,1.6)--cycle;% @@ -1182,7 +1204,6 @@ \draw(0,0)node[above]{O};% \draw(0,0)circle[radius=2];% \end{tikzpicture}% - \空行% \[\angle\mathrm{APB}=2\angle\mathrm{AOB},\angle\mathrm{AQB}=2\angle\mathrm{AOB}\]% \[\Leftrightarrow\angle\mathrm{AQB}=\angle\mathrm{APB}\]が成立。 \証明終了% @@ -1250,6 +1271,7 @@ \ifthenelse{\equal{#1}{接弦定理の証明}}% {% \証明開始% + \vspace{-1\zw}% \begin{enumerate}% \item 鋭角のとき% \空行% @@ -1270,9 +1292,9 @@ \draw pic[draw,black,thin,angle radius=0.3cm] {right angle=E--B--A};% \end{tikzpicture}% \空行% - 三角形ACBとABEについて円周角の定理より，% + $\triangle{\text{ACB}}$と$\triangle{\text{ABE}}$について円周角の定理より，% \[\angle\mathrm{ACB}=\angle\mathrm{AEB}\]% - ここで，三角形ABEについて% + ここで，$\triangle{\text{ABE}}$について% \[\angle\mathrm{BEA}+\angle\mathrm{BAE}=90^\circ\]% また，ATが円の接線なので$\angle\mathrm{BAE}+\angle\mathrm{BAT}=90^\circ$から，% \[\angle\mathrm{BAT}=\angle\mathrm{AEB}\]% @@ -1314,7 +1336,7 @@ \空行% 鋭角のときの接弦定理より，% \[\angle\mathrm{BCA}=\angle\mathrm{BAS}\]% - また，三角形ABCにおいて% + また，$\triangle{\text{ABC}}$において% \[\angle\mathrm{ABC}=\angle\mathrm{ACB}+\angle\mathrm{BAC}\]% \[\Leftrightarrow\angle\mathrm{ABC}=\angle\mathrm{CAT}\]% \空行% @@ -1376,7 +1398,7 @@ \空行% 円周角の定理より，% \[\angle\mathrm{CAP}=\angle\mathrm{BDP},\quad\angle\mathrm{ACP}=\angle\mathrm{DBP}\]% - 三角形ACPと三角形DBPは相似なので，\par% + $\triangle{\text{ACP}}$と$\triangle{\text{DBP}}$は相似なので，% \[\text{PA}\cdot\text{PB}=\text{PC}\cdot\text{PD}\]% \証明終了% }% @@ -1414,7 +1436,7 @@ \空行% 内接四角形の証明より，% \[\angle\mathrm{CDB}=\angle\mathrm{CAP}\数式カンマスペース\angle\mathrm{DBA}=\angle\mathrm{PCA}\]% - 三角形ACPと三角形DPBは相似なので，% + $\triangle{\text{ACP}}$と$\triangle{\text{DPB}}$は相似なので，% \[\text{PA}\cdot\text{PB}=\text{PC}\cdot\text{PD}\]% \証明終了% }% @@ -1451,7 +1473,7 @@ \空行% 接弦定理より，% \[\angle\mathrm{TBA}=\angle\mathrm{PTA}\]% - これと，$\angle\mathrm{P}$共通なので三角形PTAと三角形PBTは相似より，% + これと，$\angle\mathrm{P}$共通なので$\triangle{\text{PTA}}$と$\triangle{\text{PBT}}$は相似より，% \[\text{PA}\cdot\text{PB}=\text{PT}^2\]% \証明終了% }% @@ -1548,22 +1570,22 @@ \NewDocumentCommand{\相加相乗平均}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {$a>0\数式カンマスペース b>0$のとき，$\bunsuu{a+b}{2}\geqq\sqrt{ab}$}{\relax}% + {$a>0\数式カンマスペース b>0$のとき，$\bunsuu{a+b}{2}\geqq\根号{ab}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% $a>0\数式カンマスペース b>0$のとき，% - \[\bunsuu{a+b}{2}\geqq\sqrt{ab}\]% + \[\bunsuu{a+b}{2}\geqq\根号{ab}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% - $a+b-2\sqrt{ab}\geqq0$を示す。% - \[a+b-2\sqrt{ab}=\Ttyuukakko{\sqrt{a}-\sqrt{b}}^2\]% - より，$\sqrt{a}-\sqrt{b}$は実数なので，% - \[\Ttyuukakko{\sqrt{a}-\sqrt{b}}^2\geqq0\]% + $a+b-2\根号{ab}\geqq0$を示す。% + \[a+b-2\根号{ab}=\Ttyuukakko{\根号{a}-\根号{b}}^2\]% + より，$\根号{a}-\根号{b}$は実数なので，% + \[\Ttyuukakko{\根号{a}-\根号{b}}^2\geqq0\]% よって，$a>0\数式カンマスペース b>0$のとき，% - \[\bunsuu{a+b}{2}\geqq\sqrt{ab}\text{\ （等号成立条件は$a=b$）}\]% + \[\bunsuu{a+b}{2}\geqq\根号{ab}\text{\ （等号成立条件は$a=b$）}\]% \証明終了% }% {\relax}% @@ -1573,9 +1595,9 @@ \NewDocumentCommand{\虚数の定義}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {$i=\sqrt{-1}$}{\relax}% + {$i=\根号{-1}$}{\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% - {\[i=\sqrt{-1}\]}{\relax}% + {\[i=\根号{-1}\]}{\relax}% }% @@ -1623,9 +1645,10 @@ \[\alpha\beta=\bunsuu{c}{a}\]% }% {\relax}% - \ifthenelse{\equal{#1}{二次方程式の解と係数の関係の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{二次方程式の解と係数の関係の証明}}% {% \証明開始% + \vspace{-2.5\zw}% \[ax^2+bx+c=a\Ttyuukakko{x-\alpha}\Ttyuukakko{x-\beta}=a\Tdaikakko{x^2-\Ttyuukakko{\alpha+\beta}x+\alpha\beta}\]% \[\Leftrightarrow ax^2+bx+c=a\Ttyuukakko{x^2+\bunsuu{b}{a}x+\bunsuu{c}{a}}\]% 係数比較することで，% @@ -1657,10 +1680,10 @@ \[\alpha\beta\gamma=-\bunsuu{d}{a}\]% }% {\relax}% - \ifthenelse{\equal{#1}{三次方程式の解と係数の関係の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{三次方程式の解と係数の関係の証明}}% {% \証明開始% - \vspace{-1\zw} + \vspace{-2.5\zw}% \[ax^{3}+bx^2+cx+d=a\Ttyuukakko{x-\alpha}\Ttyuukakko{x-\beta}\Ttyuukakko{x-\gamma}=a\Tdaikakko{x^3-\Ttyuukakko{\alpha+\beta+\gamma}x^2+\Ttyuukakko{\alpha\beta+\beta\gamma+\gamma\alpha}x-\alpha\beta\gamma}\]% \[\Leftrightarrow ax^{3}+bx^2+cx+d=a\Ttyuukakko{x^3+\bunsuu{b}{a}x^2+\bunsuu{c}{a}x+\bunsuu{d}{a}}\]% 係数比較することで，\par% @@ -1732,48 +1755,49 @@ \NewDocumentCommand{\点の座標}{ m O{i} }% {% \ifthenelse{\equal{#1}{二点間の距離}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$間の距離は，$\sqrt{\Ttyuukakko{x_{2}-x_{1}}^2-\Ttyuukakko{y_{2}-y_{1}}^2}$}{\relax}% + {$\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$間の距離は，$\根号{\Ttyuukakko{x_{2}-x_{1}}^2-\Ttyuukakko{y_{2}-y_{1}}^2}$}{\relax}% \ifthenelse{\equal{#1}{二点間の距離}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$間の距離は，% - \[\sqrt{\Ttyuukakko{x_{2}-x_{1}}^2-\Ttyuukakko{y_{2}-y_{1}}^2}\]% + $\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$間の距離は，% + \[\根号{\Ttyuukakko{x_{2}-x_{1}}^2-\Ttyuukakko{y_{2}-y_{1}}^2}\]% }% {\relax}% \ifthenelse{\equal{#1}{内分点の座標}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$を$m:n$に内分する点の座標は，$\Ttyuukakko{\bunsuu{nx_{1}+mx_{2}}{n+m}\数式カンマスペース\bunsuu{ny_{1}+my_{2}}{n+m}}$}{\relax}% + {$\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$を$m:n$に内分する点の座標は，$\Ttyuukakko{\bunsuu{nx_{1}+mx_{2}}{n+m}\数式カンマスペース\bunsuu{ny_{1}+my_{2}}{n+m}}$}{\relax}% \ifthenelse{\equal{#1}{内分点の座標}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$を$m:n$に内分する点の座標は，% + $\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$を$m:n$に内分する点の座標は，% \[\Ttyuukakko{\bunsuu{nx_{1}+mx_{2}}{n+m}\数式カンマスペース\bunsuu{ny_{1}+my_{2}}{n+m}}\]% }% {\relax}% - \ifthenelse{\equal{#1}{内分点の座標の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{内分点の座標の証明}}% {% \証明開始% - $m:n$に内分する点の座標を$P\Ttyuukakko{x\数式カンマスペース y}$として，% + $m:n$に内分する点の座標を$\text{P}\Ttyuukakko{x\数式カンマスペース y}$として，% \[m:n=x-x_{1}:x_{2}-x\]% \[\Leftrightarrow\Ttyuukakko{\bunsuu{nx_{1}+mx_{2}}{n+m}\数式カンマスペース\bunsuu{ny_{1}+my_{2}}{n+m}}\]% \証明終了% }% {\relax}% \ifthenelse{\equal{#1}{外分点の座標}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$を$m:n$に外分する点の座標は，$\Ttyuukakko{\bunsuu{-nx_{1}+mx_{2}}{m-n}\数式カンマスペース \bunsuu{-ny_{1}+my_{2}}{m-n}}$}{\relax}% + {$\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$を$m:n$に外分する点の座標は，$\Ttyuukakko{\bunsuu{-nx_{1}+mx_{2}}{m-n}\数式カンマスペース \bunsuu{-ny_{1}+my_{2}}{m-n}}$}{\relax}% \ifthenelse{\equal{#1}{外分点の座標}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$を$m:n$に外分する点の座標は，% + $\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$を$m:n$に外分する点の座標は，% \[\Ttyuukakko{\bunsuu{-nx_{1}+mx_{2}}{m-n}\数式カンマスペース \bunsuu{-ny_{1}+my_{2}}{m-n}}\]% }% {\relax}% - \ifthenelse{\equal{#1}{外分点の座標の証明}\AND\equal{#2}{b}}% + \ifthenelse{\equal{#1}{外分点の座標の証明}}% {% \証明開始% + \vspace{-1\zw}% \begin{enumerate}% \item $m>n$のとき\par% - $n:m$に外分する点の座標を$P\Ttyuukakko{x\数式カンマスペース y}$として，% + $n:m$に外分する点の座標を$\text{P}\Ttyuukakko{x\数式カンマスペース y}$として，% \[m:n=x-x_{1}:x-x_{2}\]% \[\Leftrightarrow\Ttyuukakko{\bunsuu{-nx_{1}+mx_{2}}{m-n}\数式カンマスペース \bunsuu{-ny_{1}+my_{2}}{m-n}}\]% \item $m<n$のとき\par% - $n:m$に外分する点の座標を$P\Ttyuukakko{x\数式カンマスペース y}$として，% + $n:m$に外分する点の座標を$\text{P}\Ttyuukakko{x\数式カンマスペース y}$として，% \[m:n=x-x_{2}:x-x_{1}\]% \[\Leftrightarrow\Ttyuukakko{\bunsuu{-nx_{1}+mx_{2}}{m-n}\数式カンマスペース \bunsuu{-ny_{1}+my_{2}}{m-n}}\]% \end{enumerate}% @@ -1784,14 +1808,14 @@ }% {\relax}% \ifthenelse{\equal{#1}{中点の座標}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$の中点は，$\Ttyuukakko{\bunsuu{x_{1}+x_{2}}{2}\数式カンマスペース\bunsuu{y_{1}+y_{2}}{2}}$}{\relax}% + {$\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$の中点は，$\Ttyuukakko{\bunsuu{x_{1}+x_{2}}{2}\数式カンマスペース\bunsuu{y_{1}+y_{2}}{2}}$}{\relax}% \ifthenelse{\equal{#1}{中点の座標}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$AB$の中点は，% + $\text{A}\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース \text{B}\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}$として，線分$\text{AB}$の中点は，% \[\Ttyuukakko{\bunsuu{x_{1}+x_{2}}{2}\数式カンマスペース\bunsuu{y_{1}+y_{2}}{2}}\]% }% {\relax}% - \ifthenelse{\equal{#1}{中点の座標の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{中点の座標の証明}}% {% \証明開始% 内分点の公式において$m=n$のとき，% @@ -1800,14 +1824,14 @@ }% {\relax}% \ifthenelse{\equal{#1}{重心の座標}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}\数式カンマスペース C\Ttyuukakko{x_{3}\数式カンマスペース y_{3}}$として，三角形$ABC$の重心の座標は，$\Ttyuukakko{\bunsuu{x_{1}+x_{2}+x_{3}}{3}\数式カンマスペース\bunsuu{y_{1}+y_{2}+y_{3}}{3}}$}{\relax}% + {$A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}\数式カンマスペース C\Ttyuukakko{x_{3}\数式カンマスペース y_{3}}$として，$\triangle{\text{ABC}}$の重心の座標は，$\Ttyuukakko{\bunsuu{x_{1}+x_{2}+x_{3}}{3}\数式カンマスペース\bunsuu{y_{1}+y_{2}+y_{3}}{3}}$}{\relax}% \ifthenelse{\equal{#1}{重心の座標}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}\数式カンマスペース C\Ttyuukakko{x_{3}\数式カンマスペース y_{3}}$として，三角形$ABC$の重心の座標は，% + $A\Ttyuukakko{x_{1}\数式カンマスペース y_{1}}\数式カンマスペース B\Ttyuukakko{x_{2}\数式カンマスペース y_{2}}\数式カンマスペース C\Ttyuukakko{x_{3}\数式カンマスペース y_{3}}$として，$\triangle{\text{ABC}}$の重心の座標は，% \[\Ttyuukakko{\bunsuu{x_{1}+x_{2}+x_{3}}{3}\数式カンマスペース\bunsuu{y_{1}+y_{2}+y_{3}}{3}}\]% }% {\relax}% - \ifthenelse{\equal{#1}{重心の座標の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{重心の座標の証明}}% {% \証明開始% $A$と$B$の中点$M$の座標は$\Ttyuukakko{\bunsuu{x_{1}+x_{2}}{2}\数式カンマスペース\bunsuu{y_{1}+y_{2}}{2}}$\par% @@ -1844,7 +1868,7 @@ \ifthenelse{\equal{#1}{公式Bの証明}}% {% \証明開始% - 傾き$m$なので，$y=mx+a$と置ける（$a$は切片）。\par% + 傾き$m$なので，$y=mx+a$と置ける（\,$a$は切片）。\par% ここで，$\Ttyuukakko{x_{1\数式カンマスペース x_{2}}}$を通るので，$y_{1}=mx_{1}+a$となり，連立することで% \[y-y_{1}=m\Ttyuukakko{x-x_{1}}\]% を得る。% @@ -1872,7 +1896,7 @@ \[\Leftrightarrow m_{1}m_{2}=-1\]% }% {\relax}% - \ifthenelse{\equal{#1}{公式Bの証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{公式Bの証明}}% {% \証明開始% $y=mx_{1}$上に点A$\Ttyuukakko{1\数式カンマスペース m_{1}}$\数式カンマスペース $y=mx_{2}$上にB$\Ttyuukakko{-m_{1}\数式カンマスペース 1}$をとる。\par% @@ -1888,12 +1912,12 @@ {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% {% - 点$\Ttyuukakko{x_{1}\数式カンマスペース y_{2}}$と直線$ax+bx+c=0$の距離は，$\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\sqrt{a^2+b^2}}$% + 点$\Ttyuukakko{x_{1}\数式カンマスペース y_{2}}$と直線$ax+bx+c=0$の距離は，$\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\根号{a^2+b^2}}$% }{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% 点$\Ttyuukakko{x_{1}\数式カンマスペース y_{2}}$と直線$ax+bx+c=0$の距離は，% - \[\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\sqrt{a^2+b^2}}\]% + \[\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\根号{a^2+b^2}}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明}}% @@ -1901,14 +1925,15 @@ \証明開始% 全体を$x$軸方向に$-x_{1}$\数式カンマスペース $y$軸方向に$-y_{1}$平行移動するとき，直線$l$は$a\Ttyuukakko{x+x_{1}}+b\Ttyuukakko{y+y_{1}}+c=0$となる。\par% また，直線$l$に原点Oからおろした垂線との交点をHとする。ここでOH間の距離を$d$と置くと，% + \vspace{-1\zw}% \begin{enumerate}% \item $a\neq0$のとき\par% 直線$l$の垂線の傾きは$b$の値に依らず，$y=\bunsuu{b}{a}$となる。\par% よって，Hの座標は二式を連立することで得られ，% \[\Ttyuukakko{\bunsuu{-a\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}\数式カンマスペース\bunsuu{-b\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}}\]% \begin{align*}% - \Leftrightarrow d&=\sqrt{\Tdaikakko{\Ttyuukakko{\bunsuu{-a\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}}^2+\Tdaikakko{\bunsuu{-b\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}}}^2}&\\% - &=\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\sqrt{a^2+b^2}} % + \Leftrightarrow d&=\根号{\Tdaikakko{\Ttyuukakko{\bunsuu{-a\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}}^2+\Tdaikakko{\bunsuu{-b\Ttyuukakko{ax_{1}+by_{1}+c}}{a^2+b^2}}}^2}&\\% + &=\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\根号{a^2+b^2}} % \end{align*}% \item $a=0$のとき\par% 直線$l$は$y=-\bunsuu{by_{1}+c}{b}$となるので，% @@ -1916,10 +1941,10 @@ d&=\Tzettaiti{-\bunsuu{by_{1}+c}{b}}&\\% &=\bunsuu{\Tzettaiti{by_{1}+c}}{\Tzettaiti{b}}&\\% \end{align*}% - これは，$\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\sqrt{a^2+b^2}}$に$a=0$を代入したものである。 + これは，$\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\根号{a^2+b^2}}$に$a=0$を代入したものである。 \end{enumerate}% よって，いずれの場合も% - \[\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\sqrt{a^2+b^2}}\]% + \[\bunsuu{\Tzettaiti{ax_{1}+by_{2}+c}}{\根号{a^2+b^2}}\]% を得る。% \証明終了% }% @@ -1930,8 +1955,8 @@ \NewDocumentCommand{\円の方程式}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {中心$\Ttyuukakko{a\数式カンマスペース b}$で半径$r$の円は，$\Ttyuukakko{x-a}^2+\Ttyuukakko{y-b}^2=r^2$と表す（$x^2+y^2+Ax+By+C=0\Ttyuukakko{l^2+m^2-4n>0}$の形でもよい）。}{\relax}% - \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% + {中心$\Ttyuukakko{a\数式カンマスペース b}$で半径$r$の円は，$\Ttyuukakko{x-a}^2+\Ttyuukakko{y-b}^2=r^2$と表す（\,$x^2+y^2+Ax+By+C=0\Ttyuukakko{A^2+B^2-4C>0}$の形でもよい）。}{\relax}% + \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% 中心$\Ttyuukakko{a\数式カンマスペース b}$で半径$r$の円は，% \[\Ttyuukakko{x-a}^2+\Ttyuukakko{y-b}^2=r^2\]% @@ -1943,7 +1968,7 @@ \ifthenelse{\equal{#1}{証明}}% {% \証明開始% - 円の中心をO\数式カンマスペース 円周上の任意の点を$P\Ttyuukakko{x\数式カンマスペース y}$として，三平方の定理より% + 円の中心をO\数式カンマスペース 円周上の任意の点を$\text{P}\Ttyuukakko{x\数式カンマスペース y}$として，三平方の定理より% \[\Ttyuukakko{x-a}^2+\Ttyuukakko{y-b}^2=r^2\]% \証明終了% }% @@ -1964,15 +1989,16 @@ \ifthenelse{\equal{#1}{証明}}% {% \証明開始% + \vspace{-1\zw}% \begin{enumerate}% \item $x_{0}\neq0\数式カンマスペース y_{0}\neq0$のとき\par% $A\Ttyuukakko{x_{0}\数式カンマスペース y_{0}}$と置いて，OAの傾きは$\bunsuu{y_{0}}{x_{0}}$となる。接線の傾きはこれに垂直なので，$-\bunsuu{x_{0}}{y_{0}}$また接線は点$\Ttyuukakko{x_{0}\数式カンマスペース y_{0}}$を通るので% \[y=-\bunsuu{x_{0}}{y_{0}}\Ttyuukakko{x-x_{0}}+y_{0}\]% より，$\Ttyuukakko{x_{0}\数式カンマスペース y_{0}}$が$x^2+y^2=r^2$上に存在することに留意して，$x_{0}x+y_{0}y=r^2$となる。\par% \item $x_{0}\neq0$のとき\par% - $y_{0}=\pm r$より接線は$y=\pm r\text{\ （複合同順）}$\par% + $y_{0}=\pm r$より接線は$y=\pm r\text{\ （複号同順）}$\par% \item $y_{0}=0$のとき\par% - $x_{0}=\pm r$より接線は$x=\pm r\text{\ （複合同順）}$% + $x_{0}=\pm r$より接線は$x=\pm r\text{\ （複号同順）}$% \end{enumerate}% よって，接線の方程式は% \[xx_{1}+yy_{1}=r^2\]% @@ -2103,17 +2129,17 @@ \NewDocumentCommand{\三角関数の加法定理}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$\sin\Ttyuukakko{\alpha\pm\beta}=\sin\alpha \cos\beta\pm \cos\alpha \sin\beta$}{\relax}% + {$\sin\Ttyuukakko{\alpha\pm\beta}=\sin\alpha \cos\beta\pm \cos\alpha \sin\beta\text{\ （複号同順）}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% - {\[\sin\Ttyuukakko{\alpha\pm\beta}=\sin\alpha \cos\beta\pm \cos\alpha \sin\beta\]}{\relax}% + {\[\sin\Ttyuukakko{\alpha\pm\beta}=\sin\alpha \cos\beta\pm \cos\alpha \sin\beta\text{\ （複号同順）}\]}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$\cos\Ttyuukakko{\alpha\pm\beta}=\cos\alpha \cos\beta\mp \sin\alpha \sin\beta$}{\relax}% + {$\cos\Ttyuukakko{\alpha\pm\beta}=\cos\alpha \cos\beta\mp \sin\alpha \sin\beta\text{\ （複号同順）}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% - {\[\cos\Ttyuukakko{\alpha\pm\beta}=\cos\alpha \cos\beta\mp \sin\alpha \sin\beta\]}{\relax}% + {\[\cos\Ttyuukakko{\alpha\pm\beta}=\cos\alpha \cos\beta\mp \sin\alpha \sin\beta\]\text{\ （複号同順）}}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}$}{\relax}% + {$\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}\text{\ （複号同順）}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% - {\[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}\]}{\relax}% + {\[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}\text{\ （複号同順）}\]}{\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% @@ -2137,7 +2163,7 @@ \draw pic["$\beta$",draw=black,-,thin,angle eccentricity=1.4,angle radius=0.4cm] {angle=R--O--Q};% \end{tikzpicture}% \空行% - 図において，三角関数の性質より$\cos\Ttyuukakko{\beta-\alpha}=\cos\Ttyuukakko{\alpha-\beta}$なので，三角形QOPについて余弦定理より% + 図において，三角関数の性質より$\cos\Ttyuukakko{\beta-\alpha}=\cos\Ttyuukakko{\alpha-\beta}$なので，$\triangle{\text{QOP}}$について余弦定理より% \[\mathrm{QP}^2=1^2+1^2-2\cdot1\cdot1\cdot\cos\Ttyuukakko{\alpha-\beta}\]% また，QP間の距離について三平方の定理を用いて% \[\mathrm{QP}^2=\Ttyuukakko{\cos\beta-\cos\alpha}^2+\Ttyuukakko{\sin\alpha-\sin\beta}^2\]% @@ -2155,9 +2181,9 @@ \[\sin\Ttyuukakko{\alpha-\beta}=\sin\alpha \cos\beta-\cos\alpha \sin\beta\]% \空行% $\tan\theta=\bunsuu{\sin\theta}{\cos\theta}$より，% - \[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\sin\alpha \cos\beta\pm \cos\alpha \sin\beta}{\cos\alpha \cos\beta\mp \sin\alpha \sin\beta}\]% + \[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\sin\alpha \cos\beta\pm \cos\alpha \sin\beta}{\cos\alpha \cos\beta\mp \sin\alpha \sin\beta}\text{\ （複号同順）}\]% 両辺を$\cos\alpha\cos\beta$でわることで，% - \[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}\]% + \[\tan\Ttyuukakko{\alpha\pm\beta}=\bunsuu{\tan\alpha \pm \tan\beta}{1\mp \tan\alpha \tan\beta}\text{\ （複号同順）}\]% を得る。% \証明終了% }% @@ -2184,20 +2210,26 @@ \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {\[\cos2\alpha=1-2\sin^{2}\alpha\]}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{i}}% - {$\tan2\alpha=\frac{2\tan\alpha}{1-\tan^{2}\alpha}$}{\relax}% + {$\tan2\alpha=\bunsuu{2\tan\alpha}{1-\tan^{2}\alpha}$}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{b}}% - {\[\tan2\alpha=\frac{2\tan\alpha}{1-\tan^{2}\alpha}\]}{\relax}% + {\[\tan2\alpha=\bunsuu{2\tan\alpha}{1-\tan^{2}\alpha}\]}{\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% - 三角関数の加法定理\par% - \[\sin\Ttyuukakko{\alpha+\beta}=\sin\alpha \cos\beta+ \cos\alpha \sin\beta\]% - \[\cos\Ttyuukakko{\alpha+\beta}=\cos\alpha \cos\beta- \sin\alpha \sin\beta\]% - \[\tan\Ttyuukakko{\alpha+\beta}=\bunsuu{\tan\alpha + \tan\beta}{1- \tan\alpha \tan\beta}\]% - において，$\alpha=\beta=\theta$として，% - \[\sin2\theta=2\sin\theta\cos\theta\]% - \[\cos2\theta=\cos^{2}\theta-\sin^{2}\theta\]% - \[\tan2\theta=\bunsuu{2\tan\theta}{1-\tan^{2}\theta}\]% + 三角関数の加法定理% + \phrases@math[c]% + {% + $\sin\Ttyuukakko{\alpha+\beta}=\sin\alpha \cos\beta+\cos\alpha \sin\beta$\\% + $\cos\Ttyuukakko{\alpha+\beta}=\cos\alpha \cos\beta-\sin\alpha \sin\beta$\\% + $\tan\Ttyuukakko{\alpha+\beta}=\bunsuu{\tan\alpha+\tan\beta}{1-\tan\alpha \tan\beta}$% + }% + において，$\alpha=\beta=\theta$として，\par% + \hspace{3\zw}\phrases@math[c]% + {% + $\sin2\theta=2\sin\theta\cos\theta$\\% + $\cos2\theta=\cos^{2}\theta-\sin^{2}\theta$\\% + $\tan2\theta=\bunsuu{2\tan\theta}{1-\tan^{2}\theta}$% + }% を得る。\par% また，$\cos2\theta=\cos^{2}\theta-\sin^{2}\theta$において，三角関数の相互関係$\sin^2\theta+\cos^2\theta=1$を用いて，% \[\cos2\theta=2\cos^{2}\theta-1\]% @@ -2321,10 +2353,25 @@ \NewDocumentCommand{\三角関数の合成}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {$a\sin\theta+b\cos\theta=\sqrt{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\text{\ （ただし，$\sin\alpha=\bunsuu{b}{\sqrt{a^2+b^2}}\数式カンマスペース\cos\alpha=\bunsuu{a}{\sqrt{a^2+b^2}}$）}$}{\relax}% + {% + $% + a\sin\theta+b\cos\theta=\根号{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\ % + \Ttyuukakko% + {% + \text% + {% + ただし，% + $% + \sin\alpha=\bunsuu{b}{\根号{a^2+b^2}}\数式カンマスペース\cos\alpha=\bunsuu{a}{\根号{a^2+b^2}}% + $% + }% + }% + $% + }% + {\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - \[a\sin\theta+b\cos\theta=\sqrt{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\text{\ （ただし，$\sin\alpha=\bunsuu{b}{\sqrt{a^2+b^2}}\数式カンマスペース\cos\alpha=\bunsuu{a}{\sqrt{a^2+b^2}}$）}\]% + \[a\sin\theta+b\cos\theta=\根号{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\text{\ $\Ttyuukakko{\text{ただし，$\sin\alpha=\bunsuu{b}{\根号{a^2+b^2}}\数式カンマスペース\cos\alpha=\bunsuu{a}{\根号{a^2+b^2}}$}}$}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明}}% @@ -2332,9 +2379,9 @@ \証明開始% 三角関数の加法定理\par% $\sin\Ttyuukakko{\alpha+\beta}=\sin\alpha \cos\beta+ \cos\alpha \sin\beta$について，% - \[\bunsuu{a}{\sqrt{a^2+b^2}}=\cos\alpha\数式カンマスペース\bunsuu{b}{\sqrt{a^2+b^2}}=\sin\alpha\]% + \[\bunsuu{a}{\根号{a^2+b^2}}=\cos\alpha\数式カンマスペース\bunsuu{b}{\根号{a^2+b^2}}=\sin\alpha\]% とすることで，\par% - \[a\sin\theta+b\cos\theta=\sqrt{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\]% + \[a\sin\theta+b\cos\theta=\根号{a^2+b^2}\sin\Ttyuukakko{\theta+\alpha}\]% となる。% \証明終了% }% @@ -2345,19 +2392,19 @@ \NewDocumentCommand{\有理数の指数}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$a>0$また$m\数式カンマスペース n$が正の整数，$r$が正の有理数のとき，$a^{\bunsuu{m}{n}}=\sqrt[n]{a^{m}}$}{\relax}% + {$a>0$また$m\数式カンマスペース n$が正の整数，$r$が正の有理数のとき，$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% $a>0$また$m\数式カンマスペース n$が正の整数，$r$が正の有理数のとき，% - \[a^{\bunsuu{m}{n}}=\sqrt[n]{a^{m}}\]% + \[a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$a>0$また$n$が正の整数のとき，$a^{\bunsuu{1}{n}}=\sqrt[n]{a}$}{\relax}% + {$a>0$また$n$が正の整数のとき，$a^{\frac{1}{n}}=\根号[n]{a}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% $a>0$また$n$が正の整数のとき，% - \[a^{\bunsuu{1}{n}}=\sqrt[n]{a}\]% + \[a^{\frac{1}{n}}=\根号[n]{a}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% @@ -2420,13 +2467,13 @@ {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% {% - $a>0\数式カンマスペース b>0$また，$r\数式カンマスペース s$は有理数とする。\par% + $a>0\数式カンマスペース b>0$で，$r\数式カンマスペース s$は有理数とする。\par% $a^{p}=M$ならば，$\log_{a}M$，$\log_{a}M \log_{a}M$ならば，$a^{p}=M$% }% {\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% - $a>0\数式カンマスペース b>0$また，$r\数式カンマスペース s$は有理数とする。\par% + $a>0\数式カンマスペース b>0$で，$r\数式カンマスペース s$は有理数とする。\par% $a^{p}=M$ならば，$\log_{a}M$\par% $\log_{a}M$ならば，$a^{p}=M$% }% @@ -2612,12 +2659,11 @@ \NewDocumentCommand{\不定積分の定義}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {$F'\Ttyuukakko{x}=f\Ttyuukakko{x}$のとき，$\int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C$($C$は積分定数)}{\relax}% + {$F'\Ttyuukakko{x}=f\Ttyuukakko{x}$のとき，$\displaystyle\int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\text{（$C$は積分定数）}$}{\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% $F'\Ttyuukakko{x}=f\Ttyuukakko{x}$のとき，% - \[\int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\]% - ($C$は積分定数)% + \[\int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\text{\ （\,$C$は積分定数）}\]% }% {\relax}% }% @@ -2626,10 +2672,10 @@ \NewDocumentCommand{\べき乗関数の不定積分}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {$\int_{}^{} x^{n}dx=\bunsuu{1}{n+1}x^{n+1}+C\text{\ （$C$は積分定数）}$}{\relax}% + {$\displaystyle\int_{}^{} x^{n}dx=\bunsuu{1}{n+1}x^{n+1}+C\text{\ （\,$C$は積分定数）}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - \[\int_{}^{} x^{n}dx=\bunsuu{1}{n+1}x^{n+1}+C\text{\ （$C$は積分定数）}\]% + \[\int_{}^{} x^{n}dx=\bunsuu{1}{n+1}x^{n+1}+C\text{\ （\,$C$は積分定数）}\]% }% {\relax}% }% @@ -2638,15 +2684,15 @@ \NewDocumentCommand{\不定積分の性質}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$\displaystyle \int_{}^{} kf\Ttyuukakko{x}dx=k\displaystyle \int_{}^{} f\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{}^{} kf\Ttyuukakko{x}dx=k\displaystyle \int_{}^{} f\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {\[\int_{}^{} kf\Ttyuukakko{x}dx=k\int_{}^{} f\Ttyuukakko{x}dx\]}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$\displaystyle \int_{}^{} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\displaystyle \int_{}^{} f\Ttyuukakko{x}dx\pm\displaystyle \int_{}^{} g\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{}^{} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\displaystyle \int_{}^{} f\Ttyuukakko{x}dx\pm\displaystyle \int_{}^{} g\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {\[\int_{}^{} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\int_{}^{} f\Ttyuukakko{x}dx\pm\int_{}^{} g\Ttyuukakko{x}dx\]}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\displaystyle \int_{}^{} {kf\Ttyuukakko{x}+lg\Ttyuukakko{x}}dx=k\displaystyle \int_{}^{} f\Ttyuukakko{x}dx+l\displaystyle \int_{}^{} g\Ttyuukakko{x}$}{\relax}% + {$\displaystyle\int_{}^{} {kf\Ttyuukakko{x}+lg\Ttyuukakko{x}}dx=k\displaystyle \int_{}^{} f\Ttyuukakko{x}dx+l\displaystyle \int_{}^{} g\Ttyuukakko{x}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% {\[\int_{}^{} {kf\Ttyuukakko{x}+lg\Ttyuukakko{x}}dx=k\int_{}^{} f\Ttyuukakko{x}dx+l\int_{}^{} g\Ttyuukakko{x}\]}{\relax}% }% @@ -2668,23 +2714,23 @@ \NewDocumentCommand{\定積分の性質}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$\int_{b}^{a} kf\Ttyuukakko{x}dx=k\int_{b}^{a} f\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{b}^{a} kf\Ttyuukakko{x}dx=k\int_{b}^{a} f\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {\[\int_{b}^{a} kf\Ttyuukakko{x}dx=k\int_{b}^{a} f\Ttyuukakko{x}dx\]}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$\int_{b}^{a} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\int_{b}^{a} f\Ttyuukakko{x}dx\pm\int_{b}^{a} g\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{b}^{a} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\int_{b}^{a} f\Ttyuukakko{x}dx\pm\int_{b}^{a} g\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {\[\int_{b}^{a} {f\Ttyuukakko{x}\pm g\Ttyuukakko{x}}dx=\int_{b}^{a} f\Ttyuukakko{x}dx\pm\int_{b}^{a} g\Ttyuukakko{x}dx\]}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\int_{a}^{a} f\Ttyuukakko{x}dx=0$}{\relax}% + {$\displaystyle\int_{a}^{a} f\Ttyuukakko{x}dx=0$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% {\[\int_{a}^{a} f\Ttyuukakko{x}dx=0\]}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {$\int_{b}^{a} f\Ttyuukakko{x}dx=-\int_{a}^{b} f\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{b}^{a} f\Ttyuukakko{x}dx=-\int_{a}^{b} f\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {\[\int_{b}^{a} f\Ttyuukakko{x}dx=-\int_{a}^{b} f\Ttyuukakko{x}dx\]}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{i}}% - {$\int_{b}^{a} f\Ttyuukakko{x}dx=\int_{a}^{c} f\Ttyuukakko{x}dx+\int_{c}^{b} f\Ttyuukakko{x}dx$}{\relax}% + {$\displaystyle\int_{b}^{a} f\Ttyuukakko{x}dx=\int_{a}^{c} f\Ttyuukakko{x}dx+\int_{c}^{b} f\Ttyuukakko{x}dx$}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{b}}% {\[\int_{b}^{a} f\Ttyuukakko{x}dx=\int_{a}^{c} f\Ttyuukakko{x}dx+\int_{c}^{b} f\Ttyuukakko{x}dx\]}{\relax}% }% @@ -2693,84 +2739,84 @@ \NewDocumentCommand{\ベクトルの演算}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$k\数式カンマスペース l$が実数のとき，$\vec{a}+\vec{b}=\vec{b}+\vec{a}$}{\relax}% + {$k\数式カンマスペース l$が実数のとき，$\ベクトル{a}+\ベクトル{b}=\ベクトル{b}+\ベクトル{a}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% $k\数式カンマスペース l$が実数のとき% - \[\vec{a}+\vec{b}=\vec{b}+\vec{a}\]% + \[\ベクトル{a}+\ベクトル{b}=\ベクトル{b}+\ベクトル{a}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$k\数式カンマスペース l$が実数のとき，$\Ttyuukakko{\vec{a}+\vec{b}}+\vec{c}=\vec{a}+\Ttyuukakko{\vec{b}+\vec{c}}$}{\relax}% + {$k\数式カンマスペース l$が実数のとき，$\Ttyuukakko{\ベクトル{a}+\ベクトル{b}}+\ベクトル{c}=\ベクトル{a}+\Ttyuukakko{\ベクトル{b}+\ベクトル{c}}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% $k\数式カンマスペース l$が実数のとき% - \[\Ttyuukakko{\vec{a}+\vec{b}}+\vec{c}=\vec{a}+\Ttyuukakko{\vec{b}+\vec{c}}\]% + \[\Ttyuukakko{\ベクトル{a}+\ベクトル{b}}+\ベクトル{c}=\ベクトル{a}+\Ttyuukakko{\ベクトル{b}+\ベクトル{c}}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\vec{a}+\Ttyuukakko{a\vec{a}}=\vec{0}$}{\relax}% + {$\ベクトル{a}+\Ttyuukakko{a\ベクトル{a}}=\ベクトル{0}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% - {\[\vec{a}+\Ttyuukakko{a\vec{a}}=\vec{0}\]}{\relax}% + {\[\ベクトル{a}+\Ttyuukakko{a\ベクトル{a}}=\ベクトル{0}\]}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {$\vec{a}+\vec{0}=\vec{a}$}{\relax}% + {$\ベクトル{a}+\ベクトル{0}=\ベクトル{a}$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% - {\[\vec{a}+\vec{0}=\vec{a}\]}{\relax}% + {\[\ベクトル{a}+\ベクトル{0}=\ベクトル{a}\]}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{i}}% - {$\vec{a}-\vec{b}=\vec{a}+\Ttyuukakko{-\vec{b}}$}{\relax}% + {$\ベクトル{a}-\ベクトル{b}=\ベクトル{a}+\Ttyuukakko{-\ベクトル{b}}$}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{b}}% - {\[\vec{a}-\vec{b}=\vec{a}+\Ttyuukakko{-\vec{b}}\]}{\relax}% + {\[\ベクトル{a}-\ベクトル{b}=\ベクトル{a}+\Ttyuukakko{-\ベクトル{b}}\]}{\relax}% \ifthenelse{\equal{#1}{公式F}\AND\equal{#2}{i}}% - {$k\数式カンマスペース l$が実数のとき，$k\Ttyuukakko{l\vec{a}}=l\Ttyuukakko{k\vec{b}}$}{\relax}% + {$k\数式カンマスペース l$が実数のとき，$k\Ttyuukakko{l\ベクトル{a}}=l\Ttyuukakko{k\ベクトル{b}}$}{\relax}% \ifthenelse{\equal{#1}{公式F}\AND\equal{#2}{b}}% {% $k\数式カンマスペース l$が実数のとき% - \[k\Ttyuukakko{l\vec{a}}=l\Ttyuukakko{k\vec{b}}\]% + \[k\Ttyuukakko{l\ベクトル{a}}=l\Ttyuukakko{k\ベクトル{b}}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式G}\AND\equal{#2}{i}}% - {$k\数式カンマスペース l$が実数のとき，$\Ttyuukakko{k+l}\vec{a}=k\vec{a}+l\vec{a}$}{\relax}% + {$k\数式カンマスペース l$が実数のとき，$\Ttyuukakko{k+l}\ベクトル{a}=k\ベクトル{a}+l\ベクトル{a}$}{\relax}% \ifthenelse{\equal{#1}{公式G}\AND\equal{#2}{b}}% {% $k\数式カンマスペース l$が実数のとき% - \[\Ttyuukakko{k+l}\vec{a}=k\vec{a}+l\vec{a}\]% + \[\Ttyuukakko{k+l}\ベクトル{a}=k\ベクトル{a}+l\ベクトル{a}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式H}\AND\equal{#2}{i}}% - {$k$が実数のとき，$k\Ttyuukakko{\vec{a}+\vec{b}}=k\vec{a}+k\vec{b}$}{\relax}% + {$k$が実数のとき，$k\Ttyuukakko{\ベクトル{a}+\ベクトル{b}}=k\ベクトル{a}+k\ベクトル{b}$}{\relax}% \ifthenelse{\equal{#1}{公式H}\AND\equal{#2}{b}}% {% $k$が実数のとき% - \[k\Ttyuukakko{\vec{a}+\vec{b}}=k\vec{a}+k\vec{b}\]% + \[k\Ttyuukakko{\ベクトル{a}+\ベクトル{b}}=k\ベクトル{a}+k\ベクトル{b}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式I}\AND\equal{#2}{i}}% - {$\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}$}{\relax}% + {$\overrightarrowtext{AB}+\overrightarrowtext{BC}=\overrightarrowtext{AC}$}{\relax}% \ifthenelse{\equal{#1}{公式I}\AND\equal{#2}{b}}% - {\[\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}\]}{\relax}% + {\[\overrightarrowtext{AB}+\overrightarrowtext{BC}=\overrightarrowtext{AC}\]}{\relax}% \ifthenelse{\equal{#1}{公式J}\AND\equal{#2}{i}}% - {$\overrightarrow{OA}-\overrightarrow{OB}=\overrightarrow{BA}$}{\relax}% + {$\overrightarrowtext{OA}-\overrightarrowtext{OB}=\overrightarrowtext{BA}$}{\relax}% \ifthenelse{\equal{#1}{公式J}\AND\equal{#2}{b}}% - {\[\overrightarrow{OA}-\overrightarrow{OB}=\overrightarrow{BA}\]}{\relax}% + {\[\overrightarrowtext{OA}-\overrightarrowtext{OB}=\overrightarrowtext{BA}\]}{\relax}% \ifthenelse{\equal{#1}{公式K}\AND\equal{#2}{i}}% - {$\overrightarrow{AA}=\vec{0}$}{\relax}% + {$\overrightarrowtext{AA}=\ベクトル{0}$}{\relax}% \ifthenelse{\equal{#1}{公式K}\AND\equal{#2}{b}}% - {\[\overrightarrow{AA}=\vec{0}\]}{\relax}% + {\[\overrightarrowtext{AA}=\ベクトル{0}\]}{\relax}% \ifthenelse{\equal{#1}{公式L}\AND\equal{#2}{i}}% - {$\overrightarrow{BA}=\overrightarrow{AB}$}{\relax}% + {$\overrightarrowtext{BA}=\overrightarrowtext{AB}$}{\relax}% \ifthenelse{\equal{#1}{公式L}\AND\equal{#2}{b}}% - {\[\overrightarrow{BA}=\overrightarrow{AB}\]}{\relax}% + {\[\overrightarrowtext{BA}=\overrightarrowtext{AB}\]}{\relax}% }% \NewDocumentCommand{\平面ベクトルの分解}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {$\vec{a}\neq0\数式カンマスペース\vec{b}\neq0$で，$\vec{a}$と$\vec{b}$が平行でないとき，任意の$\vec{p}$はただ一通りに，$\vec{p}=s\vec{a}+t\vec{b}$の形に表せられる。}{\relax}% + {$\ベクトル{a}\neq0\数式カンマスペース\ベクトル{b}\neq0$で，$\ベクトル{a}$と$\ベクトル{b}$が平行でないとき，任意の$\ベクトル{p}$はただ一通りに，$\ベクトル{p}=s\ベクトル{a}+t\ベクトル{b}$の形に表せられる。}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% - $\vec{a}\neq0\数式カンマスペース\vec{b}\neq0$で，$\vec{a}$と$\vec{b}$が平行でないとき，任意の$\vec{p}$はただ一通りに，% - \[\vec{p}=s\vec{a}+t\vec{b}\]% + $\ベクトル{a}\neq0\数式カンマスペース\ベクトル{b}\neq0$で，$\ベクトル{a}$と$\ベクトル{b}$が平行でないとき，任意の$\ベクトル{p}$はただ一通りに，% + \[\ベクトル{p}=s\ベクトル{a}+t\ベクトル{b}\]% の形に表せられる。% }% {\relax}% @@ -2780,37 +2826,37 @@ \NewDocumentCommand{\平面ベクトルの成分}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\vec{a}=\vec{b}\Leftrightarrow a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}$}{\relax}% + {$\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\ベクトル{a}=\ベクトル{b}\Leftrightarrow a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% - $\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% - $\vec{a}=\vec{b}$% + $\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% + $\ベクトル{a}=\ベクトル{b}$% \[\Leftrightarrow a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}\Leftrightarrow\vec{a}=\vec{b}$}{\relax}% + {$\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}\Leftrightarrow\ベクトル{a}=\ベクトル{b}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% - $\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% + $\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% $a_{1}=b_{1}\数式カンマスペース a_{2}=b_{2}$% - \[\Leftrightarrow\vec{a}=\vec{b}\]% + \[\Leftrightarrow\ベクトル{a}=\ベクトル{b}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}$とすると，$\Tzettaiti{\vec{a}}=\sqrt{a_{1}^2+a_{2}^2}$}{\relax}% + {$\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}$とすると，$\Tzettaiti{\ベクトル{a}}=\根号{a_{1}^2+a_{2}^2}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% {% - $\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}$とすると，% - \[\Tzettaiti{\vec{a}}=\sqrt{a_{1}^2+a_{2}^2}\]% + $\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}$とすると，% + \[\Tzettaiti{\ベクトル{a}}=\根号{a_{1}^2+a_{2}^2}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {$\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$また，$k\数式カンマスペース l$を実数として，$k\vec{a}+l\vec{b}=k\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}+l\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}=\Ttyuukakko{ka_{1}+lb_{1}\数式カンマスペース ka_{2}+lb_{2}}$}{\relax}% + {$\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$また，$k\数式カンマスペース l$を実数として，$k\ベクトル{a}+l\ベクトル{b}=k\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}+l\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}=\Ttyuukakko{ka_{1}+lb_{1}\数式カンマスペース ka_{2}+lb_{2}}$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {% - $\vec{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\vec{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$また，$k\数式カンマスペース l$を実数として，% - \[k\vec{a}+l\vec{b}=k\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}+l\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}=\Ttyuukakko{ka_{1}+lb_{1}\数式カンマスペース ka_{2}+lb_{2}}\]% + $\ベクトル{a}=\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース\ベクトル{b}=\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$また，$k\数式カンマスペース l$を実数として，% + \[k\ベクトル{a}+l\ベクトル{b}=k\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}+l\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}=\Ttyuukakko{ka_{1}+lb_{1}\数式カンマスペース ka_{2}+lb_{2}}\]% }% {\relax}% }% @@ -2819,26 +2865,26 @@ \NewDocumentCommand{\ベクトルの成分と大きさ}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\overrightarrow{AB}=\Ttyuukakko{b_{1}-a_{1}\数式カンマスペース b_{2}-a_{2}}$}{\relax}% + {$A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\overrightarrowtext{AB}=\Ttyuukakko{b_{1}-a_{1}\数式カンマスペース b_{2}-a_{2}}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% $A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% - \[\overrightarrow{AB}=\Ttyuukakko{b_{1}-a_{1}\数式カンマスペース b_{2}-a_{2}}\]% + \[\overrightarrowtext{AB}=\Ttyuukakko{b_{1}-a_{1}\数式カンマスペース b_{2}-a_{2}}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\Tzettaiti{\overrightarrow{AB}}=\sqrt{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}$}{\relax}% + {$A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，$\Tzettaiti{\overrightarrowtext{AB}}=\根号{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% $A\Ttyuukakko{a_{1}\数式カンマスペース a_{2}}\数式カンマスペース B\Ttyuukakko{b_{1}\数式カンマスペース b_{2}}$とすると，% - \[\Tzettaiti{\overrightarrow{AB}}=\sqrt{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}\]% + \[\Tzettaiti{\overrightarrowtext{AB}}=\根号{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}\]% }% {\relax}% \ifthenelse{\equal{#1}{証明}}% {% \証明開始% 三平方の定理より，% - \[\Tzettaiti{\overrightarrow{AB}}=\sqrt{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}\]% + \[\Tzettaiti{\overrightarrowtext{AB}}=\根号{\Ttyuukakko{b_{1}-a_{1}}^2+\Ttyuukakko{b_{2}-a_{2}}^2}\]% \証明終了% }% {\relax}% @@ -2848,11 +2894,11 @@ \NewDocumentCommand{\平面ベクトルの内積}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{i}}% - {ベクトルの内積は，$\vec{a} \cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta \Ttyuukakko{0^{\circ} \leqq \theta \leqq 180^{\circ}}\text{\ （ただし，$\theta$は$\vec{a}$と$\vec{b}$のなす角}$}{\relax}% + {ベクトルの内積は，$\ベクトル{a} \cdot\ベクトル{b}=|\ベクトル{a}||\ベクトル{b}|\cos\theta \Ttyuukakko{0^{\circ} \leqq \theta \leqq 180^{\circ}}\text{\ （ただし，$\theta$は$\ベクトル{a}$と$\ベクトル{b}$のなす角）}$}{\relax}% \ifthenelse{\equal{#1}{公式}\AND\equal{#2}{b}}% {% ベクトルの内積は，% - \[\vec{a} \cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta \Ttyuukakko{0^{\circ} \leqq \theta \leqq 180^{\circ}}\text{\ （ただし，$\theta$は$\vec{a}$と$\vec{b}$のなす角}\]% + \[\ベクトル{a} \cdot\ベクトル{b}=|\ベクトル{a}||\ベクトル{b}|\cos\theta \Ttyuukakko{0^{\circ} \leqq \theta \leqq 180^{\circ}}\text{\ （ただし，$\theta$は$\ベクトル{a}$と$\ベクトル{b}$のなす角）}\]% }% {\relax}% }% @@ -2861,33 +2907,33 @@ \NewDocumentCommand{\内積の性質}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$\vec{a} \cdot\vec{b}=\vec{b} \cdot\vec{a}$}{\relax}% + {$\ベクトル{a} \cdot\ベクトル{b}=\ベクトル{b} \cdot\ベクトル{a}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% - {\[\vec{a} \cdot\vec{b}=\vec{b} \cdot\vec{a}\]}{\relax}% + {\[\ベクトル{a} \cdot\ベクトル{b}=\ベクトル{b} \cdot\ベクトル{a}\]}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$\Ttyuukakko{\vec{a}+\vec{b}} \cdot\vec{c}=\vec{a} \cdot\vec{c}+\vec{b} \cdot\vec{c}$}{\relax}% + {$\Ttyuukakko{\ベクトル{a}+\ベクトル{b}} \cdot\ベクトル{c}=\ベクトル{a} \cdot\ベクトル{c}+\ベクトル{b} \cdot\ベクトル{c}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% - {\[\Ttyuukakko{\vec{a}+\vec{b}} \cdot\vec{c}=\vec{a} \cdot\vec{c}+\vec{b} \cdot\vec{c}\]}{\relax}% + {\[\Ttyuukakko{\ベクトル{a}+\ベクトル{b}} \cdot\ベクトル{c}=\ベクトル{a} \cdot\ベクトル{c}+\ベクトル{b} \cdot\ベクトル{c}\]}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$\vec{c} \cdot\Ttyuukakko{\vec{b}+\vec{c}}=\vec{a} \cdot\vec{c}+\vec{b} \cdot\vec{c}$}{\relax}% + {$\ベクトル{c} \cdot\Ttyuukakko{\ベクトル{b}+\ベクトル{c}}=\ベクトル{a} \cdot\ベクトル{c}+\ベクトル{b} \cdot\ベクトル{c}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% - {\[\vec{c} \cdot\Ttyuukakko{\vec{b}+\vec{c}}=\vec{a} \cdot\vec{c}+\vec{b} \cdot\vec{c}\]}{\relax}% + {\[\ベクトル{c} \cdot\Ttyuukakko{\ベクトル{b}+\ベクトル{c}}=\ベクトル{a} \cdot\ベクトル{c}+\ベクトル{b} \cdot\ベクトル{c}\]}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {$k$が実数のとき，$\Ttyuukakko{k\vec{a}} \cdot\vec{b}=\vec{a} \cdot\Ttyuukakko{k\vec{b}}=k\Ttyuukakko{\vec{a} \cdot\vec{b}}$}{\relax}% + {$k$が実数のとき，$\Ttyuukakko{k\ベクトル{a}} \cdot\ベクトル{b}=\ベクトル{a} \cdot\Ttyuukakko{k\ベクトル{b}}=k\Ttyuukakko{\ベクトル{a} \cdot\ベクトル{b}}$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {% $k$が実数のとき，% - \[\Ttyuukakko{k\vec{a}} \cdot\vec{b}=\vec{a} \cdot\Ttyuukakko{k\vec{b}}=k\Ttyuukakko{\vec{a} \cdot\vec{b}}\]% + \[\Ttyuukakko{k\ベクトル{a}} \cdot\ベクトル{b}=\ベクトル{a} \cdot\Ttyuukakko{k\ベクトル{b}}=k\Ttyuukakko{\ベクトル{a} \cdot\ベクトル{b}}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{i}}% - {$\vec{a} \cdot\vec{a}=\Tzettaiti{\vec{a}}^2$}{\relax}% + {$\ベクトル{a} \cdot\ベクトル{a}=\Tzettaiti{\ベクトル{a}}^2$}{\relax}% \ifthenelse{\equal{#1}{公式E}\AND\equal{#2}{b}}% - {\[\vec{a} \cdot\vec{a}=\Tzettaiti{\vec{a}}^2\]}{\relax}% + {\[\ベクトル{a} \cdot\ベクトル{a}=\Tzettaiti{\ベクトル{a}}^2\]}{\relax}% \ifthenelse{\equal{#1}{公式F}\AND\equal{#2}{i}}% - {$\Tzettaiti{\vec{a}}=\sqrt{\vec{a} \cdot\vec{a}}$}{\relax}% + {$\Tzettaiti{\ベクトル{a}}=\根号{\ベクトル{a} \cdot\ベクトル{a}}$}{\relax}% \ifthenelse{\equal{#1}{公式F}\AND\equal{#2}{b}}% - {\[\Tzettaiti{\vec{a}}=\sqrt{\vec{a} \cdot\vec{a}}\]}{\relax}% + {\[\Tzettaiti{\ベクトル{a}}=\根号{\ベクトル{a} \cdot\ベクトル{a}}\]}{\relax}% }% @@ -2895,15 +2941,15 @@ {% \ifthenelse{\equal{#1}{条件}\AND\equal{#2}{i}}% {% - $\vec{a}\neq\vec{0}\数式カンマスペース\vec{b}\neq\vec{0}$また，$k$は実数とする，\par% - $\vec{a}/ \!/ \vec{b}\Leftrightarrow\vec{b}=k\vec{a}$，$\vec{b}=k\vec{a}$% + $\ベクトル{a}\neq\ベクトル{0}\数式カンマスペース\ベクトル{b}\neq\ベクトル{0}$また，$k$は実数とする，\par% + $\ベクトル{a}/ \!/ \ベクトル{b}\Leftrightarrow\ベクトル{b}=k\ベクトル{a}$，$\ベクトル{b}=k\ベクトル{a}$% }% {\relax}% \ifthenelse{\equal{#1}{条件}\AND\equal{#2}{b}}% {% - $\vec{a}\neq\vec{0}\数式カンマスペース\vec{b}\neq\vec{0}$また，$k$は実数とする，\par% - $\vec{a}/ \!/ \vec{b}$% - \[\Leftrightarrow\vec{b}=k\vec{a}\]% + $\ベクトル{a}\neq\ベクトル{0}\数式カンマスペース\ベクトル{b}\neq\ベクトル{0}$また，$k$は実数とする，\par% + $\ベクトル{a}/ \!/ \ベクトル{b}$% + \[\Leftrightarrow\ベクトル{b}=k\ベクトル{a}\]% }% {\relax}% }% @@ -2913,15 +2959,14 @@ {% \ifthenelse{\equal{#1}{条件}\AND\equal{#2}{i}}% {% - $\vec{a}\neq\vec{0}\数式カンマスペース\vec{b}\neq\vec{0}$また，$k$は実数とする，\par% - $\vec{a} \perp \vec{b}\Leftrightarrow\vec{a} \cdot\vec{b}=0$% + $\ベクトル{a}\neq\ベクトル{0}\数式カンマスペース\ベクトル{b}\neq\ベクトル{0}$で，$k$は実数とすると，% + $\ベクトル{a} \perp \ベクトル{b}\Leftrightarrow\ベクトル{a} \cdot\ベクトル{b}=0$% }% {\relax}% \ifthenelse{\equal{#1}{条件}\AND\equal{#2}{b}}% {% - $\vec{a}\neq\vec{0}\数式カンマスペース\vec{b}\neq\vec{0}$また，$k$は実数とする，\par% - $\vec{a} \perp \vec{b}$% - \[\Leftrightarrow\vec{a} \cdot\vec{b}=0\]% + $\ベクトル{a}\neq\ベクトル{0}\数式カンマスペース\ベクトル{b}\neq\ベクトル{0}$で，$k$は実数とすると，% + \[\ベクトル{a} \perp \ベクトル{b}\Leftrightarrow\ベクトル{a} \cdot\ベクトル{b}=0\]% }% {\relax}% }% @@ -2930,53 +2975,53 @@ \NewDocumentCommand{\位置ベクトル}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$を$m:n$に内分する点は，$\bunsuu{n\vec{a}+m\vec{b}}{m+n}$}{\relax}% + {$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とすると，線分$\text{AB}$を$m:n$に内分する点は，$\bunsuu{n\ベクトル{a}+m\ベクトル{b}}{m+n}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$を$m:n$に内分する点は，% - \[\bunsuu{n\vec{a}+m\vec{b}}{m+n}\]% + $A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とすると，線分$\text{AB}$を$m:n$に内分する点は，% + \[\bunsuu{n\ベクトル{a}+m\ベクトル{b}}{m+n}\]% }% {\relax}% - \ifthenelse{\equal{#1}{内分点の位置ベクトルの証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{内分点の位置ベクトルの証明}}% {% \証明開始% - $P\Ttyuukakko{\vec{p}}$が$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$を$m:n$に内分するとき，% + $P\Ttyuukakko{\ベクトル{p}}$が$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$を$m:n$に内分するとき，% \begin{align*}% - \vec{p}&=\vec{a}+\bunsuu{m}{m+n}\Ttyuukakko{\vec{b}-\vec{a}}&\\% - &=\bunsuu{n\vec{a}+m\vec{b}}{m+n}&\\% + \ベクトル{p}&=\ベクトル{a}+\bunsuu{m}{m+n}\Ttyuukakko{\ベクトル{b}-\ベクトル{a}}&\\% + &=\bunsuu{n\ベクトル{a}+m\ベクトル{b}}{m+n}&\\% \end{align*}% \証明終了% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$を$m:n$に外分する点は，$\bunsuu{-n\vec{a}+m\vec{b}}{m-n}$}{\relax}% + {$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とする，線分$\text{AB}$を$m:n$に外分する点は，$\bunsuu{-n\ベクトル{a}+m\ベクトル{b}}{m-n}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$を$m:n$に外分する点は，% - \[\bunsuu{-n\vec{a}+m\vec{b}}{m-n}\]% + $A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とする，線分$\text{AB}$を$m:n$に外分する点は，% + \[\bunsuu{-n\ベクトル{a}+m\ベクトル{b}}{m-n}\]% }% {\relax}% - \ifthenelse{\equal{#1}{外分点の位置ベクトルの証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{外分点の位置ベクトルの証明}}% {% \証明開始% - $m:n$に外分ということは$m:-n$に内分ということなので，$\bunsuu{-n\vec{a}+m\vec{b}}{m-n}$% + $m:n$に外分ということは$m:-n$に内分ということなので，$\bunsuu{-n\ベクトル{a}+m\ベクトル{b}}{m-n}$% \証明終了% }% {\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$の中点は，$\bunsuu{\vec{a}+\vec{b}}{2}$}{\relax}% + {$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とする，線分$\text{AB}$の中点は，$\bunsuu{\ベクトル{a}+\ベクトル{b}}{2}$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$とする，線分$AB$の中点は，% - \[\bunsuu{\vec{a}+\vec{b}}{2}\]% + $A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$とする，線分$\text{AB}$の中点は，% + \[\bunsuu{\ベクトル{a}+\ベクトル{b}}{2}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}\数式カンマスペース C\Ttyuukakko{\vec{c}}$とする，三角形$ABC$の重心は，$\bunsuu{\vec{a}+\vec{b}+\vec{c}}{3}$}{\relax}% + {$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}\数式カンマスペース C\Ttyuukakko{\ベクトル{c}}$とする，$\triangle{\text{ABC}}$の重心は，$\bunsuu{\ベクトル{a}+\ベクトル{b}+\ベクトル{c}}{3}$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {% - $A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}\数式カンマスペース C\Ttyuukakko{\vec{c}}$とする，三角形$ABC$の重心は，% - \[\bunsuu{\vec{a}+\vec{b}+\vec{c}}{3}\]% + $A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}\数式カンマスペース C\Ttyuukakko{\ベクトル{c}}$とする，$\triangle{\text{ABC}}$の重心は，% + \[\bunsuu{\ベクトル{a}+\ベクトル{b}+\ベクトル{c}}{3}\]% }% {\relax}% }% @@ -2985,36 +3030,36 @@ \NewDocumentCommand{\ベクトル方程式}{ m O{i} }% {% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{i}}% - {$s\数式カンマスペース t$を実数とする。点$A\Ttyuukakko{\vec{a}}$をとおり，$\vec{d}$に平行な直線は，$\vec{p}=\vec{a}+t\vec{b}$}{\relax}% + {$s\数式カンマスペース t$を実数とする。点$A\Ttyuukakko{\ベクトル{a}}$をとおり，$\ベクトル{d}$に平行な直線は，$\ベクトル{p}=\ベクトル{a}+t\ベクトル{b}$}{\relax}% \ifthenelse{\equal{#1}{公式A}\AND\equal{#2}{b}}% {% - $s\数式カンマスペース t$を実数とする。点$A\Ttyuukakko{\vec{a}}$をとおり，$\vec{d}$に平行な直線は，% - \[\vec{p}=\vec{a}+t\vec{b}\]% + $s\数式カンマスペース t$を実数とする。点$A\Ttyuukakko{\ベクトル{a}}$をとおり，$\ベクトル{d}$に平行な直線は，% + \[\ベクトル{p}=\ベクトル{a}+t\ベクトル{b}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{i}}% - {$s\数式カンマスペース t$を実数とする。二点$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$を通る直線は，$\vec{p}=\Ttyuukakko{1-t}\vec{a}+t\vec{b}\数式カンマスペース\vec{p}=a\vec{a}+t\vec{b}\text{\ （ただし，$s+t=1$）}$}{\relax}% + {$s\数式カンマスペース t$を実数とする。二点$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$を通る直線は，$\ベクトル{p}=\Ttyuukakko{1-t}\ベクトル{a}+t\ベクトル{b}\数式カンマスペース\ベクトル{p}=a\ベクトル{a}+t\ベクトル{b}\text{\ （ただし，$s+t=1$）}$}{\relax}% \ifthenelse{\equal{#1}{公式B}\AND\equal{#2}{b}}% {% - $s\数式カンマスペース t$を実数とする。二点$A\Ttyuukakko{\vec{a}}\数式カンマスペース B\Ttyuukakko{\vec{b}}$を通る直線は，% - \[\vec{p}=\Ttyuukakko{1-t}\vec{a}+t\vec{b}\数式カンマスペース\vec{p}=a\vec{a}+t\vec{b}\text{\ （ただし，$s+t=1$）}\]% + $s\数式カンマスペース t$を実数とする。二点$A\Ttyuukakko{\ベクトル{a}}\数式カンマスペース B\Ttyuukakko{\ベクトル{b}}$を通る直線は，% + \[\ベクトル{p}=\Ttyuukakko{1-t}\ベクトル{a}+t\ベクトル{b}\数式カンマスペース\ベクトル{p}=a\ベクトル{a}+t\ベクトル{b}\text{\ （ただし，$s+t=1$）}\]% }% {\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{i}}% - {点$A\Ttyuukakko{\vec{a}}$を通り，$\vec{n}$に垂直な直線$\vec{p}$について，$\vec{n}\cdot\Ttyuukakko{\vec{p}-\vec{a}}=0$}{\relax}% + {点$A\Ttyuukakko{\ベクトル{a}}$を通り，$\ベクトル{n}$に垂直な直線$\ベクトル{p}$について，$\ベクトル{n}\cdot\Ttyuukakko{\ベクトル{p}-\ベクトル{a}}=0$}{\relax}% \ifthenelse{\equal{#1}{公式C}\AND\equal{#2}{b}}% {% - 点$A\Ttyuukakko{\vec{a}}$を通り，$\vec{n}$に垂直な直線$\vec{p}$について，% - \[\vec{n}\cdot\Ttyuukakko{\vec{p}-\vec{a}}=0\]% + 点$A\Ttyuukakko{\ベクトル{a}}$を通り，$\ベクトル{n}$に垂直な直線$\ベクトル{p}$について，% + \[\ベクトル{n}\cdot\Ttyuukakko{\ベクトル{p}-\ベクトル{a}}=0\]% }% {\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{i}}% - {中心$C\Ttyuukakko{\vec{c}}$，半径$r$の円は，$\Tzettaiti{\vec{p}-\vec{c}}=r\数式カンマスペース\Ttyuukakko{\vec{p}-\vec{c}}\cdot\Ttyuukakko{\vec{p}-\vec{c}}=r^2$}{\relax}% + {中心$C\Ttyuukakko{\ベクトル{c}}$，半径$r$の円は，$\Tzettaiti{\ベクトル{p}-\ベクトル{c}}=r\数式カンマスペース\Ttyuukakko{\ベクトル{p}-\ベクトル{c}}\cdot\Ttyuukakko{\ベクトル{p}-\ベクトル{c}}=r^2$}{\relax}% \ifthenelse{\equal{#1}{公式D}\AND\equal{#2}{b}}% {% - 中心$C\Ttyuukakko{\vec{c}}$，半径$r$の円は，% - \[\Tzettaiti{\vec{p}-\vec{c}}=r\]% - \[\Ttyuukakko{\vec{p}-\vec{c}}\cdot\Ttyuukakko{\vec{p}-\vec{c}}=r^2\]% + 中心$C\Ttyuukakko{\ベクトル{c}}$，半径$r$の円は，% + \[\Tzettaiti{\ベクトル{p}-\ベクトル{c}}=r\]% + \[\Ttyuukakko{\ベクトル{p}-\ベクトル{c}}\cdot\Ttyuukakko{\ベクトル{p}-\ベクトル{c}}=r^2\]% }% {\relax}% }% @@ -3266,11 +3311,11 @@ \NewDocumentCommand{\複素数の絶対値}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {複素数$z=a+bi$に対して，$\Tzettaiti{z}=\Tzettaiti{a+bi}=\sqrt{a^2+b^2}$}{\relax}% + {複素数$z=a+bi$に対して，$\Tzettaiti{z}=\Tzettaiti{a+bi}=\根号{a^2+b^2}$}{\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% 複素数$z=a+bi$に対して，% - \[\Tzettaiti{z}=\Tzettaiti{a+bi}=\sqrt{a^2+b^2}\]% + \[\Tzettaiti{z}=\Tzettaiti{a+bi}=\根号{a^2+b^2}\]% }% {\relax}% \ifthenelse{\equal{#1}{性質A}\AND\equal{#2}{i}}% @@ -3287,12 +3332,12 @@ \NewDocumentCommand{\極形式}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {複素数$\alpha=a+bi$について，$\alpha=r\Ttyuukakko{\cos\theta+i\sin\theta}\text{\ （ただし$z>0$）}$また，$r=\Tzettaiti{\alpha}=\sqrt{a^2+b^2}\数式カンマスペース\cos\theta=\bunsuu{a}{r}\数式カンマスペース\sin\theta=\bunsuu{b}{r}$を極形式という。}{\relax}% + {複素数$\alpha=a+bi$について，$\alpha=r\Ttyuukakko{\cos\theta+i\sin\theta}\text{\ （ただし$z>0$）}$また，$r=\Tzettaiti{\alpha}=\根号{a^2+b^2}\数式カンマスペース\cos\theta=\bunsuu{a}{r}\数式カンマスペース\sin\theta=\bunsuu{b}{r}$を極形式という。}{\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% 複素数$\alpha=a+bi$について，% \[\alpha=r\Ttyuukakko{\cos\theta+i\sin\theta}\text{\ （ただし$z>0$）}\]% - また，$r=\Tzettaiti{\alpha}=\sqrt{a^2+b^2}\数式カンマスペース\cos\theta=\bunsuu{a}{r}\数式カンマスペース\sin\theta=\bunsuu{b}{r}$を極形式という。% + また，$r=\Tzettaiti{\alpha}=\根号{a^2+b^2}\数式カンマスペース\cos\theta=\bunsuu{a}{r}\数式カンマスペース\sin\theta=\bunsuu{b}{r}$を極形式という。% }% {\relax}% \ifthenelse{\equal{#1}{性質A}\AND\equal{#2}{i}}% @@ -3440,11 +3485,11 @@ }% {\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{i}}% - {楕円の焦点は$F\Ttyuukakko{\sqrt{a^2-b^2}\数式カンマスペース 0}$と，$F'\Ttyuukakko{\sqrt{a^2-b^2}\数式カンマスペース 0}$}{\relax}% + {楕円の焦点は$F\Ttyuukakko{\根号{a^2-b^2}\数式カンマスペース 0}$と，$F'\Ttyuukakko{\根号{a^2-b^2}\数式カンマスペース 0}$}{\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{b}}% {% 楕円の焦点は% - \[F\Ttyuukakko{\sqrt{a^2-b^2}\数式カンマスペース 0} F'\Ttyuukakko{\sqrt{a^2-b^2}\数式カンマスペース 0}\]% + \[F\Ttyuukakko{\根号{a^2-b^2}\数式カンマスペース 0} F'\Ttyuukakko{\根号{a^2-b^2}\数式カンマスペース 0}\]% }% {\relax}% \ifthenelse{\equal{#1}{性質C}\AND\equal{#2}{i}}% @@ -3474,11 +3519,11 @@ }% {\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{i}}% - {双曲線の焦点は$F\Ttyuukakko{\sqrt{a^2+b^2}\数式カンマスペース 0}$と，$F'\Ttyuukakko{\sqrt{a^2+b^2}\数式カンマスペース 0}$}{\relax}% + {双曲線の焦点は$F\Ttyuukakko{\根号{a^2+b^2}\数式カンマスペース 0}$と，$F'\Ttyuukakko{\根号{a^2+b^2}\数式カンマスペース 0}$}{\relax}% \ifthenelse{\equal{#1}{性質B}\AND\equal{#2}{b}}% {% 双曲線の焦点は% - \[F\Ttyuukakko{\sqrt{a^2+b^2}\数式カンマスペース 0} F'\Ttyuukakko{\sqrt{a^2+b^2}\数式カンマスペース 0}\]% + \[F\Ttyuukakko{\根号{a^2+b^2}\数式カンマスペース 0} F'\Ttyuukakko{\根号{a^2+b^2}\数式カンマスペース 0}\]% }% {\relax}% \ifthenelse{\equal{#1}{性質C}\AND\equal{#2}{i}}% @@ -3600,7 +3645,7 @@ {$\Ttyuukakko{a^{x}}'=a^{x}\log a$}{\relax}% \ifthenelse{\equal{#1}{初等関数の微分公式I}\AND\equal{#2}{b}}% {\[\Ttyuukakko{a^{x}}'=a^{x}\log a\]}{\relax}% - \ifthenelse{\equal{#1}{三角関数の微分公式の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{三角関数の微分公式の証明}}% {% \証明開始% \begin{align*}% @@ -3617,7 +3662,7 @@ \証明終了% }% {\relax}% - \ifthenelse{\equal{#1}{対数関数の微分公式の証明}\AND\equal{#2}{i}}% + \ifthenelse{\equal{#1}{対数関数の微分公式の証明}}% {% \証明開始% \begin{align*}% @@ -3628,7 +3673,7 @@ \begin{align*}% \Ttyuukakko{\log x}'&=\displaystyle\lim_{h \to 0} \bunsuu{\log\Ttyuukakko{1+t}}{xt}&\\% &=\displaystyle\lim_{h \to 0} \Tdaikakko{\bunsuu{\log\Ttyuukakko{1+t}}{t}\cdot\bunsuu{1}{x}}&\\% - &=\displaystyle\lim_{h \to 0} \log\Ttyuukakko{1+t}^{\bunsuu{1}{t}}\cdot\bunsuu{1}{x}&\\% + &=\displaystyle\lim_{h \to 0} \log\Ttyuukakko{1+t}^{\frac{1}{t}}\cdot\bunsuu{1}{x}&\\% &=\log e\cdot\bunsuu{1}{x}&\\% &=\bunsuu{1}{x} \end{align*}% @@ -3667,12 +3712,11 @@ \NewDocumentCommand{\不定積分}{ m O{i} }% {% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{i}}% - {$F'\Ttyuukakko{x}=f\Ttyuukakko{x}$とすると，$\displaystyle \int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C$ ($C$は積分定数)}{\relax}% + {$F'\Ttyuukakko{x}=f\Ttyuukakko{x}$とすると，$\displaystyle \int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\text{\ （\,$C$は積分定数）}$}{\relax}% \ifthenelse{\equal{#1}{定義}\AND\equal{#2}{b}}% {% $F'\Ttyuukakko{x}=f\Ttyuukakko{x}$とすると，% - \[\displaystyle \int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\]% - ($C$は積分定数)% + \[\displaystyle \int_{}^{} f\Ttyuukakko{x}dx=F\Ttyuukakko{x}+C\text{\ （\,$C$は積分定数）}\]% }% {\relax}% \ifthenelse{\equal{#1}{置換積分}\AND\equal{#2}{i}}% diff --git a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.tex b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.tex index f63a375bb5..7c68dffbd7 100644 --- a/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.tex +++ b/macros/luatex/latex/japanese-mathformulas/japanese-mathformulas.tex @@ -1,8 +1,8 @@ \documentclass[fleqn]{ltjsarticle}% !lualatex \usepackage[hiragino-pron,deluxe,expert,bold]{luatexja-preset}% -\usepackage{mathformula,framed,comment}% -\usepackage[usetype1]{uline--} +\usepackage{japanese-mathformulas,framed,comment}% +\usepackage[usetype1]{uline--}% \title{\LARGE\uline{japanese-mathformulas.sty}\Large\\manual pdf\\(mainly for Japanese, lulatex)}% \author{\Large Hugh / Ponkichi}% \date{\today} @@ -15,8 +15,10 @@ \newlength{\@tempdimi} \let\@@vspace@@\vspace \def\vspace{\@ifstar{\@@vspace@}{\@vspace@}} -\def\@vspace@#1{\par\setlength{\@tempdimi}{#1}\@@vspace@@{\@tempdimi}} -\def\@@vspace@#1{\par\setlength{\@tempdimi}{#1}\@@vspace@@*{\@tempdimi}} +\def\@vspace@#1{ +\setlength{\@tempdimi}{#1}\@@vspace@@{\@tempdimi}} +\def\@@vspace@#1{ +\setlength{\@tempdimi}{#1}\@@vspace@@*{\@tempdimi}} \newlength{\pseprule} % 段仕切り線の太さ \setlength{\pseprule}{.5truept} @@ -70,38 +72,38 @@ \maketitle \begin{multicolparx}{2} -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% -機能紹介と注記- \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% - Function Introduction and Notes - \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% 中学高校で習う数学の定理や公式を出力するためのstyファイル。\\ \detokenize{\NewDocumentCommand}によって，インデント数式か別行立て数式かを指定できる。 \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% This is a style file for compiling basic math formulas.\\ \detokenize{\NewDocumentCommand} allows you to specify whether the formula should be used within a sentence or on a new line. \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% 後の例では記述がないが，$\Ttyuubracket{\mathrm{i}}$か$\Ttyuubracket{\mathrm{b}}$かの指定をしない場合は自動的に$\Ttyuubracket{\mathrm{i}}$とみなされる。 \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% Although not shown in the examples below, if $\Ttyuubracket{\mathrm{i}}$ or $\Ttyuubracket{\mathrm{b}}$ is not specified, it is automatically assumed to be $\Ttyuubracket{\mathrm{i}}$. \end{center}}% -\parbox[t]{\hsize}{\begin{center}% +\noindent\parbox[t]{\hsize}{\begin{center}% 二段組の文書を作成するときは，数式の上下間スペースを減らすために，以下をpreambleに記述するとよい。 \end{center}}% -\parbox[t]{\hsize}{\begin{center}% -When making two-column document, you are recommended to put these lines at preamble.\par +\noindent\parbox[t]{\hsize}{\begin{center}% +When making two-column document, you are recommended to put these lines at preamble.\\ These reduce the space above and below math expressions. \end{center}}% \end{multicolparx} @@ -117,149 +119,253 @@ These reduce the space above and below math expressions. \end{framed} \begin{multicolparx}{2} -\parbox[t]{\hsize}{\begin{center}% + +\noindent\parbox[t]{\hsize}{\begin{center}% 以下が実例。 \end{center}}% -\parbox[t]{\hsize}{\begin{center}% + +\noindent\parbox[t]{\hsize}{\begin{center}% Now, here are the actual examples! \end{center}}% \end{multicolparx} -\auto{1}{\detokenize{\二次式展開{公式A}[i]}}\par -\二次式展開{公式A}[i]\par +\auto{1}{\detokenize{\二次式展開{公式A}[i]}} + +\二次式展開{公式A}[i] + \auto{2}{\detokenize{\二次式展開{公式A}[b]}} + \二次式展開{公式A}[b] -\auto{33}{\detokenize{\二次式因数分解{公式A}[i]}}\par -\二次式因数分解{公式A}[i]\par + +\auto{33}{\detokenize{\二次式因数分解{公式A}[i]}} + +\二次式因数分解{公式A}[i] + \auto{34}{\detokenize{\二次式因数分解{公式A}[b]}} + \二次式因数分解{公式A}[b] + %\begin{simplesquarebox}{二次式展開} %\begin{description} -\auto{1}{\detokenize{\二次式展開{公式A}[i]}}\par -\二次式展開{公式A}[i]\par +\auto{1}{\detokenize{\二次式展開{公式A}[i]}} + +\二次式展開{公式A}[i] + \auto{2}{\detokenize{\二次式展開{公式A}[b]}} + \二次式展開{公式A}[b] -\auto{3}{\detokenize{\二次式展開{公式B}[i]}}\par -\二次式展開{公式B}[i]\par + +\auto{3}{\detokenize{\二次式展開{公式B}[i]}} + +\二次式展開{公式B}[i] + \auto{4}{\detokenize{\二次式展開{公式B}[b]}} + \二次式展開{公式B}[b] -\auto{5}{\detokenize{\二次式展開{公式C}[i]}}\par -\二次式展開{公式C}[i]\par + +\auto{5}{\detokenize{\二次式展開{公式C}[i]}} + +\二次式展開{公式C}[i] + \auto{6}{\detokenize{\二次式展開{公式C}[b]}} + \二次式展開{公式C}[b] -\auto{7}{\detokenize{\二次式展開{公式D}[i]}}\par -\二次式展開{公式D}[i]\par + +\auto{7}{\detokenize{\二次式展開{公式D}[i]}} + +\二次式展開{公式D}[i] + \auto{8}{\detokenize{\二次式展開{公式D}[b]}} + \二次式展開{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{二次式因数分解} %\begin{description} -\auto{9}{\detokenize{\二次式因数分解{公式A}[i]}}\par -\二次式因数分解{公式A}[i]\par +\auto{9}{\detokenize{\二次式因数分解{公式A}[i]}} + +\二次式因数分解{公式A}[i] + \auto{10}{\detokenize{\二次式因数分解{公式A}[b]}} + \二次式因数分解{公式A}[b] -\auto{11}{\detokenize{\二次式因数分解{公式B}[i]}}\par -\二次式因数分解{公式B}[i]\par + +\auto{11}{\detokenize{\二次式因数分解{公式B}[i]}} + +\二次式因数分解{公式B}[i] + \auto{12}{\detokenize{\二次式因数分解{公式B}[b]}} + \二次式因数分解{公式B}[b] -\auto{13}{\detokenize{\二次式因数分解{公式C}[i]}}\par -\二次式因数分解{公式C}[i]\par + +\auto{13}{\detokenize{\二次式因数分解{公式C}[i]}} + +\二次式因数分解{公式C}[i] + \auto{14}{\detokenize{\二次式因数分解{公式C}[b]}} + \二次式因数分解{公式C}[b] -\auto{15}{\detokenize{\二次式因数分解{公式D}[i]}}\par -\二次式因数分解{公式D}[i]\par + +\auto{15}{\detokenize{\二次式因数分解{公式D}[i]}} + +\二次式因数分解{公式D}[i] + \auto{16}{\detokenize{\二次式因数分解{公式D}[b]}} + \二次式因数分解{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平方根} %\begin{description} -\auto{17}{\detokenize{\平方根{定義}[i]}}\par -\平方根{定義}[i]\par -\auto{18}{\detokenize{\平方根{定義}[b]}}\par +\auto{17}{\detokenize{\平方根{定義}[i]}} + +\平方根{定義}[i] + +\auto{18}{\detokenize{\平方根{定義}[b]}} + + \平方根{定義}[b] -\auto{19}{\detokenize{\平方根{性質A}[i]}}\par -\平方根{性質A}[i]\par -\auto{20}{\detokenize{\平方根{性質A}[b]}}\par + +\auto{19}{\detokenize{\平方根{性質A}[i]}} + +\平方根{性質A}[i] + +\auto{20}{\detokenize{\平方根{性質A}[b]}} + + \平方根{性質A}[b] -\auto{21}{\detokenize{\平方根{性質B}[i]}}\par -\平方根{性質B}[i]\par + +\auto{21}{\detokenize{\平方根{性質B}[i]}} + +\平方根{性質B}[i] + \auto{22}{\detokenize{\平方根{性質B}[b]}} + \平方根{性質B}[b] -\auto{23}{\detokenize{\平方根{性質C}[i]}}\par -\平方根{性質C}[i]\par + +\auto{23}{\detokenize{\平方根{性質C}[i]}} + +\平方根{性質C}[i] + \auto{24}{\detokenize{\平方根{性質C}[b]}} + \平方根{性質C}[b] -\auto{25}{\detokenize{\平方根{性質D}[i]}}\par -\平方根{性質D}[i]\par + +\auto{25}{\detokenize{\平方根{性質D}[i]}} + +\平方根{性質D}[i] + \auto{26}{\detokenize{\平方根{性質D}[b]}} + \平方根{性質D}[b] -\auto{27}{\detokenize{\平方根{性質E}[i]}}\par -\平方根{性質E}[i]\par + +\auto{27}{\detokenize{\平方根{性質E}[i]}} + +\平方根{性質E}[i] + \auto{28}{\detokenize{\平方根{性質E}[b]}} + \平方根{性質E}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{一次不等式} %\begin{description} -\auto{29}{\detokenize{\一次不等式{性質A}[i]}}\par -\一次不等式{性質A}[i]\par -\auto{30}{\detokenize{\一次不等式{性質A}[b]}}\par +\auto{29}{\detokenize{\一次不等式{性質A}[i]}} + +\一次不等式{性質A}[i] + +\auto{30}{\detokenize{\一次不等式{性質A}[b]}} + + \一次不等式{性質A}[b] -\auto{31}{\detokenize{\一次不等式{性質B}[i]}}\par -\一次不等式{性質B}[i]\par -\auto{32}{\detokenize{\一次不等式{性質B}[b]}}\par + +\auto{31}{\detokenize{\一次不等式{性質B}[i]}} + +\一次不等式{性質B}[i] + +\auto{32}{\detokenize{\一次不等式{性質B}[b]}} + + \一次不等式{性質B}[b] -\auto{33}{\detokenize{\一次不等式{性質C}[i]}}\par -\一次不等式{性質C}[i]\par -\auto{34}{\detokenize{\一次不等式{性質C}[b]}}\par + +\auto{33}{\detokenize{\一次不等式{性質C}[i]}} + +\一次不等式{性質C}[i] + +\auto{34}{\detokenize{\一次不等式{性質C}[b]}} + + \一次不等式{性質C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{集合} %\begin{description} -\auto{35}{\detokenize{\集合{積集合}[i]}}\par -\集合{積集合}[i]\par +\auto{35}{\detokenize{\集合{積集合}[i]}} + +\集合{積集合}[i] + \auto{36}{\detokenize{\集合{積集合}[b]}} + \集合{積集合}[b] -\auto{37}{\detokenize{\集合{和集合}[i]}}\par -\集合{和集合}[i]\par + +\auto{37}{\detokenize{\集合{和集合}[i]}} + +\集合{和集合}[i] + \auto{38}{\detokenize{\集合{和集合}[b]}} + \集合{和集合}[b] -\auto{39}{\detokenize{\集合{補集合}[i]}}\par -\集合{補集合}[i]\par + +\auto{39}{\detokenize{\集合{補集合}[i]}} + +\集合{補集合}[i] + \auto{40}{\detokenize{\集合{補集合}[b]}} + \集合{補集合}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{対偶} %\begin{description} -\auto{41}{\detokenize{\対偶{定理}[i]}}\par -\対偶{定理}[i]\par -\auto{41}{\detokenize{\対偶{定理}[b]}}\par -\対偶{定理}[b]\par -\auto{41}{\detokenize{\対偶{証明}}}\par -\対偶{証明}\par +\auto{41}{\detokenize{\対偶{定理}[i]}} + +\対偶{定理}[i] + +\auto{41}{\detokenize{\対偶{定理}[b]}} + + +\対偶{定理}[b] + + +\auto{41}{\detokenize{\対偶{証明}}} + +\対偶{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{背理法} %\begin{description} -\auto{42}{\detokenize{\背理法}}\par +\auto{42}{\detokenize{\背理法}} + \背理法 %\end{description} @@ -267,239 +373,433 @@ Now, here are the actual examples! %\begin{simplesquarebox}{二次関数} %\begin{description} -\auto{43}{\detokenize{\二次関数{標準形}[i]}}\par -\二次関数{標準形}[i]\par +\auto{43}{\detokenize{\二次関数{標準形}[i]}} + +\二次関数{標準形}[i] + \auto{44}{\detokenize{\二次関数{標準形}[b]}} + \二次関数{標準形}[b] -\auto{45}{\detokenize{\二次関数{一般形}[i]}}\par -\二次関数{一般形}[i]\par + +\auto{45}{\detokenize{\二次関数{一般形}[i]}} + +\二次関数{一般形}[i] + \auto{46}{\detokenize{\二次関数{一般形}[b]}} + \二次関数{一般形}[b] -\auto{47}{\detokenize{\二次関数{切片形}[i]}}\par -\二次関数{切片形}[i]\par + +\auto{47}{\detokenize{\二次関数{切片形}[i]}} + +\二次関数{切片形}[i] + \auto{48}{\detokenize{\二次関数{切片形}[b]}} + \二次関数{切片形}[b] -\auto{49}{\detokenize{\二次関数{平方完成}[i]}}\par -\二次関数{平方完成}[i]\par -\auto{50}{\detokenize{\二次関数{平方完成}[b]}}\par + +\auto{49}{\detokenize{\二次関数{平方完成}[i]}} + +\二次関数{平方完成}[i] + +\auto{50}{\detokenize{\二次関数{平方完成}[b]}} + + \二次関数{平方完成}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{二次方程式の解の公式} %\begin{description} -\auto{51}{\detokenize{\二次方程式の解の公式{公式}[i]}}\par -\二次方程式の解の公式{公式}[i]\par -\auto{52}{\detokenize{\二次方程式の解の公式{公式}[b]}}\par +\auto{51}{\detokenize{\二次方程式の解の公式{公式}[i]}} + +\二次方程式の解の公式{公式}[i] + +\auto{52}{\detokenize{\二次方程式の解の公式{公式}[b]}} + + \二次方程式の解の公式{公式}[b] -\auto{52}{\detokenize{\二次方程式の解の公式{証明A}[i]}}\par -\二次方程式の解の公式{証明A}[i]\par -\auto{52}{\detokenize{\二次方程式の解の公式{証明B}[i]}}\par -\二次方程式の解の公式{証明B}[i]\par + +\auto{52}{\detokenize{\二次方程式の解の公式{証明A}[i]}} + +\二次方程式の解の公式{証明A}[i] + +\auto{52}{\detokenize{\二次方程式の解の公式{証明B}[i]}} + +\二次方程式の解の公式{証明B}[i] + %\end{description} %\end{simplesquarebox} -\auto{52}{\detokenize{\三角比の定義{定義A}[i]}}\par -\三角比の定義{定義A}[i]\par -\auto{52}{\detokenize{\三角比の定義{定義B}[i]}}\par -\三角比の定義{定義B}[i]\par +\auto{52}{\detokenize{\三角比の定義{定義A}[i]}} + +\三角比の定義{定義A}[i] + +\auto{52}{\detokenize{\三角比の定義{定義B}[i]}} + +\三角比の定義{定義B}[i] + %\begin{simplesquarebox}{三角比の相互関係} %\begin{description} -\auto{53}{\detokenize{\三角比の相互関係{公式A}[i]}}\par -\三角比の相互関係{公式A}[i]\par +\auto{53}{\detokenize{\三角比の相互関係{公式A}[i]}} + +\三角比の相互関係{公式A}[i] + \auto{54}{\detokenize{\三角比の相互関係{公式A}[b]}} + \三角比の相互関係{公式A}[b] -\auto{55}{\detokenize{\三角比の相互関係{公式B}[i]}}\par -\三角比の相互関係{公式B}[i]\par + +\auto{55}{\detokenize{\三角比の相互関係{公式B}[i]}} + +\三角比の相互関係{公式B}[i] + \auto{56}{\detokenize{\三角比の相互関係{公式B}[b]}} + \三角比の相互関係{公式B}[b] -\auto{57}{\detokenize{\三角比の相互関係{公式C}[i]}}\par -\三角比の相互関係{公式C}[i]\par + +\auto{57}{\detokenize{\三角比の相互関係{公式C}[i]}} + +\三角比の相互関係{公式C}[i] + \auto{58}{\detokenize{\三角比の相互関係{公式C}[b]}} + \三角比の相互関係{公式C}[b] -\auto{57}{\detokenize{\三角比の相互関係{証明}}}\par -\三角比の相互関係{証明}\par + +\auto{57}{\detokenize{\三角比の相互関係{証明}}} + +\三角比の相互関係{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{正弦定理} %\begin{description} -\auto{59}{\detokenize{\正弦定理{公式}[i]}}\par -\正弦定理{公式}[i]\par +\auto{59}{\detokenize{\正弦定理{公式}[i]}} + +\正弦定理{公式}[i] + \auto{60}{\detokenize{\正弦定理{公式}[b]}} -\正弦定理{公式}[b]\par -\auto{59}{\detokenize{\正弦定理{証明}}}\par -\正弦定理{証明}\par + +\正弦定理{公式}[b] + + +\auto{59}{\detokenize{\正弦定理{証明}}} + +\正弦定理{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{余弦定理} %\begin{description} -\auto{61}{\detokenize{\余弦定理{公式}[i]}}\par -\余弦定理{公式}[i]\par +\auto{61}{\detokenize{\余弦定理{公式}[i]}} + +\余弦定理{公式}[i] + \auto{62}{\detokenize{\余弦定理{公式}[b]}} + \余弦定理{公式}[b] -\auto{61}{\detokenize{\余弦定理{証明}}}\par -\余弦定理{証明}\par + +\auto{61}{\detokenize{\余弦定理{証明}}} + +\余弦定理{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{三角形の面積} %\begin{description} -\auto{63}{\detokenize{\三角形の面積{公式}[i]}}\par -\三角形の面積{公式}[i]\par +\auto{63}{\detokenize{\三角形の面積{公式}[i]}} + +\三角形の面積{公式}[i] + \auto{64}{\detokenize{\三角形の面積{公式}[b]}} + \三角形の面積{公式}[b] -\auto{63}{\detokenize{\三角形の面積{証明}}}\par -\三角形の面積{証明}\par + +\auto{63}{\detokenize{\三角形の面積{証明}}} + +\三角形の面積{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{場合の数と確率} %\begin{description} -\auto{65}{\detokenize{\場合の数と確率{和集合の要素の個数}[i]}}\par -\場合の数と確率{和集合の要素の個数}[i]\par +\auto{65}{\detokenize{\場合の数と確率{和集合の要素の個数}[i]}} + +\場合の数と確率{和集合の要素の個数}[i] + \auto{66}{\detokenize{\場合の数と確率{和集合の要素の個数}[b]}} + \場合の数と確率{和集合の要素の個数}[b] -%\auto{67}{\detokenize{\場合の数と確率{積集合の要素の個数}[i]}}\par -%\場合の数と確率{積集合の要素の個数}[i]\par + +%\auto{67}{\detokenize{\場合の数と確率{積集合の要素の個数}[i]}} + +%\場合の数と確率{積集合の要素の個数}[i] + %\auto{68}{\detokenize{\場合の数と確率{積集合の要素の個数}[b]}} + %\場合の数と確率{積集合の要素の個数}[b] -\auto{69}{\detokenize{\場合の数と確率{補集合の要素の個数}[i]}}\par -\場合の数と確率{補集合の要素の個数}[i]\par + +\auto{69}{\detokenize{\場合の数と確率{補集合の要素の個数}[i]}} + +\場合の数と確率{補集合の要素の個数}[i] + \auto{70}{\detokenize{\場合の数と確率{補集合の要素の個数}[b]}} + \場合の数と確率{補集合の要素の個数}[b] -\auto{71}{\detokenize{\場合の数と確率{和の法則}[i]}}\par -\場合の数と確率{和の法則}[i]\par + +\auto{71}{\detokenize{\場合の数と確率{和の法則}[i]}} + +\場合の数と確率{和の法則}[i] + \auto{72}{\detokenize{\場合の数と確率{和の法則}[b]}} + \場合の数と確率{和の法則}[b] -\auto{73}{\detokenize{\場合の数と確率{積の法則}[i]}}\par -\場合の数と確率{積の法則}[i]\par + +\auto{73}{\detokenize{\場合の数と確率{積の法則}[i]}} + +\場合の数と確率{積の法則}[i] + \auto{74}{\detokenize{\場合の数と確率{積の法則}[b]}} + \場合の数と確率{積の法則}[b] -\auto{75}{\detokenize{\場合の数と確率{順列}[i]}}\par -\場合の数と確率{順列}[i]\par + +\auto{75}{\detokenize{\場合の数と確率{順列}[i]}} + +\場合の数と確率{順列}[i] + \auto{76}{\detokenize{\場合の数と確率{順列}[b]}} + \場合の数と確率{順列}[b] -\auto{75}{\detokenize{\場合の数と確率{順列の証明}[i]}}\par -\場合の数と確率{順列の証明}[i]\par -\auto{77}{\detokenize{\場合の数と確率{円順列}[i]}}\par -\場合の数と確率{円順列}[i]\par + +\auto{75}{\detokenize{\場合の数と確率{順列の証明}}} + +\場合の数と確率{順列の証明} + +\auto{77}{\detokenize{\場合の数と確率{円順列}[i]}} + +\場合の数と確率{円順列}[i] + \auto{78}{\detokenize{\場合の数と確率{円順列}[b]}} + \場合の数と確率{円順列}[b] -\auto{77}{\detokenize{\場合の数と確率{円順列の証明}[i]}}\par -\場合の数と確率{円順列の証明}[i]\par -\auto{79}{\detokenize{\場合の数と確率{重複順列}[i]}}\par -\場合の数と確率{重複順列}[i]\par + +\auto{77}{\detokenize{\場合の数と確率{円順列の証明}}} + +\場合の数と確率{円順列の証明} + +\auto{79}{\detokenize{\場合の数と確率{重複順列}[i]}} + +\場合の数と確率{重複順列}[i] + \auto{80}{\detokenize{\場合の数と確率{重複順列}[b]}} + \場合の数と確率{重複順列}[b] -\auto{81}{\detokenize{\場合の数と確率{組み合わせ}[i]}}\par -\場合の数と確率{組み合わせ}[i]\par + +\auto{81}{\detokenize{\場合の数と確率{組み合わせ}[i]}} + +\場合の数と確率{組み合わせ}[i] + \auto{82}{\detokenize{\場合の数と確率{組み合わせ}[b]}} + \場合の数と確率{組み合わせ}[b] -\auto{81}{\detokenize{\場合の数と確率{組み合わせの証明}[i]}}\par -\場合の数と確率{組み合わせの証明}[i]\par -\auto{83}{\detokenize{\場合の数と確率{同じものを含む順列}[i]}}\par -\場合の数と確率{同じものを含む順列}[i]\par + +\auto{81}{\detokenize{\場合の数と確率{組み合わせの証明}}} + +\場合の数と確率{組み合わせの証明} + +\auto{83}{\detokenize{\場合の数と確率{同じものを含む順列}[i]}} + +\場合の数と確率{同じものを含む順列}[i] + \auto{84}{\detokenize{\場合の数と確率{同じものを含む順列}[b]}} + \場合の数と確率{同じものを含む順列}[b] -\auto{83}{\detokenize{\場合の数と確率{同じものを含む順列の証明}[i]}}\par -\場合の数と確率{同じものを含む順列の証明}[i]\par -\auto{85}{\detokenize{\場合の数と確率{確率の定義}[i]}}\par -\場合の数と確率{確率の定義}[i]\par + +\auto{83}{\detokenize{\場合の数と確率{同じものを含む順列の証明}}} + +\場合の数と確率{同じものを含む順列の証明} + +\auto{85}{\detokenize{\場合の数と確率{確率の定義}[i]}} + +\場合の数と確率{確率の定義}[i] + \auto{86}{\detokenize{\場合の数と確率{確率の定義}[b]}} + \場合の数と確率{確率の定義}[b] -\auto{87}{\detokenize{\場合の数と確率{排反の定義}[i]}}\par -\場合の数と確率{排反の定義}[i]\par + +\auto{87}{\detokenize{\場合の数と確率{排反の定義}[i]}} + +\場合の数と確率{排反の定義}[i] + \auto{88}{\detokenize{\場合の数と確率{排反の定義}[b]}} -\場合の数と確率{排反の定義}[b]\par -\auto{89}{\detokenize{\場合の数と確率{確率の性質A}[i]}}\par -\場合の数と確率{確率の性質A}[i]\par + +\場合の数と確率{排反の定義}[b] + + +\auto{89}{\detokenize{\場合の数と確率{確率の性質A}[i]}} + +\場合の数と確率{確率の性質A}[i] + \auto{90}{\detokenize{\場合の数と確率{確率の性質A}[b]}} + \場合の数と確率{確率の性質A}[b] -\auto{91}{\detokenize{\場合の数と確率{確率の性質B}[i]}}\par -\場合の数と確率{確率の性質B}[i]\par + +\auto{91}{\detokenize{\場合の数と確率{確率の性質B}[i]}} + +\場合の数と確率{確率の性質B}[i] + \auto{92}{\detokenize{\場合の数と確率{確率の性質B}[b]}} + \場合の数と確率{確率の性質B}[b] -\auto{93}{\detokenize{\場合の数と確率{和事象の確率}[i]}}\par -\場合の数と確率{和事象の確率}[i]\par + +\auto{93}{\detokenize{\場合の数と確率{和事象の確率}[i]}} + +\場合の数と確率{和事象の確率}[i] + \auto{94}{\detokenize{\場合の数と確率{和事象の確率}[b]}} + \場合の数と確率{和事象の確率}[b] -\auto{95}{\detokenize{\場合の数と確率{積事象の確率}[i]}}\par -%\場合の数と確率{積事象の確率}[i]\par + +\auto{95}{\detokenize{\場合の数と確率{積事象の確率}[i]}} + +%\場合の数と確率{積事象の確率}[i] + %\auto{96}{\detokenize{\場合の数と確率{積事象の確率}[b]}} + %\場合の数と確率{積事象の確率}[b] -%\auto{97}{\detokenize{\場合の数と確率{余事象の確率}[i]}}\par -\場合の数と確率{余事象の確率}[i]\par + +%\auto{97}{\detokenize{\場合の数と確率{余事象の確率}[i]}} + +\場合の数と確率{余事象の確率}[i] + \auto{98}{\detokenize{\場合の数と確率{余事象の確率}[b]}} + \場合の数と確率{余事象の確率}[b] -\auto{99}{\detokenize{\場合の数と確率{独立な事象の確率}[i]}}\par -\場合の数と確率{独立な事象の確率}[i]\par + +\auto{99}{\detokenize{\場合の数と確率{独立な事象の確率}[i]}} + +\場合の数と確率{独立な事象の確率}[i] + \auto{100}{\detokenize{\場合の数と確率{独立な事象の確率}[b]}} + \場合の数と確率{独立な事象の確率}[b] -\auto{101}{\detokenize{\場合の数と確率{反復試行の確率}[i]}}\par -\場合の数と確率{反復試行の確率}[i]\par + +\auto{101}{\detokenize{\場合の数と確率{反復試行の確率}[i]}} + +\場合の数と確率{反復試行の確率}[i] + \auto{102}{\detokenize{\場合の数と確率{反復試行の確率}[b]}} + \場合の数と確率{反復試行の確率}[b] -\auto{101}{\detokenize{\場合の数と確率{反復試行の確率の証明}[i]}}\par -\場合の数と確率{反復試行の確率の証明}[i]\par -\auto{103}{\detokenize{\場合の数と確率{条件付き確率}[i]}}\par -\場合の数と確率{条件付き確率}[i]\par + +\auto{101}{\detokenize{\場合の数と確率{反復試行の確率の証明}}} + +\場合の数と確率{反復試行の確率の証明} + +\auto{103}{\detokenize{\場合の数と確率{条件付き確率}[i]}} + +\場合の数と確率{条件付き確率}[i] + \auto{104}{\detokenize{\場合の数と確率{条件付き確率}[b]}} + \場合の数と確率{条件付き確率}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{図形の性質} %\begin{description} -\auto{105}{\detokenize{\図形の性質{内心}}}\par -\図形の性質{内心}\par -\auto{106}{\detokenize{\図形の性質{外心}}}\par -\図形の性質{外心}\par -\auto{107}{\detokenize{\図形の性質{垂心}}}\par -\図形の性質{垂心}\par -\auto{108}{\detokenize{\図形の性質{重心}}}\par -\図形の性質{重心}\par -\auto{109}{\detokenize{\図形の性質{傍心}}}\par -\図形の性質{傍心}\par -\auto{110}{\detokenize{\図形の性質{チェバの定理}}}\par -\図形の性質{チェバの定理}\par -\auto{110}{\detokenize{\図形の性質{チェバの定理の証明}}}\par -\図形の性質{チェバの定理の証明}\par -\auto{111}{\detokenize{\図形の性質{メネラウスの定理}}}\par -\図形の性質{メネラウスの定理}\par -\auto{111}{\detokenize{\図形の性質{メネラウスの定理の証明}}}\par +\auto{105}{\detokenize{\図形の性質{内心}}} + +\図形の性質{内心} + +\auto{106}{\detokenize{\図形の性質{外心}}} + +\図形の性質{外心} + +\auto{107}{\detokenize{\図形の性質{垂心}}} + +\図形の性質{垂心} + +\auto{108}{\detokenize{\図形の性質{重心}}} + +\図形の性質{重心} + +\auto{109}{\detokenize{\図形の性質{傍心}}} + +\図形の性質{傍心} + +\auto{110}{\detokenize{\図形の性質{チェバの定理}}} + +\図形の性質{チェバの定理} + +\auto{110}{\detokenize{\図形の性質{チェバの定理の証明}}} + +\図形の性質{チェバの定理の証明} + +\auto{111}{\detokenize{\図形の性質{メネラウスの定理}}} + +\図形の性質{メネラウスの定理} + +\auto{111}{\detokenize{\図形の性質{メネラウスの定理の証明}}} + \図形の性質{メネラウスの定理の証明} -\auto{112}{\detokenize{\図形の性質{円周角の定理}}}\par -\図形の性質{円周角の定理}\par -\auto{112}{\detokenize{\図形の性質{円周角の定理の証明}}}\par -\図形の性質{円周角の定理の証明}\par -\auto{113}{\detokenize{\図形の性質{内接四角形の定理}}}\par -\図形の性質{内接四角形の定理}\par -\auto{113}{\detokenize{\図形の性質{内接四角形の定理の証明}}}\par -\図形の性質{内接四角形の定理の証明}\par -\auto{114}{\detokenize{\図形の性質{接弦定理}}}\par -\図形の性質{接弦定理}\par -\auto{114}{\detokenize{\図形の性質{接弦定理の証明}}}\par -\図形の性質{接弦定理の証明}\par -\auto{115}{\detokenize{\図形の性質{内角と外角の二等分線}}}\par -\図形の性質{内角と外角の二等分線}\par -\auto{116}{\detokenize{\図形の性質{方べきの定理A}}}\par -\図形の性質{方べきの定理A}\par -\auto{116}{\detokenize{\図形の性質{方べきの定理Aの証明}}}\par +\auto{112}{\detokenize{\図形の性質{円周角の定理}}} + +\図形の性質{円周角の定理} + +\auto{112}{\detokenize{\図形の性質{円周角の定理の証明}}} + +\図形の性質{円周角の定理の証明} + +\auto{113}{\detokenize{\図形の性質{内接四角形の定理}}} + +\図形の性質{内接四角形の定理} + +\auto{113}{\detokenize{\図形の性質{内接四角形の定理の証明}}} + +\図形の性質{内接四角形の定理の証明} + +\auto{114}{\detokenize{\図形の性質{接弦定理}}} + +\図形の性質{接弦定理} + +\auto{114}{\detokenize{\図形の性質{接弦定理の証明}}} + +\図形の性質{接弦定理の証明} + +\auto{115}{\detokenize{\図形の性質{内角と外角の二等分線}}} + +\図形の性質{内角と外角の二等分線} + +\auto{116}{\detokenize{\図形の性質{方べきの定理A}}} + +\図形の性質{方べきの定理A} + +\auto{116}{\detokenize{\図形の性質{方べきの定理Aの証明}}} + \図形の性質{方べきの定理Aの証明} -\auto{117}{\detokenize{\図形の性質{方べきの定理B}}}\par -\図形の性質{方べきの定理B}\par -\auto{117}{\detokenize{\図形の性質{方べきの定理Bの証明}}}\par +\auto{117}{\detokenize{\図形の性質{方べきの定理B}}} + +\図形の性質{方べきの定理B} + +\auto{117}{\detokenize{\図形の性質{方べきの定理Bの証明}}} + \図形の性質{方べきの定理Bの証明} -\auto{118}{\detokenize{\図形の性質{方べきの定理C}}}\par -\図形の性質{方べきの定理C}\par -\auto{118}{\detokenize{\図形の性質{方べきの定理Cの証明}}}\par +\auto{118}{\detokenize{\図形の性質{方べきの定理C}}} + +\図形の性質{方べきの定理C} + +\auto{118}{\detokenize{\図形の性質{方べきの定理Cの証明}}} + \図形の性質{方べきの定理Cの証明} %\end{description} %\end{simplesquarebox} @@ -508,119 +808,193 @@ Now, here are the actual examples! %n-118=個数 %\begin{simplesquarebox}{展開} %\begin{description} -\auto{119}{\detokenize{\三次式展開{公式A}[i]}}\par -\三次式展開{公式A}[i]\par +\auto{119}{\detokenize{\三次式展開{公式A}[i]}} + +\三次式展開{公式A}[i] + \auto{120}{\detokenize{\三次式展開{公式A}[b]}} + \三次式展開{公式A}[b] -\auto{121}{\detokenize{\三次式展開{公式B}[i]}}\par -\三次式展開{公式B}[i]\par + +\auto{121}{\detokenize{\三次式展開{公式B}[i]}} + +\三次式展開{公式B}[i] + \auto{122}{\detokenize{\三次式展開{公式B}[b]}} + \三次式展開{公式B}[b] -\auto{123}{\detokenize{\三次式展開{公式C}[i]}}\par -\三次式展開{公式C}[i]\par + +\auto{123}{\detokenize{\三次式展開{公式C}[i]}} + +\三次式展開{公式C}[i] + \auto{124}{\detokenize{\三次式展開{公式C}[b]}} + \三次式展開{公式C}[b] -\auto{125}{\detokenize{\三次式展開{公式D}[i]}}\par -\三次式展開{公式D}[i]\par + +\auto{125}{\detokenize{\三次式展開{公式D}[i]}} + +\三次式展開{公式D}[i] + \auto{126}{\detokenize{\三次式展開{公式D}[b]}} + \三次式展開{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{因数分解} %\begin{description} -\auto{127}{\detokenize{\三次式因数分解{公式A}[i]}}\par -\三次式因数分解{公式A}[i]\par +\auto{127}{\detokenize{\三次式因数分解{公式A}[i]}} + +\三次式因数分解{公式A}[i] + \auto{128}{\detokenize{\三次式因数分解{公式A}[b]}} + \三次式因数分解{公式A}[b] -\auto{129}{\detokenize{\三次式因数分解{公式B}[i]}}\par -\三次式因数分解{公式B}[i]\par + +\auto{129}{\detokenize{\三次式因数分解{公式B}[i]}} + +\三次式因数分解{公式B}[i] + \auto{130}{\detokenize{\三次式因数分解{公式B}[b]}} + \三次式因数分解{公式B}[b] -\auto{131}{\detokenize{\三次式因数分解{公式C}[i]}}\par -\三次式因数分解{公式C}[i]\par + +\auto{131}{\detokenize{\三次式因数分解{公式C}[i]}} + +\三次式因数分解{公式C}[i] + \auto{132}{\detokenize{\三次式因数分解{公式C}[b]}} + \三次式因数分解{公式C}[b] -\auto{133}{\detokenize{\三次式因数分解{公式D}[i]}}\par -\三次式因数分解{公式D}[i]\par + +\auto{133}{\detokenize{\三次式因数分解{公式D}[i]}} + +\三次式因数分解{公式D}[i] + \auto{134}{\detokenize{\三次式因数分解{公式D}[b]}} + \三次式因数分解{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{二項定理} %\begin{description} -\auto{135}{\detokenize{\二項定理{公式}[i]}}\par -\二項定理{公式}[i]\par +\auto{135}{\detokenize{\二項定理{公式}[i]}} + +\二項定理{公式}[i] + \auto{136}{\detokenize{\二項定理{公式}[b]}} + \二項定理{公式}[b] -\auto{137}{\detokenize{\二項定理{一般項}[i]}}\par -\二項定理{一般項}[i]\par + +\auto{137}{\detokenize{\二項定理{一般項}[i]}} + +\二項定理{一般項}[i] + \auto{138}{\detokenize{\二項定理{一般項}[b]}} + \二項定理{一般項}[b] -\auto{135}{\detokenize{\二項定理{証明}}}\par -\二項定理{証明}\par + +\auto{135}{\detokenize{\二項定理{証明}}} + +\二項定理{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{分数式} %\begin{description} -\auto{139}{\detokenize{\分数式{公式A}[i]}}\par -\分数式{公式A}[i]\par +\auto{139}{\detokenize{\分数式{公式A}[i]}} + +\分数式{公式A}[i] + \auto{140}{\detokenize{\分数式{公式A}[b]}} + \分数式{公式A}[b] -\auto{141}{\detokenize{\分数式{公式B}[i]}}\par -\分数式{公式B}[i]\par + +\auto{141}{\detokenize{\分数式{公式B}[i]}} + +\分数式{公式B}[i] + \auto{142}{\detokenize{\分数式{公式B}[b]}} + \分数式{公式B}[b] -\auto{143}{\detokenize{\分数式{公式C}[i]}}\par -\分数式{公式C}[i]\par + +\auto{143}{\detokenize{\分数式{公式C}[i]}} + +\分数式{公式C}[i] + \auto{144}{\detokenize{\分数式{公式C}[b]}} + \分数式{公式C}[b] -\auto{145}{\detokenize{\分数式{公式D}[i]}}\par -\分数式{公式D}[i]\par + +\auto{145}{\detokenize{\分数式{公式D}[i]}} + +\分数式{公式D}[i] + \auto{146}{\detokenize{\分数式{公式D}[b]}} + \分数式{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{相加相乗平均} %\begin{description} -\auto{147}{\detokenize{\相加相乗平均{公式}[i]}}\par -\相加相乗平均{公式}[i]\par +\auto{147}{\detokenize{\相加相乗平均{公式}[i]}} + +\相加相乗平均{公式}[i] + \auto{148}{\detokenize{\相加相乗平均{公式}[b]}} + \相加相乗平均{公式}[b] -\auto{147}{\detokenize{\相加相乗平均{証明}}}\par -\相加相乗平均{証明}\par + +\auto{147}{\detokenize{\相加相乗平均{証明}}} + +\相加相乗平均{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{虚数の定義} %\begin{description} -\auto{149}{\detokenize{\虚数の定義{定義}[i]}}\par -\虚数の定義{定義}[i]\par +\auto{149}{\detokenize{\虚数の定義{定義}[i]}} + +\虚数の定義{定義}[i] + \auto{150}{\detokenize{\虚数の定義{定義}[b]}} + \虚数の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{複素数の定義} %\begin{description} -\auto{151}{\detokenize{\複素数の定義{定義}[i]}}\par -\複素数の定義{定義}[i]\par -\auto{152}{\detokenize{\複素数の定義{定義}[b]}}\par +\auto{151}{\detokenize{\複素数の定義{定義}[i]}} + +\複素数の定義{定義}[i] + +\auto{152}{\detokenize{\複素数の定義{定義}[b]}} + + \複素数の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{二次方程式の解の判別} %\begin{description} -\auto{153}{\detokenize{\二次方程式の解の判別}}\par +\auto{153}{\detokenize{\二次方程式の解の判別}} + \二次方程式の解の判別 %\end{description} @@ -628,888 +1002,1611 @@ Now, here are the actual examples! %\begin{simplesquarebox}{解と係数の関係} %\begin{description} -\auto{154}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係A}[i]}}\par -\解と係数の関係{二次方程式の解と係数の関係A}[i]\par +\auto{154}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係A}[i]}} + +\解と係数の関係{二次方程式の解と係数の関係A}[i] + \auto{155}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係A}[b]}} + \解と係数の関係{二次方程式の解と係数の関係A}[b] -\auto{156}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係B}[i]}}\par -\解と係数の関係{二次方程式の解と係数の関係B}[i]\par + +\auto{156}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係B}[i]}} + +\解と係数の関係{二次方程式の解と係数の関係B}[i] + \auto{157}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係B}[b]}} + \解と係数の関係{二次方程式の解と係数の関係B}[b] -\auto{154}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係の証明}[i]}}\par -\解と係数の関係{二次方程式の解と係数の関係の証明}[i]\par -\auto{158}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係A}[i]}}\par -\解と係数の関係{三次方程式の解と係数の関係A}[i]\par + +\auto{154}{\detokenize{\解と係数の関係{二次方程式の解と係数の関係の証明}}} + +\解と係数の関係{二次方程式の解と係数の関係の証明} + +\auto{158}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係A}[i]}} + +\解と係数の関係{三次方程式の解と係数の関係A}[i] + \auto{159}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係A}[b]}} + \解と係数の関係{三次方程式の解と係数の関係A}[b] -\auto{160}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係B}[i]}}\par -\解と係数の関係{三次方程式の解と係数の関係B}[i]\par + +\auto{160}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係B}[i]}} + +\解と係数の関係{三次方程式の解と係数の関係B}[i] + \auto{161}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係B}[b]}} + \解と係数の関係{三次方程式の解と係数の関係B}[b] -\auto{162}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係C}[i]}}\par -\解と係数の関係{三次方程式の解と係数の関係C}[i]\par + +\auto{162}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係C}[i]}} + +\解と係数の関係{三次方程式の解と係数の関係C}[i] + \auto{163}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係C}[b]}} + \解と係数の関係{三次方程式の解と係数の関係C}[b] -\auto{158}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係の証明}[i]}}\par -\解と係数の関係{三次方程式の解と係数の関係の証明}[i]\par + +\auto{158}{\detokenize{\解と係数の関係{三次方程式の解と係数の関係の証明}}} + +\解と係数の関係{三次方程式の解と係数の関係の証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{剰余定理} %\begin{description} -\auto{164}{\detokenize{\剰余定理{定理A}[i]}}\par -\剰余定理{定理A}[i]\par +\auto{164}{\detokenize{\剰余定理{定理A}[i]}} + +\剰余定理{定理A}[i] + \auto{165}{\detokenize{\剰余定理{定理A}[b]}} + \剰余定理{定理A}[b] -\auto{166}{\detokenize{\剰余定理{定理B}[i]}}\par -\剰余定理{定理B}[i]\par + +\auto{166}{\detokenize{\剰余定理{定理B}[i]}} + +\剰余定理{定理B}[i] + \auto{167}{\detokenize{\剰余定理{定理B}[b]}} + \剰余定理{定理B}[b] -\auto{164}{\detokenize{\剰余定理{証明}}}\par -\剰余定理{証明}\par + +\auto{164}{\detokenize{\剰余定理{証明}}} + +\剰余定理{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{因数定理} %\begin{description} -\auto{168}{\detokenize{\因数定理{定理}[i]}}\par -\因数定理{定理}[i]\par +\auto{168}{\detokenize{\因数定理{定理}[i]}} + +\因数定理{定理}[i] + \auto{168}{\detokenize{\因数定理{定理}[b]}} + \因数定理{定理}[b] -\auto{168}{\detokenize{\因数定理{証明}}}\par -\因数定理{証明}\par +\auto{168}{\detokenize{\因数定理{証明}}} + +\因数定理{証明} + +\auto{168}{\detokenize{\ユークリッド幾何の公理{公理A}}} + +\ユークリッド幾何の公理{公理A} + +\auto{168}{\detokenize{\ユークリッド幾何の公理{公理B}}} + +\ユークリッド幾何の公理{公理B} + +\auto{168}{\detokenize{\直線}} + +\直線 + +\auto{168}{\detokenize{\線分}} + +\線分 + +\auto{168}{\detokenize{\半直線}} + +\半直線 + +\auto{168}{\detokenize{\距離}} + +\距離 + +\auto{168}{\detokenize{\円}} + +\円 + +\auto{168}{\detokenize{\弧}} + +\弧 + +\auto{168}{\detokenize{\弦}} + +\弦 + +\auto{168}{\detokenize{\中心角}} + +\中心角 + +\auto{168}{\detokenize{\対頂角{定義}}} + +\対頂角{定義} + +\auto{168}{\detokenize{\対頂角{性質}}} + +\対頂角{性質} + +\auto{168}{\detokenize{\対頂角{証明}}} + +\対頂角{証明} + +\auto{168}{\detokenize{\錯角{定義}}} + +\錯角{定義} + +\auto{168}{\detokenize{\錯角{性質}}} + +\錯角{性質} + +\auto{168}{\detokenize{\錯角{証明}}} + +\錯角{証明} + +\auto{168}{\detokenize{\同位角{定義}}} + +\同位角{定義} + +\auto{168}{\detokenize{\同位角{公理}}} + +\同位角{公理} %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{点の座標} %\begin{description} -\auto{169}{\detokenize{\点の座標{二点間の距離}[i]}}\par -\点の座標{二点間の距離}[i]\par +\auto{169}{\detokenize{\点の座標{二点間の距離}[i]}} + +\点の座標{二点間の距離}[i] + \auto{170}{\detokenize{\点の座標{二点間の距離}[b]}} + \点の座標{二点間の距離}[b] -\auto{171}{\detokenize{\点の座標{内分点の座標}[i]}}\par -\点の座標{内分点の座標}[i]\par + +\auto{171}{\detokenize{\点の座標{内分点の座標}[i]}} + +\点の座標{内分点の座標}[i] + \auto{172}{\detokenize{\点の座標{内分点の座標}[b]}} + \点の座標{内分点の座標}[b] -\auto{171}{\detokenize{\点の座標{内分点の座標の証明}[i]}}\par -\点の座標{内分点の座標の証明}[i]\par -\auto{173}{\detokenize{\点の座標{外分点の座標}[i]}}\par -\点の座標{外分点の座標}[i]\par + +\auto{171}{\detokenize{\点の座標{内分点の座標の証明}}} + +\点の座標{内分点の座標の証明} + +\auto{173}{\detokenize{\点の座標{外分点の座標}[i]}} + +\点の座標{外分点の座標}[i] + \auto{174}{\detokenize{\点の座標{外分点の座標}[b]}} + \点の座標{外分点の座標}[b] -\auto{173}{\detokenize{\点の座標{外分点の座標の証明}[i]}}\par -\点の座標{外分点の座標の証明}[i]\par -\auto{175}{\detokenize{\点の座標{中点の座標}[i]}}\par -\点の座標{中点の座標}[i]\par + +\auto{173}{\detokenize{\点の座標{外分点の座標の証明}}} + +\点の座標{外分点の座標の証明} + +\auto{175}{\detokenize{\点の座標{中点の座標}[i]}} + +\点の座標{中点の座標}[i] + \auto{176}{\detokenize{\点の座標{中点の座標}[b]}} + \点の座標{中点の座標}[b] -\auto{175}{\detokenize{\点の座標{中点の座標の証明}[i]}}\par -\点の座標{中点の座標の証明}[i]\par -\auto{177}{\detokenize{\点の座標{重心の座標}[i]}}\par -\点の座標{重心の座標}[i]\par + +\auto{175}{\detokenize{\点の座標{中点の座標の証明}}} + +\点の座標{中点の座標の証明} + +\auto{177}{\detokenize{\点の座標{重心の座標}[i]}} + +\点の座標{重心の座標}[i] + \auto{178}{\detokenize{\点の座標{重心の座標}[b]}} + \点の座標{重心の座標}[b] -\auto{177}{\detokenize{\点の座標{重心の座標の証明}[i]}}\par -\点の座標{重心の座標の証明}[i]\par + +\auto{177}{\detokenize{\点の座標{重心の座標の証明}}} + +\点の座標{重心の座標の証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{直線の方程式} %\begin{description} -\auto{179}{\detokenize{\直線の方程式{公式A}[i]}}\par -\直線の方程式{公式A}[i]\par +\auto{179}{\detokenize{\直線の方程式{公式A}[i]}} + +\直線の方程式{公式A}[i] + \auto{180}{\detokenize{\直線の方程式{公式A}[b]}} + \直線の方程式{公式A}[b] -\auto{181}{\detokenize{\直線の方程式{公式B}[i]}}\par -\直線の方程式{公式B}[i]\par + +\auto{181}{\detokenize{\直線の方程式{公式B}[i]}} + +\直線の方程式{公式B}[i] + \auto{182}{\detokenize{\直線の方程式{公式B}[b]}} + \直線の方程式{公式B}[b] -\auto{183}{\detokenize{\直線の方程式{公式C}[i]}}\par -\直線の方程式{公式C}[i]\par + +\auto{183}{\detokenize{\直線の方程式{公式C}[i]}} + +\直線の方程式{公式C}[i] + \auto{184}{\detokenize{\直線の方程式{公式C}[b]}} + \直線の方程式{公式C}[b] -\auto{183}{\detokenize{\直線の方程式{公式Bの証明}}}\par -\直線の方程式{公式Bの証明}\par + +\auto{183}{\detokenize{\直線の方程式{公式Bの証明}}} + +\直線の方程式{公式Bの証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{二直線の関係} %\begin{description} -\auto{185}{\detokenize{\二直線の関係{公式A}[i]}}\par -\二直線の関係{公式A}[i]\par +\auto{185}{\detokenize{\二直線の関係{公式A}[i]}} + +\二直線の関係{公式A}[i] + \auto{186}{\detokenize{\二直線の関係{公式A}[b]}} + \二直線の関係{公式A}[b] -\auto{187}{\detokenize{\二直線の関係{公式B}[i]}}\par -\二直線の関係{公式B}[i]\par + +\auto{187}{\detokenize{\二直線の関係{公式B}[i]}} + +\二直線の関係{公式B}[i] + \auto{188}{\detokenize{\二直線の関係{公式B}[b]}} + \二直線の関係{公式B}[b] -\auto{185}{\detokenize{\二直線の関係{公式Bの証明}[i]}}\par -\二直線の関係{公式Bの証明}[i]\par + +\auto{185}{\detokenize{\二直線の関係{公式Bの証明}}} + +\二直線の関係{公式Bの証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{点と直線の距離} %\begin{description} -\auto{189}{\detokenize{\点と直線の距離{公式}[i]}}\par -\点と直線の距離{公式}[i]\par +\auto{189}{\detokenize{\点と直線の距離{公式}[i]}} + +\点と直線の距離{公式}[i] + \auto{190}{\detokenize{\点と直線の距離{公式}[b]}} + \点と直線の距離{公式}[b] -\auto{189}{\detokenize{\点と直線の距離{証明}}}\par -\点と直線の距離{証明}\par + +\auto{189}{\detokenize{\点と直線の距離{証明}}} + +\点と直線の距離{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{円の方程式} %\begin{description} -\auto{191}{\detokenize{\円の方程式{公式}[i]}}\par -\円の方程式{公式}[i]\par +\auto{191}{\detokenize{\円の方程式{公式}[i]}} + +\円の方程式{公式}[i] + \auto{192}{\detokenize{\円の方程式{公式}[b]}} + \円の方程式{公式}[b] -\auto{191}{\detokenize{\円の方程式{証明}}}\par -\円の方程式{証明}\par + +\auto{191}{\detokenize{\円の方程式{証明}}} + +\円の方程式{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{円と直線} %\begin{description} -\auto{193}{\detokenize{\円と直線{公式}[i]}}\par -\円と直線{公式}[i]\par +\auto{193}{\detokenize{\円と直線{公式}[i]}} + +\円と直線{公式}[i] + \auto{194}{\detokenize{\円と直線{公式}[b]}} + \円と直線{公式}[b] -\auto{193}{\detokenize{\円と直線{証明}}}\par -\円と直線{証明}\par + +\auto{193}{\detokenize{\円と直線{証明}}} + +\円と直線{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{三角関数の相互関係} %\begin{description} -\auto{195}{\detokenize{\三角関数の相互関係{公式A}[i]}}\par -\三角関数の相互関係{公式A}[i]\par +\auto{195}{\detokenize{\三角関数の相互関係{公式A}[i]}} + +\三角関数の相互関係{公式A}[i] + \auto{196}{\detokenize{\三角関数の相互関係{公式A}[b]}} + \三角関数の相互関係{公式A}[b] -\auto{197}{\detokenize{\三角関数の相互関係{公式B}[i]}}\par -\三角関数の相互関係{公式B}[i]\par + +\auto{197}{\detokenize{\三角関数の相互関係{公式B}[i]}} + +\三角関数の相互関係{公式B}[i] + \auto{198}{\detokenize{\三角関数の相互関係{公式B}[b]}} + \三角関数の相互関係{公式B}[b] -\auto{199}{\detokenize{\三角関数の相互関係{公式C}[i]}}\par -\三角関数の相互関係{公式C}[i]\par + +\auto{199}{\detokenize{\三角関数の相互関係{公式C}[i]}} + +\三角関数の相互関係{公式C}[i] + \auto{200}{\detokenize{\三角関数の相互関係{公式C}[b]}} + \三角関数の相互関係{公式C}[b] -\auto{195}{\detokenize{\三角関数の相互関係{証明}}}\par -\三角関数の相互関係{証明}\par + +\auto{195}{\detokenize{\三角関数の相互関係{証明}}} + +\三角関数の相互関係{証明} + %\end{description} %\end{simplesquarebox} -\auto{201}{\detokenize{\三角関数の性質{性質A}[i]}}\par -\三角関数の性質{性質A}[i]\par +\auto{201}{\detokenize{\三角関数の性質{性質A}[i]}} + +\三角関数の性質{性質A}[i] + \auto{202}{\detokenize{\三角関数の性質{性質A}[b]}} + \三角関数の性質{性質A}[b] -\auto{203}{\detokenize{\三角関数の性質{性質B}[i]}}\par -\三角関数の性質{性質B}[i]\par + +\auto{203}{\detokenize{\三角関数の性質{性質B}[i]}} + +\三角関数の性質{性質B}[i] + \auto{204}{\detokenize{\三角関数の性質{性質B}[b]}} + \三角関数の性質{性質B}[b] -\auto{205}{\detokenize{\三角関数の性質{性質C}[i]}}\par -\三角関数の性質{性質C}[i]\par + +\auto{205}{\detokenize{\三角関数の性質{性質C}[i]}} + +\三角関数の性質{性質C}[i] + \auto{206}{\detokenize{\三角関数の性質{性質C}[b]}} + \三角関数の性質{性質C}[b] -\auto{207}{\detokenize{\三角関数の性質{性質D}[i]}}\par -\三角関数の性質{性質D}[i]\par + +\auto{207}{\detokenize{\三角関数の性質{性質D}[i]}} + +\三角関数の性質{性質D}[i] + \auto{208}{\detokenize{\三角関数の性質{性質D}[b]}} + \三角関数の性質{性質D}[b] -\auto{209}{\detokenize{\三角関数の性質{性質E}[i]}}\par -\三角関数の性質{性質E}[i]\par + +\auto{209}{\detokenize{\三角関数の性質{性質E}[i]}} + +\三角関数の性質{性質E}[i] + \auto{210}{\detokenize{\三角関数の性質{性質E}[b]}} + \三角関数の性質{性質E}[b] -\auto{211}{\detokenize{\三角関数の性質{性質F}[i]}}\par -\三角関数の性質{性質F}[i]\par + +\auto{211}{\detokenize{\三角関数の性質{性質F}[i]}} + +\三角関数の性質{性質F}[i] + \auto{212}{\detokenize{\三角関数の性質{性質F}[b]}} + \三角関数の性質{性質F}[b] -\auto{213}{\detokenize{\三角関数の性質{性質G}[i]}}\par -\三角関数の性質{性質G}[i]\par + +\auto{213}{\detokenize{\三角関数の性質{性質G}[i]}} + +\三角関数の性質{性質G}[i] + \auto{214}{\detokenize{\三角関数の性質{性質G}[b]}} + \三角関数の性質{性質G}[b] -\auto{215}{\detokenize{\三角関数の性質{性質H}[i]}}\par -\三角関数の性質{性質H}[i]\par + +\auto{215}{\detokenize{\三角関数の性質{性質H}[i]}} + +\三角関数の性質{性質H}[i] + \auto{216}{\detokenize{\三角関数の性質{性質H}[b]}} + \三角関数の性質{性質H}[b] -\auto{217}{\detokenize{\三角関数の性質{性質I}[i]}}\par -\三角関数の性質{性質I}[i]\par + +\auto{217}{\detokenize{\三角関数の性質{性質I}[i]}} + +\三角関数の性質{性質I}[i] + \auto{218}{\detokenize{\三角関数の性質{性質I}[b]}} + \三角関数の性質{性質I}[b] -\auto{219}{\detokenize{\三角関数の性質{性質J}[i]}}\par -\三角関数の性質{性質J}[i]\par + +\auto{219}{\detokenize{\三角関数の性質{性質J}[i]}} + +\三角関数の性質{性質J}[i] + \auto{220}{\detokenize{\三角関数の性質{性質J}[b]}} + \三角関数の性質{性質J}[b] -\auto{221}{\detokenize{\三角関数の性質{性質K}[i]}}\par -\三角関数の性質{性質K}[i]\par + +\auto{221}{\detokenize{\三角関数の性質{性質K}[i]}} + +\三角関数の性質{性質K}[i] + \auto{222}{\detokenize{\三角関数の性質{性質K}[b]}} + \三角関数の性質{性質K}[b] -\auto{223}{\detokenize{\三角関数の性質{性質L}[i]}}\par -\三角関数の性質{性質L}[i]\par + +\auto{223}{\detokenize{\三角関数の性質{性質L}[i]}} + +\三角関数の性質{性質L}[i] + \auto{224}{\detokenize{\三角関数の性質{性質L}[b]}} + \三角関数の性質{性質L}[b] -\auto{225}{\detokenize{\三角関数の性質{性質M}[i]}}\par -\三角関数の性質{性質M}[i]\par + +\auto{225}{\detokenize{\三角関数の性質{性質M}[i]}} + +\三角関数の性質{性質M}[i] + \auto{226}{\detokenize{\三角関数の性質{性質M}[b]}} + \三角関数の性質{性質M}[b] -\auto{227}{\detokenize{\三角関数の性質{性質N}[i]}}\par -\三角関数の性質{性質N}[i]\par + +\auto{227}{\detokenize{\三角関数の性質{性質N}[i]}} + +\三角関数の性質{性質N}[i] + \auto{228}{\detokenize{\三角関数の性質{性質N}[b]}} + \三角関数の性質{性質N}[b] -\auto{229}{\detokenize{\三角関数の性質{性質O}[i]}}\par -\三角関数の性質{性質O}[i]\par + +\auto{229}{\detokenize{\三角関数の性質{性質O}[i]}} + +\三角関数の性質{性質O}[i] + \auto{230}{\detokenize{\三角関数の性質{性質O}[b]}} + \三角関数の性質{性質O}[b] + %\begin{simplesquarebox}{三角関数の加法定理} %\begin{description} -\auto{231}{\detokenize{\三角関数の加法定理{公式A}[i]}}\par -\三角関数の加法定理{公式A}[i]\par +\auto{231}{\detokenize{\三角関数の加法定理{公式A}[i]}} + +\三角関数の加法定理{公式A}[i] + \auto{232}{\detokenize{\三角関数の加法定理{公式A}[b]}} + \三角関数の加法定理{公式A}[b] -\auto{233}{\detokenize{\三角関数の加法定理{公式B}[i]}}\par -\三角関数の加法定理{公式B}[i]\par + +\auto{233}{\detokenize{\三角関数の加法定理{公式B}[i]}} + +\三角関数の加法定理{公式B}[i] + \auto{234}{\detokenize{\三角関数の加法定理{公式B}[b]}} + \三角関数の加法定理{公式B}[b] -\auto{235}{\detokenize{\三角関数の加法定理{公式C}[i]}}\par -\三角関数の加法定理{公式C}[i]\par + +\auto{235}{\detokenize{\三角関数の加法定理{公式C}[i]}} + +\三角関数の加法定理{公式C}[i] + \auto{236}{\detokenize{\三角関数の加法定理{公式C}[b]}} + \三角関数の加法定理{公式C}[b] -\auto{231}{\detokenize{\三角関数の加法定理{証明}}}\par -\三角関数の加法定理{証明}\par + +\auto{231}{\detokenize{\三角関数の加法定理{証明}}} + +\三角関数の加法定理{証明} + %\end{description} %\end{simplesquarebox} -\auto{237}{\detokenize{\三角関数の二倍角の公式{公式A}[i]}}\par -\三角関数の二倍角の公式{公式A}[i]\par +\auto{237}{\detokenize{\三角関数の二倍角の公式{公式A}[i]}} + +\三角関数の二倍角の公式{公式A}[i] + \auto{238}{\detokenize{\三角関数の二倍角の公式{公式A}[b]}} + \三角関数の二倍角の公式{公式A}[b] -\auto{239}{\detokenize{\三角関数の二倍角の公式{公式B}[i]}}\par -\三角関数の二倍角の公式{公式B}[i]\par + +\auto{239}{\detokenize{\三角関数の二倍角の公式{公式B}[i]}} + +\三角関数の二倍角の公式{公式B}[i] + \auto{240}{\detokenize{\三角関数の二倍角の公式{公式B}[b]}} + \三角関数の二倍角の公式{公式B}[b] -\auto{241}{\detokenize{\三角関数の二倍角の公式{公式C}[i]}}\par -\三角関数の二倍角の公式{公式C}[i]\par + +\auto{241}{\detokenize{\三角関数の二倍角の公式{公式C}[i]}} + +\三角関数の二倍角の公式{公式C}[i] + \auto{242}{\detokenize{\三角関数の二倍角の公式{公式C}[b]}} + \三角関数の二倍角の公式{公式C}[b] -\auto{243}{\detokenize{\三角関数の二倍角の公式{公式D}[i]}}\par -\三角関数の二倍角の公式{公式D}[i]\par + +\auto{243}{\detokenize{\三角関数の二倍角の公式{公式D}[i]}} + +\三角関数の二倍角の公式{公式D}[i] + \auto{244}{\detokenize{\三角関数の二倍角の公式{公式D}[b]}} + \三角関数の二倍角の公式{公式D}[b] -\auto{245}{\detokenize{\三角関数の二倍角の公式{公式E}[i]}}\par -\三角関数の二倍角の公式{公式E}[i]\par + +\auto{245}{\detokenize{\三角関数の二倍角の公式{公式E}[i]}} + +\三角関数の二倍角の公式{公式E}[i] + \auto{246}{\detokenize{\三角関数の二倍角の公式{公式E}[b]}} + \三角関数の二倍角の公式{公式E}[b] -\auto{237}{\detokenize{\三角関数の二倍角の公式{証明}}}\par -\三角関数の二倍角の公式{証明}\par -\auto{247}{\detokenize{\三角関数の三倍角の公式{公式A}[i]}}\par -\三角関数の三倍角の公式{公式A}[i]\par + +\auto{237}{\detokenize{\三角関数の二倍角の公式{証明}}} + +\三角関数の二倍角の公式{証明} + +\auto{247}{\detokenize{\三角関数の三倍角の公式{公式A}[i]}} + +\三角関数の三倍角の公式{公式A}[i] + \auto{248}{\detokenize{\三角関数の三倍角の公式{公式A}[b]}} + \三角関数の三倍角の公式{公式A}[b] -\auto{249}{\detokenize{\三角関数の三倍角の公式{公式B}[i]}}\par -\三角関数の三倍角の公式{公式B}[i]\par + +\auto{249}{\detokenize{\三角関数の三倍角の公式{公式B}[i]}} + +\三角関数の三倍角の公式{公式B}[i] + \auto{250}{\detokenize{\三角関数の三倍角の公式{公式B}[b]}} + \三角関数の三倍角の公式{公式B}[b] -%\auto{251}{\detokenize{\三角関数の三倍角の公式{公式C}[i]}}\par -%\三角関数の三倍角の公式{公式C}[i]\par + +%\auto{251}{\detokenize{\三角関数の三倍角の公式{公式C}[i]}} + +%\三角関数の三倍角の公式{公式C}[i] + %\auto{251}{\detokenize{\三角関数の三倍角の公式{公式C}[b]}} + %\三角関数の三倍角の公式{公式C}[b] -\auto{247}{\detokenize{\三角関数の三倍角の公式{証明}}}\par -\三角関数の三倍角の公式{証明}\par -\auto{252}{\detokenize{\三角関数の積和公式{公式A}[i]}}\par -\三角関数の積和公式{公式A}[i]\par +\auto{247}{\detokenize{\三角関数の三倍角の公式{証明}}} + +\三角関数の三倍角の公式{証明} + + +\auto{252}{\detokenize{\三角関数の積和公式{公式A}[i]}} + +\三角関数の積和公式{公式A}[i] + \auto{253}{\detokenize{\三角関数の積和公式{公式A}[b]}} + \三角関数の積和公式{公式A}[b] -\auto{254}{\detokenize{\三角関数の積和公式{公式B}[i]}}\par -\三角関数の積和公式{公式B}[i]\par + +\auto{254}{\detokenize{\三角関数の積和公式{公式B}[i]}} + +\三角関数の積和公式{公式B}[i] + \auto{255}{\detokenize{\三角関数の積和公式{公式B}[b]}} + \三角関数の積和公式{公式B}[b] -\auto{256}{\detokenize{\三角関数の積和公式{公式C}[i]}}\par -\三角関数の積和公式{公式C}[i]\par + +\auto{256}{\detokenize{\三角関数の積和公式{公式C}[i]}} + +\三角関数の積和公式{公式C}[i] + \auto{257}{\detokenize{\三角関数の積和公式{公式C}[b]}} + \三角関数の積和公式{公式C}[b] -\auto{252}{\detokenize{\三角関数の積和公式{証明}}}\par -\三角関数の積和公式{証明}\par -\auto{258}{\detokenize{\三角関数の和積公式{公式A}[i]}}\par -\三角関数の和積公式{公式A}[i]\par +\auto{252}{\detokenize{\三角関数の積和公式{証明}}} + +\三角関数の積和公式{証明} + + +\auto{258}{\detokenize{\三角関数の和積公式{公式A}[i]}} + +\三角関数の和積公式{公式A}[i] + \auto{259}{\detokenize{\三角関数の和積公式{公式A}[b]}} + \三角関数の和積公式{公式A}[b] -\auto{260}{\detokenize{\三角関数の和積公式{公式B}[i]}}\par -\三角関数の和積公式{公式B}[i]\par + +\auto{260}{\detokenize{\三角関数の和積公式{公式B}[i]}} + +\三角関数の和積公式{公式B}[i] + \auto{261}{\detokenize{\三角関数の和積公式{公式B}[b]}} + \三角関数の和積公式{公式B}[b] -\auto{262}{\detokenize{\三角関数の和積公式{公式C}[i]}}\par -\三角関数の和積公式{公式C}[i]\par + +\auto{262}{\detokenize{\三角関数の和積公式{公式C}[i]}} + +\三角関数の和積公式{公式C}[i] + \auto{263}{\detokenize{\三角関数の和積公式{公式C}[b]}} + \三角関数の和積公式{公式C}[b] -\auto{264}{\detokenize{\三角関数の和積公式{公式D}[i]}}\par -\三角関数の和積公式{公式D}[i]\par + +\auto{264}{\detokenize{\三角関数の和積公式{公式D}[i]}} + +\三角関数の和積公式{公式D}[i] + \auto{265}{\detokenize{\三角関数の和積公式{公式D}[b]}} + \三角関数の和積公式{公式D}[b] -\auto{258}{\detokenize{\三角関数の和積公式{証明}}}\par -\三角関数の和積公式{証明}\par + +\auto{258}{\detokenize{\三角関数の和積公式{証明}}} + +\三角関数の和積公式{証明} + %\begin{simplesquarebox}{三角関数の合成} %\begin{description} -\auto{267}{\detokenize{\三角関数の合成{公式}[i]}}\par -\三角関数の合成{公式}[i]\par +\auto{267}{\detokenize{\三角関数の合成{公式}[i]}} + +\三角関数の合成{公式}[i] + \auto{268}{\detokenize{\三角関数の合成{公式}[b]}} -\三角関数の合成{公式}[b]\par -\auto{267}{\detokenize{\三角関数の合成{証明}}}\par -\三角関数の合成{証明}\par + +\三角関数の合成{公式}[b] + + +\auto{267}{\detokenize{\三角関数の合成{証明}}} + +\三角関数の合成{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{有理数の指数} %\begin{description} -\auto{269}{\detokenize{\有理数の指数{公式A}[i]}}\par -\有理数の指数{公式A}[i]\par +\auto{269}{\detokenize{\有理数の指数{公式A}[i]}} + +\有理数の指数{公式A}[i] + \auto{270}{\detokenize{\有理数の指数{公式A}[b]}} + \有理数の指数{公式A}[b] -\auto{271}{\detokenize{\有理数の指数{公式B}[i]}}\par -\有理数の指数{公式B}[i]\par + +\auto{271}{\detokenize{\有理数の指数{公式B}[i]}} + +\有理数の指数{公式B}[i] + \auto{272}{\detokenize{\有理数の指数{公式B}[b]}} + \有理数の指数{公式B}[b] -\auto{273}{\detokenize{\有理数の指数{公式C}[i]}}\par -\有理数の指数{公式C}[i]\par + +\auto{273}{\detokenize{\有理数の指数{公式C}[i]}} + +\有理数の指数{公式C}[i] + \auto{274}{\detokenize{\有理数の指数{公式C}[b]}} + \有理数の指数{公式C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{指数法則} %\begin{description} -\auto{275}{\detokenize{\指数法則{公式A}[i]}}\par -\指数法則{公式A}[i]\par +\auto{275}{\detokenize{\指数法則{公式A}[i]}} + +\指数法則{公式A}[i] + \auto{276}{\detokenize{\指数法則{公式A}[b]}} + \指数法則{公式A}[b] -\auto{277}{\detokenize{\指数法則{公式B}[i]}}\par -\指数法則{公式B}[i]\par + +\auto{277}{\detokenize{\指数法則{公式B}[i]}} + +\指数法則{公式B}[i] + \auto{278}{\detokenize{\指数法則{公式B}[b]}} + \指数法則{公式B}[b] -\auto{279}{\detokenize{\指数法則{公式C}[i]}}\par -\指数法則{公式C}[i]\par + +\auto{279}{\detokenize{\指数法則{公式C}[i]}} + +\指数法則{公式C}[i] + \auto{280}{\detokenize{\指数法則{公式C}[b]}} + \指数法則{公式C}[b] -\auto{281}{\detokenize{\指数法則{公式D}[i]}}\par -\指数法則{公式D}[i]\par + +\auto{281}{\detokenize{\指数法則{公式D}[i]}} + +\指数法則{公式D}[i] + \auto{282}{\detokenize{\指数法則{公式D}[b]}} + \指数法則{公式D}[b] -\auto{283}{\detokenize{\指数法則{公式E}[i]}}\par -\指数法則{公式E}[i]\par + +\auto{283}{\detokenize{\指数法則{公式E}[i]}} + +\指数法則{公式E}[i] + \auto{284}{\detokenize{\指数法則{公式E}[b]}} + \指数法則{公式E}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{対数の定義} %\begin{description} -\auto{285}{\detokenize{\対数の定義{定義}[i]}}\par -\対数の定義{定義}[i]\par +\auto{285}{\detokenize{\対数の定義{定義}[i]}} + +\対数の定義{定義}[i] + \auto{286}{\detokenize{\対数の定義{定義}[b]}} + \対数の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{対数の性質} %\begin{description} -\auto{287}{\detokenize{\対数の性質{公式A}[i]}}\par -\対数の性質{公式A}[i]\par +\auto{287}{\detokenize{\対数の性質{公式A}[i]}} + +\対数の性質{公式A}[i] + \auto{288}{\detokenize{\対数の性質{公式A}[b]}} + \対数の性質{公式A}[b] -\auto{289}{\detokenize{\対数の性質{公式B}[i]}}\par -\対数の性質{公式B}[i]\par + +\auto{289}{\detokenize{\対数の性質{公式B}[i]}} + +\対数の性質{公式B}[i] + \auto{290}{\detokenize{\対数の性質{公式B}[b]}} + \対数の性質{公式B}[b] -\auto{291}{\detokenize{\対数の性質{公式C}[i]}}\par -\対数の性質{公式C}[i]\par + +\auto{291}{\detokenize{\対数の性質{公式C}[i]}} + +\対数の性質{公式C}[i] + \auto{292}{\detokenize{\対数の性質{公式C}[b]}} + \対数の性質{公式C}[b] -\auto{293}{\detokenize{\対数の性質{公式D}[i]}}\par -\対数の性質{公式D}[i]\par + +\auto{293}{\detokenize{\対数の性質{公式D}[i]}} + +\対数の性質{公式D}[i] + \auto{294}{\detokenize{\対数の性質{公式D}[b]}} + \対数の性質{公式D}[b] -\auto{295}{\detokenize{\対数の性質{公式E}[i]}}\par -\対数の性質{公式E}[i]\par + +\auto{295}{\detokenize{\対数の性質{公式E}[i]}} + +\対数の性質{公式E}[i] + \auto{296}{\detokenize{\対数の性質{公式E}[b]}} + \対数の性質{公式E}[b] -\auto{297}{\detokenize{\対数の性質{公式F}[i]}}\par -\対数の性質{公式F}[i]\par + +\auto{297}{\detokenize{\対数の性質{公式F}[i]}} + +\対数の性質{公式F}[i] + \auto{298}{\detokenize{\対数の性質{公式F}[b]}} + \対数の性質{公式F}[b] -\auto{287}{\detokenize{\対数の性質{証明}}}\par -\対数の性質{証明}\par + +\auto{287}{\detokenize{\対数の性質{証明}}} + +\対数の性質{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{底の変換公式} %\begin{description} -\auto{299}{\detokenize{\底の変換公式{公式}[i]}}\par -\底の変換公式{公式}[i]\par +\auto{299}{\detokenize{\底の変換公式{公式}[i]}} + +\底の変換公式{公式}[i] + \auto{300}{\detokenize{\底の変換公式{公式}[b]}} + \底の変換公式{公式}[b] -\auto{299}{\detokenize{\底の変換公式{証明}}}\par -\底の変換公式{証明}\par + +\auto{299}{\detokenize{\底の変換公式{証明}}} + +\底の変換公式{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{導関数の微分} %\begin{description} -\auto{301}{\detokenize{\導関数の定義{定義}[i]}}\par -\導関数の定義{定義}[i]\par +\auto{301}{\detokenize{\導関数の定義{定義}[i]}} + +\導関数の定義{定義}[i] + \auto{302}{\detokenize{\導関数の定義{定義}[b]}} + \導関数の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{べき乗関数と定数関数の導関数} %\begin{description} -\auto{303}{\detokenize{\べき乗関数と定数関数の導関数{公式A}[i]}}\par -\べき乗関数と定数関数の導関数{公式A}[i]\par +\auto{303}{\detokenize{\べき乗関数と定数関数の導関数{公式A}[i]}} + +\べき乗関数と定数関数の導関数{公式A}[i] + \auto{304}{\detokenize{\べき乗関数と定数関数の導関数{公式A}[b]}} + \べき乗関数と定数関数の導関数{公式A}[b] -\auto{305}{\detokenize{\べき乗関数と定数関数の導関数{公式B}[i]}}\par -\べき乗関数と定数関数の導関数{公式B}[i]\par + +\auto{305}{\detokenize{\べき乗関数と定数関数の導関数{公式B}[i]}} + +\べき乗関数と定数関数の導関数{公式B}[i] + \auto{306}{\detokenize{\べき乗関数と定数関数の導関数{公式B}[b]}} + \べき乗関数と定数関数の導関数{公式B}[b] -\auto{303}{\detokenize{\べき乗関数と定数関数の導関数{証明}}}\par -\べき乗関数と定数関数の導関数{証明}\par + +\auto{303}{\detokenize{\べき乗関数と定数関数の導関数{証明}}} + +\べき乗関数と定数関数の導関数{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{導関数の性質} %\begin{description} -\auto{307}{\detokenize{\導関数の性質{公式A}[i]}}\par -\導関数の性質{公式A}[i]\par +\auto{307}{\detokenize{\導関数の性質{公式A}[i]}} + +\導関数の性質{公式A}[i] + \auto{308}{\detokenize{\導関数の性質{公式A}[b]}} + \導関数の性質{公式A}[b] -\auto{309}{\detokenize{\導関数の性質{公式B}[i]}}\par -\導関数の性質{公式B}[i]\par + +\auto{309}{\detokenize{\導関数の性質{公式B}[i]}} + +\導関数の性質{公式B}[i] + \auto{310}{\detokenize{\導関数の性質{公式B}[b]}} + \導関数の性質{公式B}[b] -\auto{311}{\detokenize{\導関数の性質{公式C}[i]}}\par -\導関数の性質{公式C}[i]\par + +\auto{311}{\detokenize{\導関数の性質{公式C}[i]}} + +\導関数の性質{公式C}[i] + \auto{312}{\detokenize{\導関数の性質{公式C}[b]}} + \導関数の性質{公式C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{接線の方程式} %\begin{description} -\auto{313}{\detokenize{\接線の方程式{公式}[i]}}\par -\接線の方程式{公式}[i]\par +\auto{313}{\detokenize{\接線の方程式{公式}[i]}} + +\接線の方程式{公式}[i] + \auto{314}{\detokenize{\接線の方程式{公式}[b]}} + \接線の方程式{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{不定積分の定義} %\begin{description} -\auto{315}{\detokenize{\不定積分の定義{定義}[i]}}\par -\不定積分の定義{定義}[i]\par +\auto{315}{\detokenize{\不定積分の定義{定義}[i]}} + +\不定積分の定義{定義}[i] + \auto{316}{\detokenize{\不定積分の定義{定義}[b]}} + \不定積分の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{べき乗関数の不定積分} %\begin{description} -\auto{317}{\detokenize{\べき乗関数の不定積分{公式}[i]}}\par -\べき乗関数の不定積分{公式}[i]\par +\auto{317}{\detokenize{\べき乗関数の不定積分{公式}[i]}} + +\べき乗関数の不定積分{公式}[i] + \auto{318}{\detokenize{\べき乗関数の不定積分{公式}[b]}} + \べき乗関数の不定積分{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{不定積分の性質} %\begin{description} -%\auto{319}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式A}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式A}[i]\par}\par -\不定積分の性質{公式A}[i]\par\par -%\auto{320}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式A}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式A}[b]}\par +%\auto{319}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式A}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式A}[i] +} + +\不定積分の性質{公式A}[i] + + +%\auto{320}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式A}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式A}[b] +} + \不定積分の性質{公式A}[b] -%\auto{321}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式B}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式B}[i]\par}\par -\不定積分の性質{公式B}[i]\par\par -%\auto{322}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式B}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式B}[b]}\par + +%\auto{321}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式B}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式B}[i] +} + +\不定積分の性質{公式B}[i] + + +%\auto{322}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式B}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式B}[b] +} + \不定積分の性質{公式B}[b] -%\auto{323}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式C}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式C}[i]\par}\par -\不定積分の性質{公式C}[i]\par\par + +%\auto{323}{\texttt{\textbackslash 不定積分の性質\h{-0.1mm}$\lbrace$\h{公式C}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式C}[i] +} + +\不定積分の性質{公式C}[i] + + %\auto{324}{\texttt{\textbackslash -%\不定積分の性質{公式C}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}}\par -\auto[1]{\不定積分の性質{公式C}[b]}\par +%\不定積分の性質{公式C}\h{-0.1mm}$\rbrace$\kakkokukuri[[]{i}}} + +\auto[1]{\不定積分の性質{公式C}[b] +} + \不定積分の性質{公式C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{定積分の定義} %\begin{description} -\auto{325}{\detokenize{\定積分の定義{定義}[i]}}\par -\定積分の定義{定義}[i]\par +\auto{325}{\detokenize{\定積分の定義{定義}[i]}} + +\定積分の定義{定義}[i] + \auto{326}{\detokenize{\定積分の定義{定義}[b]}} + \定積分の定義{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{定積分の性質} %\begin{description} -\auto{327}{\detokenize{\定積分の性質{公式A}[i]}}\par -\定積分の性質{公式A}[i]\par +\auto{327}{\detokenize{\定積分の性質{公式A}[i]}} + +\定積分の性質{公式A}[i] + \auto{328}{\detokenize{\定積分の性質{公式A}[b]}} + \定積分の性質{公式A}[b] -\auto{329}{\detokenize{\定積分の性質{公式B}[i]}}\par -\定積分の性質{公式B}[i]\par + +\auto{329}{\detokenize{\定積分の性質{公式B}[i]}} + +\定積分の性質{公式B}[i] + \auto{330}{\detokenize{\定積分の性質{公式B}[b]}} + \定積分の性質{公式B}[b] -\auto{331}{\detokenize{\定積分の性質{公式C}[i]}}\par -\定積分の性質{公式C}[i]\par + +\auto{331}{\detokenize{\定積分の性質{公式C}[i]}} + +\定積分の性質{公式C}[i] + \auto{332}{\detokenize{\定積分の性質{公式C}[b]}} + \定積分の性質{公式C}[b] -\auto{333}{\detokenize{\定積分の性質{公式D}[i]}}\par -\定積分の性質{公式D}[i]\par + +\auto{333}{\detokenize{\定積分の性質{公式D}[i]}} + +\定積分の性質{公式D}[i] + \auto{334}{\detokenize{\定積分の性質{公式D}[b]}} + \定積分の性質{公式D}[b] -\auto{335}{\detokenize{\定積分の性質{公式E}[i]}}\par -\定積分の性質{公式E}[i]\par + +\auto{335}{\detokenize{\定積分の性質{公式E}[i]}} + +\定積分の性質{公式E}[i] + \auto{336}{\detokenize{\定積分の性質{公式E}[b]}} + \定積分の性質{公式E}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{ベクトルの演算} %\begin{description} %n-336=個数 -\auto{337}{\detokenize{\ベクトルの演算{公式A}[i]}}\par -\ベクトルの演算{公式A}[i]\par +\auto{337}{\detokenize{\ベクトルの演算{公式A}[i]}} + +\ベクトルの演算{公式A}[i] + \auto{338}{\detokenize{\ベクトルの演算{公式A}[b]}} + \ベクトルの演算{公式A}[b] -\auto{339}{\detokenize{\ベクトルの演算{公式B}[i]}}\par -\ベクトルの演算{公式B}[i]\par + +\auto{339}{\detokenize{\ベクトルの演算{公式B}[i]}} + +\ベクトルの演算{公式B}[i] + \auto{340}{\detokenize{\ベクトルの演算{公式B}[b]}} + \ベクトルの演算{公式B}[b] -\auto{341}{\detokenize{\ベクトルの演算{公式C}[i]}}\par -\ベクトルの演算{公式C}[i]\par + +\auto{341}{\detokenize{\ベクトルの演算{公式C}[i]}} + +\ベクトルの演算{公式C}[i] + \auto{342}{\detokenize{\ベクトルの演算{公式C}[b]}} + \ベクトルの演算{公式C}[b] -\auto{343}{\detokenize{\ベクトルの演算{公式D}[i]}}\par -\ベクトルの演算{公式D}[i]\par + +\auto{343}{\detokenize{\ベクトルの演算{公式D}[i]}} + +\ベクトルの演算{公式D}[i] + \auto{344}{\detokenize{\ベクトルの演算{公式D}[b]}} + \ベクトルの演算{公式D}[b] -\auto{345}{\detokenize{\ベクトルの演算{公式E}[i]}}\par -\ベクトルの演算{公式E}[i]\par + +\auto{345}{\detokenize{\ベクトルの演算{公式E}[i]}} + +\ベクトルの演算{公式E}[i] + \auto{346}{\detokenize{\ベクトルの演算{公式E}[b]}} + \ベクトルの演算{公式E}[b] -\auto{347}{\detokenize{\ベクトルの演算{公式F}[i]}}\par -\ベクトルの演算{公式F}[i]\par + +\auto{347}{\detokenize{\ベクトルの演算{公式F}[i]}} + +\ベクトルの演算{公式F}[i] + \auto{348}{\detokenize{\ベクトルの演算{公式F}[b]}} + \ベクトルの演算{公式F}[b] -\auto{349}{\detokenize{\ベクトルの演算{公式G}[i]}}\par -\ベクトルの演算{公式G}[i]\par + +\auto{349}{\detokenize{\ベクトルの演算{公式G}[i]}} + +\ベクトルの演算{公式G}[i] + \auto{350}{\detokenize{\ベクトルの演算{公式G}[b]}} + \ベクトルの演算{公式G}[b] -\auto{351}{\detokenize{\ベクトルの演算{公式H}[i]}}\par -\ベクトルの演算{公式H}[i]\par + +\auto{351}{\detokenize{\ベクトルの演算{公式H}[i]}} + +\ベクトルの演算{公式H}[i] + \auto{352}{\detokenize{\ベクトルの演算{公式H}[b]}} + \ベクトルの演算{公式H}[b] -\auto{353}{\detokenize{\ベクトルの演算{公式I}[i]}}\par -\ベクトルの演算{公式I}[i]\par + +\auto{353}{\detokenize{\ベクトルの演算{公式I}[i]}} + +\ベクトルの演算{公式I}[i] + \auto{354}{\detokenize{\ベクトルの演算{公式I}[b]}} + \ベクトルの演算{公式I}[b] -\auto{355}{\detokenize{\ベクトルの演算{公式J}[i]}}\par -\ベクトルの演算{公式J}[i]\par + +\auto{355}{\detokenize{\ベクトルの演算{公式J}[i]}} + +\ベクトルの演算{公式J}[i] + \auto{356}{\detokenize{\ベクトルの演算{公式J}[b]}} + \ベクトルの演算{公式J}[b] -\auto{357}{\detokenize{\ベクトルの演算{公式K}[i]}}\par -\ベクトルの演算{公式K}[i]\par + +\auto{357}{\detokenize{\ベクトルの演算{公式K}[i]}} + +\ベクトルの演算{公式K}[i] + \auto{358}{\detokenize{\ベクトルの演算{公式K}[b]}} + \ベクトルの演算{公式K}[b] -\auto{359}{\detokenize{\ベクトルの演算{公式L}[i]}}\par -\ベクトルの演算{公式L}[i]\par + +\auto{359}{\detokenize{\ベクトルの演算{公式L}[i]}} + +\ベクトルの演算{公式L}[i] + \auto{360}{\detokenize{\ベクトルの演算{公式L}[b]}} + \ベクトルの演算{公式L}[b] -%\auto{361}{\detokenize{\ベクトルの演算{公式M}[i]}}\par -%\ベクトルの演算{公式M}[i]\par + +%\auto{361}{\detokenize{\ベクトルの演算{公式M}[i]}} + +%\ベクトルの演算{公式M}[i] + %\auto{362}{\detokenize{\ベクトルの演算{公式M}[b]}} + %\ベクトルの演算{公式M}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平面ベクトルの分解} %\begin{description} -\auto{363}{\detokenize{\平面ベクトルの分解{公式}[i]}}\par -\平面ベクトルの分解{公式}[i]\par +\auto{363}{\detokenize{\平面ベクトルの分解{公式}[i]}} + +\平面ベクトルの分解{公式}[i] + \auto{364}{\detokenize{\平面ベクトルの分解{公式}[b]}} + \平面ベクトルの分解{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平面ベクトルの成分} %\begin{description} -\auto{365}{\detokenize{\平面ベクトルの成分{公式A}[i]}}\par -\平面ベクトルの成分{公式A}[i]\par +\auto{365}{\detokenize{\平面ベクトルの成分{公式A}[i]}} + +\平面ベクトルの成分{公式A}[i] + \auto{366}{\detokenize{\平面ベクトルの成分{公式A}[b]}} + \平面ベクトルの成分{公式A}[b] -\auto{367}{\detokenize{\平面ベクトルの成分{公式B}[i]}}\par -\平面ベクトルの成分{公式B}[i]\par + +\auto{367}{\detokenize{\平面ベクトルの成分{公式B}[i]}} + +\平面ベクトルの成分{公式B}[i] + \auto{368}{\detokenize{\平面ベクトルの成分{公式B}[b]}} + \平面ベクトルの成分{公式B}[b] -\auto{369}{\detokenize{\平面ベクトルの成分{公式C}[i]}}\par -\平面ベクトルの成分{公式C}[i]\par + +\auto{369}{\detokenize{\平面ベクトルの成分{公式C}[i]}} + +\平面ベクトルの成分{公式C}[i] + \auto{370}{\detokenize{\平面ベクトルの成分{公式C}[b]}} + \平面ベクトルの成分{公式C}[b] -\auto{371}{\detokenize{\平面ベクトルの成分{公式D}[i]}}\par -\平面ベクトルの成分{公式D}[i]\par + +\auto{371}{\detokenize{\平面ベクトルの成分{公式D}[i]}} + +\平面ベクトルの成分{公式D}[i] + \auto{372}{\detokenize{\平面ベクトルの成分{公式D}[b]}} + \平面ベクトルの成分{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{ベクトルの成分と大きさ} %\begin{description} -\auto{373}{\detokenize{\ベクトルの成分と大きさ{公式A}[i]}}\par -\ベクトルの成分と大きさ{公式A}[i]\par +\auto{373}{\detokenize{\ベクトルの成分と大きさ{公式A}[i]}} + +\ベクトルの成分と大きさ{公式A}[i] + \auto{374}{\detokenize{\ベクトルの成分と大きさ{公式A}[b]}} + \ベクトルの成分と大きさ{公式A}[b] -\auto{375}{\detokenize{\ベクトルの成分と大きさ{公式B}[i]}}\par -\ベクトルの成分と大きさ{公式B}[i]\par + +\auto{375}{\detokenize{\ベクトルの成分と大きさ{公式B}[i]}} + +\ベクトルの成分と大きさ{公式B}[i] + \auto{376}{\detokenize{\ベクトルの成分と大きさ{公式B}[b]}} + \ベクトルの成分と大きさ{公式B}[b] -\auto{373}{\detokenize{\ベクトルの成分と大きさ{証明}}}\par -\ベクトルの成分と大きさ{証明}\par + +\auto{373}{\detokenize{\ベクトルの成分と大きさ{証明}}} + +\ベクトルの成分と大きさ{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平面ベクトルの内積} %\begin{description} -\auto{377}{\detokenize{\平面ベクトルの内積{公式}[i]}}\par -\平面ベクトルの内積{公式}[i]\par +\auto{377}{\detokenize{\平面ベクトルの内積{公式}[i]}} + +\平面ベクトルの内積{公式}[i] + \auto{378}{\detokenize{\平面ベクトルの内積{公式}[b]}} + \平面ベクトルの内積{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{内積の性質} %\begin{description} -\auto{379}{\detokenize{\内積の性質{公式A}[i]}}\par -\内積の性質{公式A}[i]\par +\auto{379}{\detokenize{\内積の性質{公式A}[i]}} + +\内積の性質{公式A}[i] + \auto{380}{\detokenize{\内積の性質{公式A}[b]}} + \内積の性質{公式A}[b] -\auto{381}{\detokenize{\内積の性質{公式B}[i]}}\par -\内積の性質{公式B}[i]\par + +\auto{381}{\detokenize{\内積の性質{公式B}[i]}} + +\内積の性質{公式B}[i] + \auto{382}{\detokenize{\内積の性質{公式B}[b]}} + \内積の性質{公式B}[b] -\auto{383}{\detokenize{\内積の性質{公式C}[i]}}\par -\内積の性質{公式C}[i]\par + +\auto{383}{\detokenize{\内積の性質{公式C}[i]}} + +\内積の性質{公式C}[i] + \auto{384}{\detokenize{\内積の性質{公式C}[b]}} + \内積の性質{公式C}[b] -\auto{385}{\detokenize{\内積の性質{公式D}[i]}}\par -\内積の性質{公式D}[i]\par + +\auto{385}{\detokenize{\内積の性質{公式D}[i]}} + +\内積の性質{公式D}[i] + \auto{386}{\detokenize{\内積の性質{公式D}[b]}} + \内積の性質{公式D}[b] -\auto{387}{\detokenize{\内積の性質{公式E}[i]}}\par -\内積の性質{公式E}[i]\par + +\auto{387}{\detokenize{\内積の性質{公式E}[i]}} + +\内積の性質{公式E}[i] + \auto{388}{\detokenize{\内積の性質{公式E}[b]}} + \内積の性質{公式E}[b] -\auto{389}{\detokenize{\内積の性質{公式F}[i]}}\par -\内積の性質{公式F}[i]\par + +\auto{389}{\detokenize{\内積の性質{公式F}[i]}} + +\内積の性質{公式F}[i] + \auto{390}{\detokenize{\内積の性質{公式F}[b]}} + \内積の性質{公式F}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平面ベクトルの平行条件} %\begin{description} -\auto{391}{\detokenize{\平面ベクトルの平行条件{条件}[i]}}\par -\平面ベクトルの平行条件{条件}[i]\par +\auto{391}{\detokenize{\平面ベクトルの平行条件{条件}[i]}} + +\平面ベクトルの平行条件{条件}[i] + \auto{392}{\detokenize{\平面ベクトルの平行条件{条件}[b]}} + \平面ベクトルの平行条件{条件}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平面ベクトルの垂直条件} %\begin{description} -\auto{393}{\detokenize{\平面ベクトルの垂直条件{条件}[i]}}\par -\平面ベクトルの垂直条件{条件}[i]\par +\auto{393}{\detokenize{\平面ベクトルの垂直条件{条件}[i]}} + +\平面ベクトルの垂直条件{条件}[i] + \auto{394}{\detokenize{\平面ベクトルの垂直条件{条件}[b]}} + \平面ベクトルの垂直条件{条件}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{位置ベクトル} %\begin{description} -\auto{395}{\detokenize{\位置ベクトル{公式A}[i]}}\par -\位置ベクトル{公式A}[i]\par +\auto{395}{\detokenize{\位置ベクトル{公式A}[i]}} + +\位置ベクトル{公式A}[i] + \auto{396}{\detokenize{\位置ベクトル{公式A}[b]}} + \位置ベクトル{公式A}[b] -\auto{395}{\detokenize{\位置ベクトル{公式A}[i]}}\par -\位置ベクトル{内分点の位置ベクトルの証明}[i]\par -\auto{397}{\detokenize{\位置ベクトル{公式B}[i]}}\par -\位置ベクトル{公式B}[i]\par + +\auto{395}{\detokenize{\位置ベクトル{公式A}[i]}} + +\位置ベクトル{内分点の位置ベクトルの証明} + +\auto{397}{\detokenize{\位置ベクトル{公式B}[i]}} + +\位置ベクトル{公式B}[i] + \auto{398}{\detokenize{\位置ベクトル{公式B}[b]}} + \位置ベクトル{公式B}[b] -\auto{397}{\detokenize{\位置ベクトル{外分点の位置ベクトルの証明}[i]}}\par -\位置ベクトル{外分点の位置ベクトルの証明}[i]\par -\auto{399}{\detokenize{\位置ベクトル{公式C}[i]}}\par -\位置ベクトル{公式C}[i]\par + +\auto{397}{\detokenize{\位置ベクトル{外分点の位置ベクトルの証明}}} + +\位置ベクトル{外分点の位置ベクトルの証明} + +\auto{399}{\detokenize{\位置ベクトル{公式C}[i]}} + +\位置ベクトル{公式C}[i] + \auto{400}{\detokenize{\位置ベクトル{公式C}[b]}} + \位置ベクトル{公式C}[b] -\auto{401}{\detokenize{\位置ベクトル{公式D}[i]}}\par -\位置ベクトル{公式D}[i]\par + +\auto{401}{\detokenize{\位置ベクトル{公式D}[i]}} + +\位置ベクトル{公式D}[i] + \auto{402}{\detokenize{\位置ベクトル{公式D}[b]}} + \位置ベクトル{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{ベクトル方程式} %\begin{description} -\auto{403}{\detokenize{\ベクトル方程式{公式A}[i]}}\par -\ベクトル方程式{公式A}[i]\par +\auto{403}{\detokenize{\ベクトル方程式{公式A}[i]}} + +\ベクトル方程式{公式A}[i] + \auto{404}{\detokenize{\ベクトル方程式{公式A}[b]}} + \ベクトル方程式{公式A}[b] -\auto{405}{\detokenize{\ベクトル方程式{公式B}[i]}}\par -\ベクトル方程式{公式B}[i]\par + +\auto{405}{\detokenize{\ベクトル方程式{公式B}[i]}} + +\ベクトル方程式{公式B}[i] + \auto{406}{\detokenize{\ベクトル方程式{公式B}[b]}} + \ベクトル方程式{公式B}[b] -\auto{407}{\detokenize{\ベクトル方程式{公式C}[i]}}\par -\ベクトル方程式{公式C}[i]\par + +\auto{407}{\detokenize{\ベクトル方程式{公式C}[i]}} + +\ベクトル方程式{公式C}[i] + \auto{408}{\detokenize{\ベクトル方程式{公式C}[b]}} + \ベクトル方程式{公式C}[b] -\auto{409}{\detokenize{\ベクトル方程式{公式D}[i]}}\par -\ベクトル方程式{公式D}[i]\par + +\auto{409}{\detokenize{\ベクトル方程式{公式D}[i]}} + +\ベクトル方程式{公式D}[i] + \auto{410}{\detokenize{\ベクトル方程式{公式D}[b]}} + \ベクトル方程式{公式D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{等差数列} %\begin{description} -\auto{411}{\detokenize{\等差数列{一般項}[i]}}\par -\等差数列{一般項}[i]\par +\auto{411}{\detokenize{\等差数列{一般項}[i]}} + +\等差数列{一般項}[i] + \auto{412}{\detokenize{\等差数列{一般項}[b]}} + \等差数列{一般項}[b] -\auto{413}{\detokenize{\等差数列{総和}[i]}}\par -\等差数列{総和}[i]\par + +\auto{413}{\detokenize{\等差数列{総和}[i]}} + +\等差数列{総和}[i] + \auto{414}{\detokenize{\等差数列{総和}[b]}} + \等差数列{総和}[b] -\auto{411}{\detokenize{\等差数列{証明}}}\par -\等差数列{証明}\par + +\auto{411}{\detokenize{\等差数列{証明}}} + +\等差数列{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{等比数列} %\begin{description} -\auto{415}{\detokenize{\等比数列{一般項}[i]}}\par -\等比数列{一般項}[i]\par +\auto{415}{\detokenize{\等比数列{一般項}[i]}} + +\等比数列{一般項}[i] + \auto{416}{\detokenize{\等比数列{一般項}[b]}} + \等比数列{一般項}[b] -\auto{417}{\detokenize{\等比数列{総和}[i]}}\par -\等比数列{総和}[i]\par + +\auto{417}{\detokenize{\等比数列{総和}[i]}} + +\等比数列{総和}[i] + \auto{418}{\detokenize{\等比数列{総和}[b]}} + \等比数列{総和}[b] -\auto{415}{\detokenize{\等比数列{証明}}}\par -\等比数列{証明}\par + +\auto{415}{\detokenize{\等比数列{証明}}} + +\等比数列{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{シグマの公式} %\begin{description} -\auto{419}{\detokenize{\シグマの公式{公式A}[i]}}\par -\シグマの公式{公式A}[i]\par +\auto{419}{\detokenize{\シグマの公式{公式A}[i]}} + +\シグマの公式{公式A}[i] + \auto{420}{\detokenize{\シグマの公式{公式A}[b]}} + \シグマの公式{公式A}[b] -\auto{421}{\detokenize{\シグマの公式{公式B}[i]}}\par -\シグマの公式{公式B}[i]\par + +\auto{421}{\detokenize{\シグマの公式{公式B}[i]}} + +\シグマの公式{公式B}[i] + \auto{422}{\detokenize{\シグマの公式{公式B}[b]}} + \シグマの公式{公式B}[b] -\auto{423}{\detokenize{\シグマの公式{公式C}[i]}}\par -\シグマの公式{公式C}[i]\par + +\auto{423}{\detokenize{\シグマの公式{公式C}[i]}} + +\シグマの公式{公式C}[i] + \auto{424}{\detokenize{\シグマの公式{公式C}[b]}} + \シグマの公式{公式C}[b] -\auto{425}{\detokenize{\シグマの公式{公式D}[i]}}\par -\シグマの公式{公式D}[i]\par + +\auto{425}{\detokenize{\シグマの公式{公式D}[i]}} + +\シグマの公式{公式D}[i] + \auto{426}{\detokenize{\シグマの公式{公式D}[b]}} + \シグマの公式{公式D}[b] -\auto{427}{\detokenize{\シグマの公式{公式E}[i]}}\par -\シグマの公式{公式E}[i]\par + +\auto{427}{\detokenize{\シグマの公式{公式E}[i]}} + +\シグマの公式{公式E}[i] + \auto{428}{\detokenize{\シグマの公式{公式E}[b]}} + \シグマの公式{公式E}[b] -\auto{419}{\detokenize{\シグマの公式{証明}}}\par -\シグマの公式{証明}\par + +\auto{419}{\detokenize{\シグマの公式{証明}}} + +\シグマの公式{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{シグマの性質} %\begin{description} -\auto{429}{\detokenize{\シグマの性質{性質}[i]}}\par -\シグマの性質{性質}[i]\par +\auto{429}{\detokenize{\シグマの性質{性質}[i]}} + +\シグマの性質{性質}[i] + \auto{430}{\detokenize{\シグマの性質{性質}[b]}} + \シグマの性質{性質}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{階差数列} %\begin{description} -\auto{431}{\detokenize{\階差数列{一般項}[i]}}\par -\階差数列{一般項}[i]\par +\auto{431}{\detokenize{\階差数列{一般項}[i]}} + +\階差数列{一般項}[i] + \auto{432}{\detokenize{\階差数列{一般項}[b]}} + \階差数列{一般項}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{漸化式} %\begin{description} -\auto{433}{\detokenize{\漸化式{等差型}[i]}}\par -\漸化式{等差型}[i]\par +\auto{433}{\detokenize{\漸化式{等差型}[i]}} + +\漸化式{等差型}[i] + \auto{434}{\detokenize{\漸化式{等差型}[b]}} + \漸化式{等差型}[b] -\auto{435}{\detokenize{\漸化式{等比型}[i]}}\par -\漸化式{等比型}[i]\par + +\auto{435}{\detokenize{\漸化式{等比型}[i]}} + +\漸化式{等比型}[i] + \auto{436}{\detokenize{\漸化式{等比型}[b]}} -\漸化式{等比型}[b]\par -\auto{437}{\detokenize{\漸化式{階差型}[i]}}\par -\漸化式{階差型}[i]\par + +\漸化式{等比型}[b] + + +\auto{437}{\detokenize{\漸化式{階差型}[i]}} + +\漸化式{階差型}[i] + \auto{438}{\detokenize{\漸化式{階差型}[b]}} -\漸化式{階差型}[b]\par -\auto{439}{\detokenize{\漸化式{特性方程式}[i]}}\par -\漸化式{特性方程式}[i]\par + +\漸化式{階差型}[b] + + +\auto{439}{\detokenize{\漸化式{特性方程式}[i]}} + +\漸化式{特性方程式}[i] + \auto{440}{\detokenize{\漸化式{特性方程式}[b]}} + \漸化式{特性方程式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{数学的帰納法} %\begin{description} -\auto{441}{\detokenize{\数学的帰納法}}\par +\auto{441}{\detokenize{\数学的帰納法}} + \数学的帰納法 %\end{description} @@ -1520,347 +2617,615 @@ Now, here are the actual examples! %\begin{simplesquarebox}{共役複素数} %\begin{description} %n-441=個数 -\auto{442}{\detokenize{\共役複素数{定義}[i]}}\par -\共役複素数{定義}[i]\par +\auto{442}{\detokenize{\共役複素数{定義}[i]}} + +\共役複素数{定義}[i] + \auto{443}{\detokenize{\共役複素数{定義}[b]}} + \共役複素数{定義}[b] -\auto{444}{\detokenize{\共役複素数{性質A}[i]}}\par -\共役複素数{性質A}[i]\par + +\auto{444}{\detokenize{\共役複素数{性質A}[i]}} + +\共役複素数{性質A}[i] + \auto{445}{\detokenize{\共役複素数{性質A}[b]}} -\共役複素数{性質A}[b]\par -\auto{446}{\detokenize{\共役複素数{性質B}[i]}}\par -\共役複素数{性質B}[i]\par + +\共役複素数{性質A}[b] + + +\auto{446}{\detokenize{\共役複素数{性質B}[i]}} + +\共役複素数{性質B}[i] + \auto{447}{\detokenize{\共役複素数{性質B}[b]}} + \共役複素数{性質B}[b] -\auto{448}{\detokenize{\共役複素数{性質C}[i]}}\par -\共役複素数{性質C}[i]\par + +\auto{448}{\detokenize{\共役複素数{性質C}[i]}} + +\共役複素数{性質C}[i] + \auto{449}{\detokenize{\共役複素数{性質C}[b]}} -\共役複素数{性質C}[b]\par -\auto{450}{\detokenize{\共役複素数{性質D}[i]}}\par -\共役複素数{性質D}[i]\par + +\共役複素数{性質C}[b] + + +\auto{450}{\detokenize{\共役複素数{性質D}[i]}} + +\共役複素数{性質D}[i] + \auto{451}{\detokenize{\共役複素数{性質D}[b]}} + \共役複素数{性質D}[b] -\auto{452}{\detokenize{\共役複素数{性質E}[i]}}\par -\共役複素数{性質E}[i]\par + +\auto{452}{\detokenize{\共役複素数{性質E}[i]}} + +\共役複素数{性質E}[i] + \auto{453}{\detokenize{\共役複素数{性質E}[b]}} + \共役複素数{性質E}[b] -\auto{454}{\detokenize{\共役複素数{性質F}[i]}}\par -\共役複素数{性質F}[i]\par + +\auto{454}{\detokenize{\共役複素数{性質F}[i]}} + +\共役複素数{性質F}[i] + \auto{455}{\detokenize{\共役複素数{性質F}[b]}} + \共役複素数{性質F}[b] -\auto{456}{\detokenize{\共役複素数{性質G}[i]}}\par -\共役複素数{性質G}[i]\par + +\auto{456}{\detokenize{\共役複素数{性質G}[i]}} + +\共役複素数{性質G}[i] + \auto{457}{\detokenize{\共役複素数{性質G}[b]}} + \共役複素数{性質G}[b] -\auto{442}{\detokenize{\共役複素数{証明}}}\par -\共役複素数{証明}\par + +\auto{442}{\detokenize{\共役複素数{証明}}} + +\共役複素数{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{複素数の絶対値} %\begin{description} -\auto{458}{\detokenize{\複素数の絶対値{定義}[i]}}\par -\複素数の絶対値{定義}[i]\par +\auto{458}{\detokenize{\複素数の絶対値{定義}[i]}} + +\複素数の絶対値{定義}[i] + \auto{459}{\detokenize{\複素数の絶対値{定義}[b]}} + \複素数の絶対値{定義}[b] -\auto{460}{\detokenize{\複素数の絶対値{性質A}[i]}}\par -\複素数の絶対値{性質A}[i]\par + +\auto{460}{\detokenize{\複素数の絶対値{性質A}[i]}} + +\複素数の絶対値{性質A}[i] + \auto{461}{\detokenize{\複素数の絶対値{性質A}[b]}} + \複素数の絶対値{性質A}[b] -\auto{462}{\detokenize{\複素数の絶対値{性質B}[i]}}\par -\複素数の絶対値{性質B}[i]\par + +\auto{462}{\detokenize{\複素数の絶対値{性質B}[i]}} + +\複素数の絶対値{性質B}[i] + \auto{463}{\detokenize{\複素数の絶対値{性質B}[b]}} + \複素数の絶対値{性質B}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{極形式} %\begin{description} -\auto{464}{\detokenize{\極形式{定義}[i]}}\par -\極形式{定義}[i]\par +\auto{464}{\detokenize{\極形式{定義}[i]}} + +\極形式{定義}[i] + \auto{465}{\detokenize{\極形式{定義}[b]}} -\極形式{定義}[b]\par -\auto{466}{\detokenize{\極形式{性質A}[i]}}\par -\極形式{性質A}[i]\par + +\極形式{定義}[b] + + +\auto{466}{\detokenize{\極形式{性質A}[i]}} + +\極形式{性質A}[i] + \auto{467}{\detokenize{\極形式{性質A}[b]}} + \極形式{性質A}[b] -\auto{468}{\detokenize{\極形式{性質B}[i]}}\par -\極形式{性質B}[i]\par + +\auto{468}{\detokenize{\極形式{性質B}[i]}} + +\極形式{性質B}[i] + \auto{469}{\detokenize{\極形式{性質B}[b]}} + \極形式{性質B}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{偏角} %\begin{description} -\auto{470}{\detokenize{\偏角{定義}[i]}}\par -\偏角{定義}[i]\par +\auto{470}{\detokenize{\偏角{定義}[i]}} + +\偏角{定義}[i] + \auto{471}{\detokenize{\偏角{定義}[b]}} -\偏角{定義}[b]\par -\auto{472}{\detokenize{\偏角{性質A}[i]}}\par -\偏角{性質A}[i]\par + +\偏角{定義}[b] + + +\auto{472}{\detokenize{\偏角{性質A}[i]}} + +\偏角{性質A}[i] + \auto{473}{\detokenize{\偏角{性質A}[b]}} -\偏角{性質A}[b]\par -\auto{474}{\detokenize{\偏角{性質B}[i]}}\par -\偏角{性質B}[i]\par + +\偏角{性質A}[b] + + +\auto{474}{\detokenize{\偏角{性質B}[i]}} + +\偏角{性質B}[i] + \auto{475}{\detokenize{\偏角{性質B}[b]}} + \偏角{性質B}[b] -\auto{476}{\detokenize{\偏角{性質C}[i]}}\par -\偏角{性質C}[i]\par + +\auto{476}{\detokenize{\偏角{性質C}[i]}} + +\偏角{性質C}[i] + \auto{477}{\detokenize{\偏角{性質C}[b]}} + \偏角{性質C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{ドモアブルの定理} %\begin{description} -\auto{478}{\detokenize{\ドモアブルの定理{公式}[i]}}\par -\ドモアブルの定理{公式}[i]\par +\auto{478}{\detokenize{\ドモアブルの定理{公式}[i]}} + +\ドモアブルの定理{公式}[i] + \auto{479}{\detokenize{\ドモアブルの定理{公式}[b]}} + \ドモアブルの定理{公式}[b] -\auto{478}{\detokenize{\ドモアブルの定理{証明}}}\par -\ドモアブルの定理{証明}\par + +\auto{478}{\detokenize{\ドモアブルの定理{証明}}} + +\ドモアブルの定理{証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{放物線} %\begin{description} -\auto{480}{\detokenize{\放物線{定義}[i]}}\par -\放物線{定義}[i]\par +\auto{480}{\detokenize{\放物線{定義}[i]}} + +\放物線{定義}[i] + \auto{481}{\detokenize{\放物線{定義}[b]}} + \放物線{定義}[b] -\auto{482}{\detokenize{\放物線{性質A}[i]}}\par -\放物線{性質A}[i]\par + +\auto{482}{\detokenize{\放物線{性質A}[i]}} + +\放物線{性質A}[i] + \auto{483}{\detokenize{\放物線{性質A}[b]}} -\放物線{性質A}[b]\par -\auto{484}{\detokenize{\放物線{性質B}[i]}}\par -\放物線{性質B}[i]\par + +\放物線{性質A}[b] + + +\auto{484}{\detokenize{\放物線{性質B}[i]}} + +\放物線{性質B}[i] + \auto{485}{\detokenize{\放物線{性質B}[b]}} + \放物線{性質B}[b] -\auto{486}{\detokenize{\放物線{性質C}[i]}}\par -\放物線{性質C}[i]\par + +\auto{486}{\detokenize{\放物線{性質C}[i]}} + +\放物線{性質C}[i] + \auto{487}{\detokenize{\放物線{性質C}[b]}} + \放物線{性質C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{楕円} %\begin{description} -\auto{488}{\detokenize{\楕円{定義}[i]}}\par -\楕円{定義}[i]\par +\auto{488}{\detokenize{\楕円{定義}[i]}} + +\楕円{定義}[i] + \auto{489}{\detokenize{\楕円{定義}[b]}} -\楕円{定義}[b]\par -\auto{490}{\detokenize{\楕円{性質A}[i]}}\par -\楕円{性質A}[i]\par + +\楕円{定義}[b] + + +\auto{490}{\detokenize{\楕円{性質A}[i]}} + +\楕円{性質A}[i] + \auto{491}{\detokenize{\楕円{性質A}[b]}} -\楕円{性質A}[b]\par -\auto{492}{\detokenize{\楕円{性質B}[i]}}\par -\楕円{性質B}[i]\par + +\楕円{性質A}[b] + + +\auto{492}{\detokenize{\楕円{性質B}[i]}} + +\楕円{性質B}[i] + \auto{493}{\detokenize{\楕円{性質B}[b]}} + \楕円{性質B}[b] -\auto{494}{\detokenize{\楕円{性質C}[i]}}\par -\楕円{性質C}[i]\par + +\auto{494}{\detokenize{\楕円{性質C}[i]}} + +\楕円{性質C}[i] + \auto{495}{\detokenize{\楕円{性質C}[b]}} + \楕円{性質C}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{双曲線} %\begin{description} -\auto{496}{\detokenize{\双曲線{定義}[i]}}\par -\双曲線{定義}[i]\par +\auto{496}{\detokenize{\双曲線{定義}[i]}} + +\双曲線{定義}[i] + \auto{497}{\detokenize{\双曲線{定義}[b]}} -\双曲線{定義}[b]\par -\auto{498}{\detokenize{\双曲線{性質A}[i]}}\par -\双曲線{性質A}[i]\par + +\双曲線{定義}[b] + + +\auto{498}{\detokenize{\双曲線{性質A}[i]}} + +\双曲線{性質A}[i] + \auto{499}{\detokenize{\双曲線{性質A}[b]}} -\双曲線{性質A}[b]\par -\auto{500}{\detokenize{\双曲線{性質B}[i]}}\par -\双曲線{性質B}[i]\par + +\双曲線{性質A}[b] + + +\auto{500}{\detokenize{\双曲線{性質B}[i]}} + +\双曲線{性質B}[i] + \auto{501}{\detokenize{\双曲線{性質B}[b]}} + \双曲線{性質B}[b] -\auto{502}{\detokenize{\双曲線{性質C}[i]}}\par -\双曲線{性質C}[i]\par + +\auto{502}{\detokenize{\双曲線{性質C}[i]}} + +\双曲線{性質C}[i] + \auto{503}{\detokenize{\双曲線{性質C}[b]}} + \双曲線{性質C}[b] -\auto{504}{\detokenize{\双曲線{性質D}[i]}}\par -\双曲線{性質D}[i]\par + +\auto{504}{\detokenize{\双曲線{性質D}[i]}} + +\双曲線{性質D}[i] + \auto{505}{\detokenize{\双曲線{性質D}[b]}} + \双曲線{性質D}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{連続な関数} %\begin{description} -\auto{506}{\detokenize{\連続な関数{公式}[i]}}\par -\連続な関数{公式}[i]\par +\auto{506}{\detokenize{\連続な関数{公式}[i]}} + +\連続な関数{公式}[i] + \auto{507}{\detokenize{\連続な関数{公式}[b]}} + \連続な関数{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{中間値の定理} %\begin{description} -\auto{508}{\detokenize{\中間値の定理{公式}[i]}}\par -\中間値の定理{公式}[i]\par +\auto{508}{\detokenize{\中間値の定理{公式}[i]}} + +\中間値の定理{公式}[i] + \auto{509}{\detokenize{\中間値の定理{公式}[b]}} + \中間値の定理{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{平均値の定理} %\begin{description} -\auto{510}{\detokenize{\平均値の定理{公式}[i]}}\par -\平均値の定理{公式}[i]\par +\auto{510}{\detokenize{\平均値の定理{公式}[i]}} + +\平均値の定理{公式}[i] + \auto{511}{\detokenize{\平均値の定理{公式}[b]}} + \平均値の定理{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{微分} %\begin{description} -\auto{512}{\detokenize{\微分{定義}[i]}}\par -\微分{定義}[i]\par +\auto{512}{\detokenize{\微分{定義}[i]}} + +\微分{定義}[i] + \auto{513}{\detokenize{\微分{定義}[b]}} + \微分{定義}[b] -\auto{514}{\detokenize{\微分{積の微分公式}[i]}}\par -\微分{積の微分公式}[i]\par + +\auto{514}{\detokenize{\微分{積の微分公式}[i]}} + +\微分{積の微分公式}[i] + \auto{515}{\detokenize{\微分{積の微分公式}[b]}} + \微分{積の微分公式}[b] -\auto{516}{\detokenize{\微分{商の微分公式}[i]}}\par -\微分{商の微分公式}[i]\par + +\auto{516}{\detokenize{\微分{商の微分公式}[i]}} + +\微分{商の微分公式}[i] + \auto{517}{\detokenize{\微分{商の微分公式}[b]}} + \微分{商の微分公式}[b] -\auto{518}{\detokenize{\微分{合成関数の微分}[i]}}\par -\微分{合成関数の微分}[i]\par + +\auto{518}{\detokenize{\微分{合成関数の微分}[i]}} + +\微分{合成関数の微分}[i] + \auto{519}{\detokenize{\微分{合成関数の微分}[b]}} + \微分{合成関数の微分}[b] -\auto{520}{\detokenize{\微分{初等関数の微分公式A}[i]}}\par -\微分{初等関数の微分公式A}[i]\par + +\auto{520}{\detokenize{\微分{初等関数の微分公式A}[i]}} + +\微分{初等関数の微分公式A}[i] + \auto{521}{\detokenize{\微分{初等関数の微分公式A}[b]}} + \微分{初等関数の微分公式A}[b] -\auto{522}{\detokenize{\微分{初等関数の微分公式B}[i]}}\par -\微分{初等関数の微分公式B}[i]\par + +\auto{522}{\detokenize{\微分{初等関数の微分公式B}[i]}} + +\微分{初等関数の微分公式B}[i] + \auto{523}{\detokenize{\微分{初等関数の微分公式B}[b]}} + \微分{初等関数の微分公式B}[b] -\auto{524}{\detokenize{\微分{初等関数の微分公式C}[i]}}\par -\微分{初等関数の微分公式C}[i]\par + +\auto{524}{\detokenize{\微分{初等関数の微分公式C}[i]}} + +\微分{初等関数の微分公式C}[i] + \auto{525}{\detokenize{\微分{初等関数の微分公式C}[b]}} + \微分{初等関数の微分公式C}[b] -\auto{526}{\detokenize{\微分{初等関数の微分公式D}[i]}}\par -\微分{初等関数の微分公式D}[i]\par + +\auto{526}{\detokenize{\微分{初等関数の微分公式D}[i]}} + +\微分{初等関数の微分公式D}[i] + \auto{527}{\detokenize{\微分{初等関数の微分公式D}[b]}} + \微分{初等関数の微分公式D}[b] -\auto{528}{\detokenize{\微分{初等関数の微分公式E}[i]}}\par -\微分{初等関数の微分公式E}[i]\par + +\auto{528}{\detokenize{\微分{初等関数の微分公式E}[i]}} + +\微分{初等関数の微分公式E}[i] + \auto{529}{\detokenize{\微分{初等関数の微分公式E}[b]}} + \微分{初等関数の微分公式E}[b] -\auto{530}{\detokenize{\微分{初等関数の微分公式F}[i]}}\par -\微分{初等関数の微分公式F}[i]\par + +\auto{530}{\detokenize{\微分{初等関数の微分公式F}[i]}} + +\微分{初等関数の微分公式F}[i] + \auto{531}{\detokenize{\微分{初等関数の微分公式F}[b]}} + \微分{初等関数の微分公式F}[b] -\auto{532}{\detokenize{\微分{初等関数の微分公式G}[i]}}\par -\微分{初等関数の微分公式G}[i]\par + +\auto{532}{\detokenize{\微分{初等関数の微分公式G}[i]}} + +\微分{初等関数の微分公式G}[i] + \auto{533}{\detokenize{\微分{初等関数の微分公式G}[b]}} + \微分{初等関数の微分公式G}[b] -\auto{534}{\detokenize{\微分{初等関数の微分公式H}[i]}}\par -\微分{初等関数の微分公式H}[i]\par + +\auto{534}{\detokenize{\微分{初等関数の微分公式H}[i]}} + +\微分{初等関数の微分公式H}[i] + \auto{535}{\detokenize{\微分{初等関数の微分公式H}[b]}} + \微分{初等関数の微分公式H}[b] -\auto{536}{\detokenize{\微分{初等関数の微分公式I}[i]}}\par -\微分{初等関数の微分公式I}[i]\par + +\auto{536}{\detokenize{\微分{初等関数の微分公式I}[i]}} + +\微分{初等関数の微分公式I}[i] + \auto{537}{\detokenize{\微分{初等関数の微分公式I}[b]}} + \微分{初等関数の微分公式I}[b] -\auto{512}{\detokenize{\微分{三角関数の微分公式の証明}[i]}}\par -\微分{三角関数の微分公式の証明}[i]\par -\auto{512}{\detokenize{\微分{対数関数の微分公式の証明}[i]}}\par -\微分{対数関数の微分公式の証明}[i]\par + +\auto{512}{\detokenize{\微分{三角関数の微分公式の証明}}} + +\微分{三角関数の微分公式の証明} + +\auto{512}{\detokenize{\微分{対数関数の微分公式の証明}}} + +\微分{対数関数の微分公式の証明} + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{接線の方程式} %\begin{description} -\auto{538}{\detokenize{\接線の方程式{公式}[i]}}\par -\接線の方程式{公式}[i]\par +\auto{538}{\detokenize{\接線の方程式{公式}[i]}} + +\接線の方程式{公式}[i] + \auto{539}{\detokenize{\接線の方程式{公式}[b]}} + \接線の方程式{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{法線の方程式} %\begin{description} -\auto{540}{\detokenize{\法線の方程式{公式}[i]}}\par -\法線の方程式{公式}[i]\par +\auto{540}{\detokenize{\法線の方程式{公式}[i]}} + +\法線の方程式{公式}[i] + \auto{541}{\detokenize{\法線の方程式{公式}[b]}} + \法線の方程式{公式}[b] + %\end{description %\end{simplesquarebox} %\begin{simplesquarebox}{不定積分} %\begin{description} -\auto{542}{\detokenize{\不定積分{定義}[i]}}\par -\不定積分{定義}[i]\par +\auto{542}{\detokenize{\不定積分{定義}[i]}} + +\不定積分{定義}[i] + \auto{543}{\detokenize{\不定積分{定義}[b]}} -\不定積分{定義}[b]\par -\auto{544}{\detokenize{\不定積分{置換積分}[i]}}\par -\不定積分{置換積分}[i]\par + +\不定積分{定義}[b] + + +\auto{544}{\detokenize{\不定積分{置換積分}[i]}} + +\不定積分{置換積分}[i] + \auto{545}{\detokenize{\不定積分{置換積分}[b]}} -\不定積分{置換積分}[b]\par -\auto{546}{\detokenize{\不定積分{部分積分}[i]}}\par -\不定積分{部分積分}[i]\par + +\不定積分{置換積分}[b] + + +\auto{546}{\detokenize{\不定積分{部分積分}[i]}} + +\不定積分{部分積分}[i] + \auto{547}{\detokenize{\不定積分{部分積分}[b]}} + \不定積分{部分積分}[b] -\auto{548}{\detokenize{\不定積分{初等関数の積分公式A}[i]}}\par -\不定積分{初等関数の積分公式A}[i]\par + +\auto{548}{\detokenize{\不定積分{初等関数の積分公式A}[i]}} + +\不定積分{初等関数の積分公式A}[i] + \auto{549}{\detokenize{\不定積分{初等関数の積分公式A}[b]}} + \不定積分{初等関数の積分公式A}[b] -\auto{550}{\detokenize{\不定積分{初等関数の積分公式B}[i]}}\par -\不定積分{初等関数の積分公式B}[i]\par + +\auto{550}{\detokenize{\不定積分{初等関数の積分公式B}[i]}} + +\不定積分{初等関数の積分公式B}[i] + \auto{551}{\detokenize{\不定積分{初等関数の積分公式B}[b]}} + \不定積分{初等関数の積分公式B}[b] -\auto{552}{\detokenize{\不定積分{初等関数の積分公式C}[i]}}\par -\不定積分{初等関数の積分公式C}[i]\par + +\auto{552}{\detokenize{\不定積分{初等関数の積分公式C}[i]}} + +\不定積分{初等関数の積分公式C}[i] + \auto{553}{\detokenize{\不定積分{初等関数の積分公式C}[b]}} + \不定積分{初等関数の積分公式C}[b] -\auto{554}{\detokenize{\不定積分{初等関数の積分公式D}[i]}}\par -\不定積分{初等関数の積分公式D}[i]\par + +\auto{554}{\detokenize{\不定積分{初等関数の積分公式D}[i]}} + +\不定積分{初等関数の積分公式D}[i] + \auto{555}{\detokenize{\不定積分{初等関数の積分公式D}[b]}} + \不定積分{初等関数の積分公式D}[b] -\auto{556}{\detokenize{\不定積分{初等関数の積分公式E}[i]}}\par -\不定積分{初等関数の積分公式E}[i]\par + +\auto{556}{\detokenize{\不定積分{初等関数の積分公式E}[i]}} + +\不定積分{初等関数の積分公式E}[i] + \auto{557}{\detokenize{\不定積分{初等関数の積分公式E}[b]}} + \不定積分{初等関数の積分公式E}[b] -\auto{558}{\detokenize{\不定積分{初等関数の積分公式F}[i]}}\par -\不定積分{初等関数の積分公式F}[i]\par + +\auto{558}{\detokenize{\不定積分{初等関数の積分公式F}[i]}} + +\不定積分{初等関数の積分公式F}[i] + \auto{559}{\detokenize{\不定積分{初等関数の積分公式F}[b]}} + \不定積分{初等関数の積分公式F}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{定積分} %\begin{description} -\auto{560}{\detokenize{\定積分{定義}[i]}}\par -\定積分{定義}[i]\par +\auto{560}{\detokenize{\定積分{定義}[i]}} + +\定積分{定義}[i] + \auto{561}{\detokenize{\定積分{定義}[b]}} + \定積分{定義}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{区分求積法} %\begin{description} -\auto{562}{\detokenize{\区分求積法{公式}[i]}}\par -\区分求積法{公式}[i]\par +\auto{562}{\detokenize{\区分求積法{公式}[i]}} + +\区分求積法{公式}[i] + \auto{563}{\detokenize{\区分求積法{公式}[b]}} + \区分求積法{公式}[b] + %\end{description} %\end{simplesquarebox} %\begin{simplesquarebox}{体積の積分} %\begin{description} -\auto{564}{\detokenize{\体積の積分{公式}[i]}}\par -\体積の積分{公式}[i]\par +\auto{564}{\detokenize{\体積の積分{公式}[i]}} + +\体積の積分{公式}[i] + \auto{565}{\detokenize{\体積の積分{公式}[b]}} + \体積の積分{公式}[b] + %\end{description} %\end{simplesquarebox} |