diff options
| author | Karl Berry <karl@freefriends.org> | 2020-09-06 21:19:54 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2020-09-06 21:19:54 +0000 |
| commit | da539a5083a4e436ce339377122bf143859ab814 (patch) | |
| tree | e57c25090a1763a3cf8028b42eeb23ad326ed580 /Master/texmf-dist/scripts | |
| parent | ba5b524ffb7b31ed52f06d40fa7cd2877124e46a (diff) | |
lua-physical (6sep20)
git-svn-id: svn://tug.org/texlive/trunk@56278 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/scripts')
10 files changed, 6874 insertions, 0 deletions
diff --git a/Master/texmf-dist/scripts/lua-physical/physical-astronomical.lua b/Master/texmf-dist/scripts/lua-physical/physical-astronomical.lua new file mode 100644 index 00000000000..48ca5646b86 --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-astronomical.lua @@ -0,0 +1,173 @@ +--[[ +Astronomical data + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- +local prefix = ... and (...):match '(.-%.?)[^%.]+$' or '' +local N = require(prefix..'physical-number') + +local Astronomical = {} + + + +Astronomical.Sun = { + + -- http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(1.9884e30, 0.0002e30) * _kg, + + -- Andrej Prsa, Petr Harmanec, Guillermo Torres et al. + -- Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3, + -- The Astronomical Journal, 2016, Vol. 152, No. 2, Page 41 + -- https://arxiv.org/pdf/1605.09788.pdf + Radius = N(695658, 100) * _km, + + -- https://sites.google.com/site/mamajeksstarnotes/basic-astronomical-data-for-the-sun + MeanRadiativeLuminosity = N(3.8275,0.0014) * 1e26 * _W, + + EffectiveTemperature = N(5772.0,0.8) * _K, + + SpectralType = "G2V", + + -- https://ssd.jpl.nasa.gov/?constants#pc + MassParameter = N(1.32712440018e20,8e9) * _m^3 * _s^-2, +} + +Astronomical.Mercury = { + + -- Mohr et al. 2016 + Mass = N(3.301110e23, 0.00015e23) * _kg, + + -- Perry et al. 2015 + AverageRadius = N(2439.36, 0.02) * _km, + + Density = N(5429.30, 0.28) * _kg/_m^3 +} + +Astronomical.Venus = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(4.86728e24, 0.00049e24) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(6051.8, 1.0) * _km +} + +Astronomical.Earth = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(5.9722e24, 0.0006e24) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(6378.1366, 0.0001) * _km +} + +Astronomical.Moon = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(7.34583e22, 0.00074e22) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(1737.4, 1) * _km +} + +Astronomical.Mars = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(6.41688e23, 0.00064e23) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(3396.19, 0.1) * _km +} + +Astronomical.Jupiter = { + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(1.89851e27, 0.00019e27) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(71492, 4) * _km +} + +Astronomical.Saturn = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(5.6846e26, 0.0006e26) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(60268, 4) * _km +} + +Astronomical.Uranus = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(8.68184e25, 0.00087e25) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(25559, 4) * _km +} + +Astronomical.Neptune = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(1.0243e26, 0.0001e26) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(24764, 15) * _km +} + +Astronomical.Pluto = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(1.45600e22, 0.00033e22) * _kg, + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + EquatorialRadius = N(1195, 5) * _km +} + +Astronomical.Eris = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(1.670e22, 0.019e22) * _kg, + + --Source: http://meetingorganizer.copernicus.org/EPSC-DPS2011/EPSC-DPS2011-137-8.pdf + Radius = N(1163, 6)*_km, + Density = N(2.5, 0.05) * _g/_cm^3, + Albedo = N(0.96, 0.09) * _1 +} + +Astronomical.Ceres = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(9.39e20, 0.060e20) * _kg +} + +Astronomical.Pallas = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(2.048e20, 0.060e20) * _kg +} + +Astronomical.Vesta = { + + --Source: http://asa.usno.navy.mil/static/files/2014/Astronomical_Constants_2014.pdf + Mass = N(2.684e20, 0.06e20) * _kg +} + +return Astronomical diff --git a/Master/texmf-dist/scripts/lua-physical/physical-data.lua b/Master/texmf-dist/scripts/lua-physical/physical-data.lua new file mode 100644 index 00000000000..efc1a30ffaf --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-data.lua @@ -0,0 +1,298 @@ +--[[ +This file contains the methods for accessing physical data. + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- +local prefix = ... and (...):match '(.-%.?)[^%.]+$' or '' +local N = require(prefix..'physical-number') + + +-- N class +local Data = {} +Data.__index = Data + + +-- +-- ASTRONOMICAL DATA +-- +Data.Astronomical = {} + +-- make the table callable +setmetatable(Data.Astronomical, { + __call = function(class, ...) + return Data.Astronomical.get(...) + end +}) + +function Data.Astronomical.get(name, key) + local data = require(prefix..'physical-astronomical') + + -- return all names + if name == nil then + local names = {} + for name,_ in pairs(data) do + names[#names+1] = name + end + return names + end + + if data[name] ~= nil then + local row = data[name] + + -- return all keys + if key == nil then + local result = {} + for key,_ in pairs(row) do + result[key] = row[key] + end + return result + end + + if row[key] ~= nil then + return row[key] + end + end + + return nil +end + + + +-- +-- ISOTOPE DATA +-- +Data.Isotope = {} + +-- make the table callable +setmetatable(Data.Isotope, { + __call = function(class, ...) + return Data.Isotope.get(...) + end +}) + +-- get isotope data +-- +-- 1) Get the mass excess of Helium-5 by the following commands +-- Data.Isotope("5He","MassExcess") or +-- Data.Isotope("5-He","MassExcess") or +-- Data.Isotope("5Helium","MassExcess") or +-- Data.Isotope("5-Helium","MassExcess") or +-- Data.Isotope("He5","MassExcess") or +-- Data.Isotope("He-5","MassExcess") or +-- Data.Isotope("Helium5","MassExcess") or +-- Data.Isotope("Helium-5","MassExcess") +-- +-- 2) Get the mass excess of all helium isotopes +-- Data.Isotope("He","MassExcess") or +-- Data.Isotope("Helium","MassExcess") +-- +-- 3) Get the half life of Lithium-3 +-- Data.Isotope({3,3},"HalfLife") +-- +-- 4) Get the half life of all isotopes +-- Data.Isotope(nil,"HalfLife") +-- +-- 5) Get the names of all isotopes +-- Data.Isotope(nil,nil) + +function Data.Isotope.get(isotope,key) + local data = require(prefix..'physical-isotope') + + -- match 1) and 2) or 4) + if type(isotope) == "string" then + return Data.Isotope.getByName(isotope, key) + + -- match 3) or 4) + elseif type(isotope) == "table" then + local A = isotope[1] + local Z = isotope[2] + + if type(A) == "number" and type(Z) == "number" then + return Data.Isotope.getByAZ(A, Z, key) + end + + -- match 5) + else + + local Akey = data.keys["A"] + local Zkey = data.keys["Z"] + + local names = {} + for _,row in ipairs(data.data) do + local A = row[Akey] + local Z = row[Zkey] + + names[#names + 1] = tostring(A)..data.symbols[Z+1] + end + return names + end + + return nil +end + + +-- returns isotope data by the isotope name. +function Data.Isotope.getByName(isotope, key) + local data = require(prefix..'physical-isotope') + + -- match "Helium-5", "Helium5", "He-5" or "He5" + local name, A = string.match(isotope, "^([%a]+)%-?([%d]+)$") + if name ~= nil then + local Z = data.names[name] + if Z == nil then + Z = data.symbols[name] + end + + A = tonumber(A) + + if A ~= nil and Z ~= nil then + return Data.Isotope.getByAZ(A, Z, key) + end + end + + -- match "5-Helium", "5Helium", "5-He" or "5He5" + local A,name = string.match(isotope, "^([%d]+)%-?([%a]+)$") + if name ~= nil then + local Z = data.names[name] + if Z == nil then + Z = data.symbols[name] + end + + A = tonumber(A) + + if A ~= nil and Z ~= nil then + return Data.Isotope.getByAZ(A, Z, key) + end + end + + local name = string.match(isotope, "^([%a]+)$") + if name ~= nil then + local Z = data.names[name] + if Z == nil then + Z = data.symbols[name] + end + + if Z ~= nil then + return Data.Isotope.getByZ(Z, key) + end + end + + return nil +end + + +-- return isotopes with a certain A and Z +function Data.Isotope.getByAZ(A, Z, key) + local data = require(prefix..'physical-isotope') + + -- get row number + local i = data.indexAZ[tonumber(tostring(A)..tostring(Z))] + if i == nil then + error("Isotope with (A,Z) = ("..tostring(A)..","..tostring(Z)..") not found in 'Data.Isotope'.") + end + + return Data.Isotope._getValues(data.data[i],key) +end + + +-- return all isotope data with a certain Z +function Data.Isotope.getByZ(Z, key) + local data = require(prefix..'physical-isotope') + + local Akey = data.keys["A"] + + local result = {} + for _, i in ipairs(data.indexZ[Z+1]) do + local name = tostring(data.data[i][Akey])..data.symbols[Z+1] + result[name] = Data.Isotope._getValues(data.data[i],key) + end + + return result +end + + +-- return key value pairs from a specific row +function Data.Isotope._getValues(row, keys) + local data = require(prefix..'physical-isotope') + + if keys == nil then + keys = data.keys + + elseif type(keys) == "string" then + keys = {keys} + + elseif type(keys) ~= "table" then + error("Unknown key type '"..tostring(key).."'.") + end + + local result = {} + for _,key in ipairs(keys) do + + -- name and symbol + if key == "name" then + result["name"] = data.names[row[data.keys["Z"]] + 1].."-"..row[data.keys["A"]] + + elseif key == "symbol" then + result["symbol"] = row[data.keys["A"]]..data.symbols[row[data.keys["Z"]] + 1] + + elseif key ~= "" then + + local i = data.keys[key] + local di = data.dkeys[key] + + local x = row[i] + local dx = row[di] + + -- invalid key + if x == nil then + error("Key "..key.." not found in 'Data.Isotope'.") + end + + -- get value + local value = x + + -- append uncertainty + if type(x) == "number" and type(dx) == "number" then + value = N(x, dx) + end + + -- append unit + local unit = data.units[i] + if type(x)=="number" and unit ~= "" then + value = value * _G["_"..unit] + end + + result[key] = value + end + end + + if #keys == 1 then + return result[keys[1]] + else + return result + end +end + + +return Data + + + diff --git a/Master/texmf-dist/scripts/lua-physical/physical-definition.lua b/Master/texmf-dist/scripts/lua-physical/physical-definition.lua new file mode 100644 index 00000000000..cf1576b4c54 --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-definition.lua @@ -0,0 +1,702 @@ +--[[ +This file contains the definitions for dimensions, prefixes, +SI, Imperial and U.S. Survey units + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +local prefix = ... and (...):match '(.-%.?)[^%.]+$' or '' +local D = require(prefix..'physical-dimension') +local U = require(prefix..'physical-unit') +local Q = require(prefix..'physical-quantity') + + +-- define base dimensions +local L = D.defineBase("L", "Length") +local M = D.defineBase("M", "Mass") +local T = D.defineBase("T", "Time") +local I = D.defineBase("I", "Electric Current") +local K = D.defineBase("K", "Temperature") +local N = D.defineBase("N", "Amount of Substance") +local J = D.defineBase("J", "Luminous Intensity") +local B = D.defineBase("B", "Information") +local C = D.defineBase("C", "Currency") + +-- define derived dimensions +D.define("Dimensionless", D()) +D.define("Area", L^2) +D.define("Volume", L^3) +D.define("Frequency", T^-1) +D.define("Density", L^-3 * M) +D.define("Velocity", L * T^-1) +D.define("Acceleration", L * T^-2) +D.define("Force", L * M * T^-2) +D.define("Energy", L^2 * M * T^-2) +D.define("Torque", L^2 * M * T^-2) +D.define("Power", L^2 * M * T^-3) +D.define("Pressure", L^-1 * M * T^-2) +D.define("Impulse", L * M * T^-1) +D.define("Absorbed Dose", L^2 * T^-2) +D.define("Heat Capacity", L^2 * M * T^-2 * K^-1) +D.define("Specific Heat Capacity", L^2 * T^-2 * K^-1) +D.define("Angular Momentum", L^2 * M * T^-1) +D.define("Moment of Inertia", L^2 * M) +D.define("Entropy", L^2 * M * T^-2 * K^-1) +D.define("Thermal Conductivity", L * M * T^-3 * K^-1) +D.define("Electric Charge", T * I) +D.define("Electric Permittivity", L^-3 * M^-1 * T^4 * I^2) +D.define("Electric Field Strength", L * M * T^-3 * I^-1) +D.define("Electric Potential", L^2 * M * T^-3 * I^-1) +D.define("Electric Resistance", L^2 * M * T^-3 * I^-2) +D.define("Electric Conductance", L^-2 * M^-1 * T^3 * I^2) +D.define("Electric Capacitance", L^-2 * M^-1 * T^4 * I^2) +D.define("Inductance", L^2 * M * T^-2 * I^-2) +D.define("Magnetic Permeability", L * M * T^-2 * I^-2) +D.define("Magnetic Field Strength", L^-1 * I) +D.define("Magnetic Flux", L^2 * M * T^-2 * I^-1) +D.define("Magnetic Flux Density", M * T^-2 * I^-1) +D.define("Intensity", M * T^-3) +D.define("Reaction Rate", L^-3 * T^-1 * N) +D.define("Catalytic Activity", T^-1 * N) +D.define("Chemical Potential", L^2 * M * T^-2 * N^-1) +D.define("Molar Concentration", L^-3 * N) +D.define("Molar Heat Capacity", L^2 * M * T^-2 * K^-1 * N^-1) +D.define("Illuminance", L^-2 * J) + + +-- define SI prefixes +Q.definePrefix("Y", "yotta", 1e24) +Q.definePrefix("Z", "zetta", 1e21) +Q.definePrefix("E", "exa", 1e18) +Q.definePrefix("P", "peta", 1e15) +Q.definePrefix("T", "tera", 1e12) +Q.definePrefix("G", "giga", 1e9) +Q.definePrefix("M", "mega", 1e6) +Q.definePrefix("k", "kilo", 1e3) +Q.definePrefix("h", "hecto", 1e2) +Q.definePrefix("da","deca", 1e1) +Q.definePrefix("d", "deci", 1e-1) +Q.definePrefix("c", "centi", 1e-2) +Q.definePrefix("m", "milli", 1e-3) +Q.definePrefix("u", "micro", 1e-6) +Q.definePrefix("n", "nano", 1e-9) +Q.definePrefix("p", "pico", 1e-12) +Q.definePrefix("f", "femto", 1e-15) +Q.definePrefix("a", "atto", 1e-18) +Q.definePrefix("z", "zepto", 1e-21) +Q.definePrefix("y", "yocto", 1e-24) + +local SI_prefixes = {"y","z","a","f","p","n","u","m","c","d","da","h","k","M","G","T","P","E","Z","Y"} + +-- define IEC prefixes +Q.definePrefix("Yi", "yobi", 1208925819614629174706176) +Q.definePrefix("Zi", "zebi", 1180591620717411303424) +Q.definePrefix("Ei", "exbi", 1152921504606846976) +Q.definePrefix("Pi", "pebi", 1125899906842624) +Q.definePrefix("Ti", "tebi", 1099511627776) +Q.definePrefix("Gi", "gibi", 1073741824) +Q.definePrefix("Mi", "mebi", 1048576) +Q.definePrefix("Ki", "kibi", 1024) + +local IEC_prefixes = {"Ki","Mi","Gi","Ti","Pi","Ei","Zi","Yi"} + +-- define the dimensionless base quantity for real numbers +Q.define("1", "number", Q(1)) + +-- define SI base units +Q.defineBase("m", "meter", L) +Q.defineBase("kg", "kilogram", M) +Q.defineBase("s", "second", T) +Q.defineBase("A", "ampere", I) +Q.defineBase("K", "kelvin", K) +Q.defineBase("mol", "mole", N) +Q.defineBase("cd", "candela", J) + +Q.addPrefix(SI_prefixes,{_m,_s,_A,_K,_mol,_cd}) + +-- define base unit of information +Q.defineBase("bit", "bit", B) + +Q.addPrefix(IEC_prefixes,{_bit}) + +-- define the euro as the base currency unit +Q.defineBase("EUR", "euro", C) +Q.define("cEUR", "eurocent", 0.01*_EUR) + + + + +-- SI derived units +-- **************** + +Q.define("rad", "radian", _1 ) +Q.define("sr", "steradian", _rad^2 ) +Q.define("Hz", "hertz", 1/_s) +Q.define("N", "newton", _kg*_m/_s^2) +Q.define("Pa", "pascal", _N/_m^2) +Q.define("J", "joule", _N*_m) +Q.define("W", "watt", _J/_s) +Q.define("g", "gram", 1e-3*_kg) + +-- remark: don't create the unit kilogram twice +Q.addPrefix({"y","z","a","f","p","n","u","m","c","d","da","h","M","G","T","P","E","Z","Y"},{_g}) +Q.addPrefix(SI_prefixes,{_Hz,_N,_Pa,_J,_W}) + + +Q.define("C", "coulomb", _A*_s) +Q.define("V", "volt", _J/_C) +Q.define("F", "farad", _C/_V) +Q.define("Ohm", "ohm", _V/_A) +Q.define("S", "siemens", _A/_V) +Q.define("Wb", "weber", _V*_s) +Q.define("T", "tesla", _Wb/_m^2) +Q.define("H", "henry", _Wb/_A) + +-- define degree celsius +-- T = (theta + _degC_0):to(_K) +-- theta = T:to(_degC) - _degC_0 +Q.define("degC", "celsius", _K) +Q.define("degC_0", nil, 273.15*_K) + +-- add prefixes +-- remark: Don't create "peta siemens" because its symbol is the same for "Pferdestaerke", a common german unit for power. +Q.addPrefix({"y","z","a","f","p","n","u","m","c","d","da","h","M","G","T","E","Z","Y"},{_S}) +Q.addPrefix(SI_prefixes,{_C,_V,_F,_Ohm,_Wb,_T,_H}) + +Q.define("lm", "lumen", _cd*_sr) +Q.define("lx", "lux", _lm/_m^2) +Q.define("Bq", "becquerel", 1/_s) +Q.define("Gy", "gray", _J/_kg) +Q.define("Sv", "sievert", _J/_kg) +Q.define("kat", "katal", _mol/_s) + +-- add prefixes +Q.addPrefix(SI_prefixes,{_lm,_lx,_Bq,_Gy,_Sv,_kat}) + + + + +-- MATHEMATICAL CONSTANTS +-- ********************** +local N = require(prefix..'physical-number') + +Q.define("Pi", "pi", 3.1415926535897932384626433832795028841971 * _1) +Q.define("E", "eulersnumber", 2.7182818284590452353602874713526624977572 * _1) + + + + +-- PHYSICAL CONSTANTS +-- ****************** +-- Source: https://en.wikipedia.org/wiki/Physical_constant +-- Source: https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf + +-- Universal +Q.define("c", "speedoflight", 299792458 * _m/_s) +Q.define("Gc", "gravitationalconstant", N(6.67408e-11,3.1e-15) * _m^3/(_kg*_s^2)) +Q.define("h_P", "planckconstant", 6.62607015e-34 * _J*_s) +Q.define("h_Pbar", "reducedplanckconstant", _h_P/(2*_Pi)) + +-- Electrodynamic +Q.define("e", "elementarycharge", 1.602176634e-19 * _C) +Q.define("u_0", "vacuumpermeability", 4e-7*_Pi * _N/_A^2) +Q.define("e_0", "vacuumpermitivity", 1/(_u_0*_c^2)) +Q.define("u", "atomicmassunit", N(1.66053904e-27, 2e-35) * _kg) +Q.define("m_e", "electronmass", N(9.10938356e-31, 1.1e-38) * _kg) +Q.define("m_p", "protonmass", N(1.672621898e-27, 2.1e-35) * _kg) +Q.define("m_n", "neutronmass", N(1.674927471e-27, 2.1e-35) * _kg) + +Q.define("u_B", "bohrmagneton", _e*_h_Pbar/(2*_m_e)) +Q.define("u_N", "nuclearmagneton", _e*_h_Pbar/(2*_m_p)) + +Q.define("u_e", "electronmagneticmoment", N(-928.4764620e-26,5.7e-32) * _J/_T) +Q.define("u_p", "protonmagneticmoment", N(1.4106067873e-26,9.7e-35) * _J/_T) +Q.define("u_n", "neutronmagneticmoment", N(-0.96623650e-26,2.3e-26) * _J/_T) + +Q.define("alpha", "finestructureconstant", _u_0*_e^2*_c/(2*_h_P)) +Q.define("Ry", "rydbergconstant", _alpha^2*_m_e*_c/(2*_h_P)) + +-- Thermodynamic +Q.define("N_A", "avogadronumber", 6.02214076e23/_mol) +Q.define("k_B", "boltzmannconstant", 1.380649e-23 * _J/_K) +Q.define("R", "molargasconstant", N(8.3144598, 4.8e-6) * _J/(_K*_mol)) + +-- Others +Q.define("sigma", "stefanboltzmannconstant", _Pi^2*_k_B^4/(60*_h_Pbar^3*_c^2)) +Q.define("g_0", "standardgravity", 9.80665 * _m/_s^2) + + + + +-- NON-SI UNITS BUT ACCEPTED FOR USE WITH THE SI +-- ********************************************* +-- Source: http://physics.nist.gov/cuu/Units/outside.html +-- http://m.convert-me.com/en/convert/area/township.html?u=township&v=1 +-- https://www.nist.gov/pml/nist-guide-si-appendix-b9-factors-units-listed-kind-quantity-or-field-science + +Q.define("min", "minute", 60 * _s) +Q.define("h", "hour", 60 * _min) +Q.define("d", "day", 24 * _h) + +Q.define("deg", "degree", (_Pi/180) * _rad) +Q.define("arcmin", "arcminute", _deg/60) +Q.define("arcsec", "arcsecond", _arcmin/60) + +Q.define("hectare", "hectare", 1e4 * _m^2) + +Q.define("L", "liter", 1e-3 * _m^3) +Q.addPrefix(SI_prefixes,{_L}) + +Q.define("t", "tonne", 1e3 * _kg) + + + + +-- Nominal Astronomical Units +-- ************************** +-- Source: Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3, +-- https://arxiv.org/pdf/1605.09788.pdf +-- https://arxiv.org/pdf/1510.07674.pdf + +Q.define("R_S_nom", "nomsolradius", 6.957e8 * _m) +Q.define("S_S_nom", "nomsolirradiance", 1361 * _W/_m^2) +Q.define("L_S_nom", "nomsolluminosity", 3.828e26 * _W) +Q.define("T_S_nom", "nomsolefftemperature", 5772 * _K) +Q.define("GM_S_nom", "nomsolmassparameter", 1.3271244e20 * _m^3*_s^-2) + +Q.define("Re_E_nom", "nomterreqradius", 6.3781e6 * _m) +Q.define("Rp_E_nom", "nomterrpolradius", 6.3568e6 * _m) +Q.define("GM_E_nom", "nomterrmassparameter", 3.986004e14 * _m^3*_s^-2) + +Q.define("Re_J_nom", "nomjoveqradius", 7.1492e7 * _m) +Q.define("Rp_J_nom", "nomjovpolradius", 6.6854e7 * _m) +Q.define("GM_J_nom", "nomjovmassparameter", 1.2668653e17 * _m^3*_s^-2) + + + + +-- OTHER NON-SI UNITS +-- ****************** + +-- Length +Q.define("angstrom", "angstrom", 1e-10 * _m) +Q.define("fermi", "fermi", 1e-15 * _m) + +-- Time +Q.define("svedberg", "svedberg", 1e-13 * _s) +Q.define("wk", "week", 7 * _d) +Q.define("a", "year", 365.25 * _d) + +-- Astronomical Length +Q.define("au", "astronomicalunit", 149597870700 * _m) +Q.define("ly", "lightyear", _c*_a) +Q.define("ls", "lightsecond", _c*_s) +Q.define("pc", "parsec", (648000/_Pi) * _au) + +Q.addPrefix(SI_prefixes, {_ls,_ly,_pc}) + +-- Area +Q.define("barn", "barn", 1e-28 * _m^2) +Q.define("are", "are", 1e2 * _m^2) + +Q.addPrefix(SI_prefixes,{_barn}) + +-- Volume +Q.define("tsp", "metricteaspoon", 5e-3 * _L) +Q.define("Tbsp", "metrictablespoon", 3 * _tsp) + +-- Plane Angle +Q.define("gon", "gradian", (_Pi/200) * _rad) +Q.define("tr", "turn", 2*_Pi * _rad) + +-- Solid Angle +Q.define("sp", "spat", 4*_Pi * _sr) + +--force +Q.define("kp", "kilopond", _kg*_g_0) + +-- Pressure +Q.define("bar", "bar", 1e5 * _Pa) +Q.define("atm", "standardatmosphere", 101325 * _Pa) +Q.define("at", "technicalatmosphere", _kp/_cm^2) +Q.define("mmHg", "millimeterofmercury", 133.322387415 * _Pa) +Q.define("Torr", "torr", (101325/760) * _Pa) + +Q.addPrefix({"m"}, {_bar,_Torr}) + +-- Heat +-- Source: https://www.nist.gov/pml/nist-guide-si-appendix-b9-factors-units-listed-kind-quantity-or-field-science +Q.define("cal", "thermochemicalcalorie", 4.184 * _J) +Q.define("cal_IT", "internationalcalorie", 4.1868 * _J) + +Q.addPrefix({"k"}, {_cal,_cal_IT}) + +Q.define("g_TNT", "gramoftnt", 1e3 * _cal) +Q.addPrefix({"k","M","G","T","P"}, {_g_TNT}) + +Q.define("t_TNT", "tonoftnt", 1e9*_cal) +Q.addPrefix({"u","m","k","M","G"}, {_t_TNT}) + +-- Electrical +Q.define("eV", "electronvolt", _e*_V) +Q.define("Ws", "wattsecond", _W*_s) +Q.define("Wh", "watthour", _W*_h) + +Q.define("VA", "voltampere", _V*_A) + +Q.define("As", "amperesecond", _A*_s) +Q.define("Ah", "amperehour", _A*_h) + +Q.addPrefix(SI_prefixes,{_eV,_Wh,_VA,_Ah}) + +-- Information units +Q.define("nibble", "nibble", 4 * _bit) +Q.define("B", "byte", 8 * _bit) +Q.define("bps", "bitpersecond", _bit/_s) + +Q.addPrefix(IEC_prefixes,{_nibble,_B,_bps}) +Q.addPrefix({"k","M","G","T","P","E","Z","Y"},{_bit,_nibble,_B,_bps}) + + +-- Others +Q.define("percent", "percent", 1e-2 * _1) +Q.define("permille", "permille", 1e-3 * _1) +Q.define("ppm", "partspermillion", 1e-6 * _1) +Q.define("ppb", "partsperbillion", 1e-9 * _1) +Q.define("ppt", "partspertrillion", 1e-12 * _1) +Q.define("ppq", "partsperquadrillion", 1e-15 * _1) +Q.define("dB", "decibel", _1) + + +Q.define("PS", "metrichorsepower", 75 * _g_0*_kg*_m/_s) +Q.define("Ci", "curie", 3.7e10 * _Bq) +Q.define("Rad", "rad", 1e-2 * _Gy) +Q.define("rem", "rem", 1e-2 * _Sv) +Q.define("Pl", "poiseuille", _Pa*_s) + + + + + +-- IMPERIAL UNITS +-- ************** + +-- Length +Q.define("in", "inch", 2.54e-2 * _m) +Q.define("th", "thou", 1e-3 * _in) +Q.define("pt", "point", _in/72) +Q.define("pica", "pica", 12 * _pt) +Q.define("hh", "hand", 4 * _in) +Q.define("ft", "foot", 12 * _in) +Q.define("yd", "yard", 3 * _ft) +Q.define("rd", "rod", 5.5 * _yd) +Q.define("ch", "chain", 4 * _rd) +Q.define("fur", "furlong", 10 * _ch) +Q.define("mi", "mile", 8*_fur) -- int. mile +Q.define("lea", "league", 3*_mi) + +-- International Nautical Units +Q.define("nmi", "nauticalmile", 1852 * _m) +Q.define("nlea", "nauticalleague", 3 * _nmi) +Q.define("cbl", "cable", 0.1 * _nmi) +Q.define("ftm", "fathom", 6 * _ft) +Q.define("kn", "knot", _nmi/_h) + +-- Area +Q.define("ac", "acre", 10 * _ch^2) + +-- Volume +Q.define("gal", "gallon", 4.54609*_L) +Q.define("qt", "quart", _gal/4) +Q.define("pint", "pint", _qt/2) +Q.define("cup", "cup", _pint/2) +Q.define("gi", "gill", _pint/4) +Q.define("fl_oz", "fluidounce", _gi/5) +Q.define("fl_dr", "fluiddram", _fl_oz/8) + +-- Mass (Avoirdupois) + +Q.define("gr", "grain", 64.79891*_mg) +Q.define("lb", "pound", 7000*_gr) +Q.define("oz", "ounce", _lb/16) +Q.define("dr", "dram", _lb/256) +Q.define("st", "stone", 14*_lb) +Q.define("qtr", "quarter", 2*_st) +Q.define("cwt", "hundredweight", 4*_qtr) +Q.define("ton", "longton", 20*_cwt) + +-- Mass (Troy) + +Q.define("lb_t", "troypound", 5760 * _gr) +Q.define("oz_t", "troyounce", _lb_t/12) +Q.define("dwt", "pennyweight", 24 * _gr) + +-- Mass (Other) + +Q.define("fir", "firkin", 56 * _lb) + +-- Time +Q.define("sen", "sennight", 7 * _d) +Q.define("ftn", "fortnight", 14 * _d) + +-- Temperature +-- T = (theta + _degF_0):to(_K) +-- theta = (T - _degF_0):to(_degF) +Q.define("degF", "fahrenheit", (5/9) * _K) +Q.define("degF_0", nil, (273.15 - 32*(5/9)) * _K) + + + + + +-- Others +Q.define("lbf", "poundforce", _lb*_g_0) +Q.define("pdl", "poundal", _lb*_ft/_s^2) +Q.define("slug", "slug", _lbf*_s^2/_ft) +Q.define("psi", "poundforcepersquareinch", _lbf/_in^2) +Q.define("BTU", "thchembritishthermalunit", (1897.83047608/1.8) * _J) -- = c_th * lb * °F +Q.define("BTU_it", "intbritishthermalunit", 1055.05585262*_J) -- = c_IT * lb * °F +Q.define("hp", "horsepower", 33000*_ft*_lbf/_min) + + + +-- US CUSTOMARY UNITS +-- ****************** + +-- Length +Q.define("in_US", "ussurveyinch", _m/39.37) +Q.define("hh_US", "ussurveyhand", 4 * _in_US) +Q.define("ft_US", "ussurveyfoot", 3 * _hh_US) +Q.define("li_US", "ussurveylink", 0.66 * _ft_US) +Q.define("yd_US", "ussurveyyard", 3 * _ft_US) +Q.define("rd_US", "ussurveyrod", 5.5 * _yd_US) +Q.define("ch_US", "ussurveychain", 4 * _rd_US) +Q.define("fur_US", "ussurveyfurlong", 10 * _ch_US) +Q.define("mi_US", "ussurveymile", 8 * _fur_US) +Q.define("lea_US", "ussurveyleague", 3 * _mi_US) +Q.define("ftm_US", "ussurveyfathom", 72 * _in_US) +Q.define("cbl_US", "ussurveycable", 120 * _ftm_US) + +-- Area +Q.define("ac_US", "ussurveyacre", _ch_US * _fur_US) + +-- Volume +Q.define("gal_US", "usgallon", 231 * _in^3) +Q.define("qt_US", "usquart", _gal_US/4) +Q.define("pint_US", "uspint", _qt_US/2) +Q.define("cup_US", "uscup", _pint_US/2) +Q.define("gi_US", "usgill", _pint_US/4) +Q.define("fl_oz_US", "usfluidounce", _gi_US/4) +Q.define("Tbsp_US", "ustablespoon", _fl_oz_US/2) +Q.define("tsp_US", "usteaspoon", _Tbsp_US/3) +Q.define("fl_dr_US", "usfluiddram", _fl_oz_US/8) + +-- Mass +Q.define("qtr_US", "usquarter", 25 * _lb) +Q.define("cwt_US", "ushundredweight", 4 * _qtr_US) +Q.define("ton_US", "uston", 20 *_cwt_US) + + + +-- CURRENCIES +-- ********** +-- Source: https://en.wikipedia.org/wiki/List_of_circulating_currencies +-- Exchange rates from 9.3.2019 + +function defineCurrency(iso,prefix,name,unit,minorname,minorvalue) + local u = Q.define(iso, prefix..name, unit) + if minorname ~= nil then + Q.define("c"..iso, prefix..minorname, minorvalue*u) + end +end + +-- variable currencies +defineCurrency("AFN", "Afghan", "Afghani", 0.012*_EUR, "Pul", 0.01) +defineCurrency("ALL", "Albanian", "Lek", 0.008*_EUR, nil, nil) +defineCurrency("AMD", "Armenian", "Dram", 0.0018*_EUR, "Luma", 0.01) +defineCurrency("AOA", "Angolan", "Kwanza", 0.0028*_EUR, "Centimo", 0.01) +defineCurrency("ARS", "Argentine", "Peso", 0.021*_EUR, "Centavo", 0.01) +defineCurrency("AUD", "Australian", "Dollar", 0.63*_EUR, "Cent", 0.01) +defineCurrency("AZN", "Azerbaijani", "Manat", 0.63*_EUR, "Qepik", 0.01) +defineCurrency("BAM", "Bosnian", "Mark", 0.51*_EUR, "Fenings", 0.01) +defineCurrency("BDT", "Bangladeshi", "Taka", 0.011*_EUR, "Poisha", 0.01) +defineCurrency("BIF", "Burundian", "Franc", 0.00049*_EUR, "Centime", 0.01) +defineCurrency("BOB", "Bolivian", "Boliviano", 0.13*_EUR, "Centavo", 0.01) +defineCurrency("BRL", "Brazilian", "Real", 0.23*_EUR, "Centavo", 0.01) +defineCurrency("BWP", "Botswana", "Pula", 0.083*_EUR, "Thebe", 0.01) +defineCurrency("BYN", "Belarusian", "Ruble", 0.42*_EUR, "Kapiejka", 0.01) +defineCurrency("CAD", "Canadian", "Dollar", 0.66*_EUR, "Cent", 0.01) +defineCurrency("CDF", "Congolese", "Franc", 0.00055*_EUR, "Centime", 0.01) +defineCurrency("CHF", "Swiss", "Franc", 0.88*_EUR, "Rappen", 0.01) +defineCurrency("CLP", "Chilean", "Peso", 0.0013*_EUR, "Centavo", 0.01) +defineCurrency("CNY", "ChineseRenminbi", "Yuan", 0.13*_EUR, "Fen", 0.01) +defineCurrency("COP", "Colombian", "Peso", 0.00028*_EUR, "Centavo", 0.01) +defineCurrency("CRC", "CostaRican", "Colon", 0.0015*_EUR, "Centimos", 0.01) +defineCurrency("CZK", "Czech", "Koruna", 0.039*_EUR, "Haler", 0.01) +defineCurrency("DKK", "Danish", "Krone", 0.13*_EUR, "Ore", 0.01) +defineCurrency("DOP", "Dominican", "Peso", 0.018*_EUR, "Centavo", 0.01) +defineCurrency("DZD", "Algerian", "Dinar", 0.0074*_EUR, "Santeem", 0.01) +defineCurrency("EGP", "Egyptian", "Pound", 0.051*_EUR, "Piastre", 0.01) +defineCurrency("ETB", "Ethiopian", "Birr", 0.031*_EUR, "Santim", 0.01) +defineCurrency("FJD", "Fijian", "Dollar", 0.42*_EUR, "Cent", 0.01) +defineCurrency("GBP", "", "PoundSterling", 1.16*_EUR, "PennySterling", 0.01) +defineCurrency("GEL", "Georgian", "Lari", 0.33*_EUR, "Tetri", 0.01) +defineCurrency("GHS", "Ghanaian", "Cedi", 0.16*_EUR, "Pesewa", 0.01) +defineCurrency("GMD", "Gambian", "Dalasi", 0.018*_EUR, "Butut", 0.01) +defineCurrency("GNF", "Guinean", "Franc", 0.000096*_EUR, "Centime", 0.01) +defineCurrency("GTQ", "Guatemalan", "Quetzal", 0.12*_EUR, "Centavo", 0.01) +defineCurrency("GYD", "Guyanese", "Dollar", 0.0043*_EUR, "Cent", 0.01) +defineCurrency("HKD", "HongKong", "Dollar", 0.11*_EUR, "Cent", 0.01) +defineCurrency("HNL", "Honduran", "Lempira", 0.036*_EUR, "Centavo", 0.01) +defineCurrency("HRK", "Croatian", "Kuna", 0.13*_EUR, "Lipa", 0.01) +defineCurrency("HTG", "Haitian", "Gourde", 0.011*_EUR, "Centime", 0.01) +defineCurrency("HUF", "Hungarian", "Forint", 0.0032*_EUR, "Filler", 0.01) +defineCurrency("IDR", "Indonesian", "Rupiah", 0.000062*_EUR, "Sen", 0.01) +defineCurrency("ILS", "IsraeliNew", "Shekel", 0.25*_EUR, "Agora", 0.01) +defineCurrency("INR", "Indian", "Rupee", 0.013*_EUR, "Paisa", 0.01) +defineCurrency("IQD", "Iraqi", "Dinar", 0.00074*_EUR, "Fils", 0.001) +defineCurrency("IRR", "Iranian", "Rial", 0.000027*_EUR, "Toman", 10) +defineCurrency("ISK", "Icelandic", "Krona", 0.0073*_EUR, nil, nil) +defineCurrency("JMD", "Jamaican", "Dollar", 0.007*_EUR, "Cent", 0.01) +defineCurrency("JPY", "Japanese", "Yen", 0.008*_EUR, nil, nil) +defineCurrency("KES", "Kenyan", "Shilling", 0.0089*_EUR, "Cent", 0.01) +defineCurrency("KGS", "Kyrgyzstani", "Som", 0.013*_EUR, "Tyiyn", 0.01) +defineCurrency("KHR", "Cambodian", "Riel", 0.00022*_EUR, nil, nil) +defineCurrency("KPW", "NorthKorean", "Won", 0.00099*_EUR, "Chon", 0.01) +defineCurrency("KRW", "SouthKorean", "Won", 0.00078*_EUR, "Jeon", 0.01) +defineCurrency("KWD", "Kuwaiti", "Dinar", 2.93*_EUR, "Fils", 0.001) +defineCurrency("KZT", "Kazakhstani", "Tenge", 0.0023*_EUR, "Tiyn", 0.01) +defineCurrency("LAK", "Lao", "Kip", 0.0001*_EUR, "Att", 0.01) +defineCurrency("LKR", "SriLankan", "Rupee", 0.005*_EUR, "Cent", 0.01) +defineCurrency("LRD", "Liberian", "Dollar", 0.0055*_EUR, "Cent", 0.01) +defineCurrency("LYD", "Libyan", "Dinar", 0.64*_EUR, "Dirham", 0.001) +defineCurrency("MAD", "Moroccan", "Dirham", 0.092*_EUR, "Santim", 0.01) +defineCurrency("MDL", "Moldovan", "Leu", 0.052*_EUR, "Ban", 0.01) +defineCurrency("MGA", "Malagasy", "Ariary", 0.00025*_EUR, "Iraimbilanja", 0.2) +defineCurrency("MKD", "Macedonian", "Denar", 0.016*_EUR, "Deni", 0.01) +defineCurrency("MMK", "Burmese", "Kyat", 0.00059*_EUR, "Pya", 0.01) +defineCurrency("MNT", "Mongolian", "Togrog", 0.00034*_EUR, "Mongo", 0.01) +defineCurrency("MRU", "Mauritanian", "Ouguiya", 0.025*_EUR, "Khoums", 0.2) +defineCurrency("MUR", "Mauritian", "Rupee", 0.025*_EUR, "Cent", 0.01) +defineCurrency("MVR", "Maldivian", "Rufiyaa", 0.058*_EUR, "Laari", 0.01) +defineCurrency("MWK", "Malawian", "Kwacha", 0.0012*_EUR, "Tambala", 0.01) +defineCurrency("MXN", "Mexican", "Peso", 0.046*_EUR, "Centavo", 0.01) +defineCurrency("MYR", "Malaysian", "Ringgit", 0.22*_EUR, "Sen", 0.01) +defineCurrency("MZN", "Mozambican", "Metical", 0.014*_EUR, "Centavo", 0.01) +defineCurrency("NGN", "Nigerian", "Naira", 0.0025*_EUR, "Kobo", 0.01) +defineCurrency("NIO", "Nicaraguan", "Cordoba", 0.027*_EUR, "Centavo", 0.01) +defineCurrency("NOK", "Norwegian", "Krone", 0.1*_EUR, "Ore", 0.01) +defineCurrency("NZD", "NewZealand", "Dollar", 0.61*_EUR, "Cent", 0.01) +defineCurrency("PEN", "Peruvian", "Sol", 0.27*_EUR, "Centimo", 0.01) +defineCurrency("PGK", "PapuaNewGuinean", "Kina", 0.26*_EUR, "Toea", 0.01) +defineCurrency("PHP", "Philippine", "Peso", 0.017*_EUR, "Sentimo", 0.01) +defineCurrency("PKR", "Pakistani", "Rupee", 0.0064*_EUR, "Paisa", 0.01) +defineCurrency("PLN", "Polish", "Zloty", 0.23*_EUR, "Grosz", 0.01) +defineCurrency("PYG", "Paraguayan", "Guarani", 0.00015*_EUR, "Centimo", 0.01) +defineCurrency("QAR", "Qatari", "Riyal", 0.24*_EUR, "Dirham", 0.01) +defineCurrency("RON", "Romanian", "Leu", 0.21*_EUR, "Ban", 0.01) +defineCurrency("RSD", "Serbian", "Dinar", 0.0085*_EUR, "Para", 0.01) +defineCurrency("RUB", "Russian", "Ruble", 0.013*_EUR, "Kopeyka", 0.01) +defineCurrency("RWF", "Rwandan", "Franc", 0.00098*_EUR, "Centime", 0.01) +defineCurrency("SBD", "SolomonIslands", "Dollar", 0.11*_EUR, "Cent", 0.01) +defineCurrency("SCR", "Seychellois", "Rupee", 0.065*_EUR, "Cent", 0.01) +defineCurrency("SDG", "Sudanese", "Pound", 0.019*_EUR, "Qirsh", 0.01) +defineCurrency("SEK", "Swedish", "Krona", 0.094*_EUR, "Ore", 0.01) +defineCurrency("SGD", "Singapore", "Dollar", 0.65*_EUR, "Cent", 0.01) +defineCurrency("SLL", "SierraLeonean", "Leone", 0.0001*_EUR, "Cent", 0.01) +defineCurrency("SQS", "Somaliland", "Shilling", 0.00013*_EUR, "Cent", 0.01) +defineCurrency("SOS", "Somali", "Shilling", 0.0015*_EUR, "Senti", 0.01) +defineCurrency("SRD", "Surinamese", "Dollar", 0.12*_EUR, "Cent", 0.01) +defineCurrency("SYP", "Syrian", "Pound", 0.0017*_EUR, "Piastre", 0.01) +defineCurrency("THB", "Thai", "Baht", 0.028*_EUR, "Satang", 0.01) +defineCurrency("TJS", "Tajikistani", "Samani", 0.094*_EUR, "Diram", 0.01) +defineCurrency("TOP", "Tongan", "paanga", 0.397*_EUR, "Seniti", 0.01) +defineCurrency("TRY", "Turkish", "Lira", 0.16*_EUR, "Kurus", 0.01) +defineCurrency("TTD", "TrinidadAndTobago", "Dollar", 0.13*_EUR, "Cent", 0.01) +defineCurrency("TWD", "NewTaiwan", "Dollar", 0.029*_EUR, "Cent", 0.01) +defineCurrency("TZS", "Tanzanian", "Shilling", 0.00038*_EUR, "Senti", 0.01) +defineCurrency("UAH", "Ukrainian", "Hryvnia", 0.00038*_EUR, "Kopiyka", 0.01) +defineCurrency("UGX", "Ugandan", "Shilling", 0.00024*_EUR, "Cent", 0.01) +defineCurrency("USD", "US", "Dollar", 0.89*_EUR, "Cent", 0.01) +defineCurrency("UYU", "Uruguayan", "Peso", 0.027*_EUR, "Centesimo", 0.01) +defineCurrency("UZS", "Uzbekistani", "Som", 0.00011*_EUR, "Tiyin", 0.01) +defineCurrency("VES", "Venezuelan", "BolivarSoberano", 0.0003*_EUR, "CentimoSoberano", 0.01) +defineCurrency("VND", "Vietnamese", "Dong", 0.000038*_EUR, "Xu", 0.01) +defineCurrency("WST", "Samoan", "Tala", 0.34*_EUR, "Sene", 0.01) +defineCurrency("YER", "Yemeni", "Rial", 0.0036*_EUR, "Dinar", 0.01) +defineCurrency("ZAR", "SouthAfrican", "Rand", 0.062*_EUR, "Cent", 0.01) +defineCurrency("ZMW", "Zambian", "Kwacha", 0.074*_EUR, "Ngwee", 0.01) + +-- pegged currencies +defineCurrency("AED", "UnitedArabEmirates", "Dirham", (1/3.6725) * _USD, "Fils", 0.01) +defineCurrency("ANG", "NetherlandsAntillean", "Guilder", (1/1.79) * _USD, "Cent", 0.01) +defineCurrency("AWG", "Aruban", "Florin", (1/1.79) * _USD, "Cent", 0.01) +defineCurrency("BBD", "Barbadian", "Dollar", 0.5 * _USD, "Cent", 0.01) +defineCurrency("BGN", "Bulgarian", "Lev", 0.51129 * _EUR, "Stotinka", 0.01) +defineCurrency("BHD", "Bahraini", "Dinar", (1/0.376) * _USD, "Fils", 0.001) +defineCurrency("BMD", "Bermudian", "Dollar", 1 * _USD, "Cent", 0.01) +defineCurrency("BND", "Brunei", "Dollar", 1 * _SGD, "Sen", 0.01) +defineCurrency("BSD", "Bahamian", "Dollar", 1 * _USD, "Cent", 0.01) +defineCurrency("BTN", "Bhutanese", "Ngultrum", 1 * _INR, "Chhertum", 0.01) +defineCurrency("BZD", "Belize", "Dollar", 0.5 * _USD, "Cent", 0.01) +defineCurrency("CUC", "CubanoConvertible", "Peso", 1 * _USD, "Centavo", 0.01) +defineCurrency("CUP", "Cuban", "Peso", (1/24) * _CUC, "Centavo", 0.01) +defineCurrency("CVE", "CapeVerdean", "Escudo", (1/110.265) * _EUR, "Centavo", 0.01) +defineCurrency("DJF", "Djiboutian", "Franc", (1/177.721) * _USD, "Centime", 0.01) +defineCurrency("ERN", "Eritrean", "Nakfa", (1/15)*_USD, "Cent", 0.01) +defineCurrency("FKP", "FalklandIslands", "Pound", 1 * _GBP, "Penny", 0.01) +defineCurrency("GGP", "Guernsey", "Pound", 1 * _GBP, "Penny", 0.01) +defineCurrency("GIP", "Gibraltar", "Pound", 1 * _GBP, "Penny", 0.01) +defineCurrency("IMP", "Manx", "Pound", 1*_GBP, "Penny", 0.01) +defineCurrency("JEP", "Jersey", "Pound", 1 * _GBP, "Penny", 0.01) +defineCurrency("JOD", "Jordanian", "Dinar", (1/0.708) * _USD, "Fils", 0.001) +defineCurrency("KID", "Kiribati", "Dollar", 1 * _AUD, "Cent", 0.01) +defineCurrency("KMF", "Comorian", "franc", (1/491.96775) * _EUR, "Centime", 0.01) +defineCurrency("KYD", "CaymanIslands", "Dollar", 1.2 * _USD, "Cent", 0.01) +defineCurrency("LBP", "Lebanese", "Pound", (1/1507.5) * _USD, "Qeresh", 0.01) +defineCurrency("MOP", "Macanese", "Pataca", (1/1.03) * _HKD, "Avo", 0.01) +defineCurrency("NAD", "Namibian", "Dollar", 1 * _ZAR, "Cent", 0.01) +defineCurrency("NPR", "Nepalese", "Rupee", (1/1.6) * _INR, "Paisa", 0.01) +defineCurrency("OMR", "Omani", "Rial", (1/2.6008) * _USD, "Baisa", 0.001) +defineCurrency("PAB", "Panamanian", "Balboa", 1 * _USD, "Centesimo", 0.01) +defineCurrency("PRB", "Transnistrian", "Ruble", (1/16.1) * _USD, "Kopeck", 0.01) +defineCurrency("SAR", "Saudi", "Riyal", (1/3.75) * _USD, "Halalah", 0.01) +defineCurrency("SHP", "SaintHelena", "Pound", 1 * _GBP, "Penny", 0.01) +defineCurrency("SSP", "SouthSudanese", "Pound", 1 * _SDG, "Piaster", 0.01) +defineCurrency("STN", "SaoTomeAndPrincipe", "Dobra", (1/24.5) * _EUR, "Centimo", 0.01) +defineCurrency("SZL", "Swazi", "Lilangeni", 1 * _ZAR, "Cent", 0.01) +defineCurrency("TMT", "Turkmenistan", "Manat", (1/3.5) * _USD, "Tenge", 0.01) +defineCurrency("TVD", "Tuvaluan", "Dollar", 1 * _AUD, "Cent", 0.01) +defineCurrency("XAF", "CentralAfricanCFA", "Franc", (1/655.957) * _EUR, "Centime", 0.01) +defineCurrency("XCD", "EasternCaribbean", "Dollar", (1/2.7) * _USD, "Cent", 0.01) +defineCurrency("XOF", "WestAfricanCFA", "Franc", (1/655.957) * _USD, "Centime", 0.01) +defineCurrency("XPF", "CFP", "Franc", (1000/8.38) * _EUR, "Centime", 0.01) +defineCurrency("ZWL", "Zimbabwean", "Bonds", 1 * _USD, "Cent", 0.01) + + + + + + + + + + diff --git a/Master/texmf-dist/scripts/lua-physical/physical-dimension.lua b/Master/texmf-dist/scripts/lua-physical/physical-dimension.lua new file mode 100644 index 00000000000..edd9e65997e --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-dimension.lua @@ -0,0 +1,244 @@ +--[[ +The Dimension class keeps track of the dimenionality of a physical quantity. +It can be used to perform validity checks on mathematical operations such as +addition and subtraction. + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +local Dimension = {} +Dimension.__index = Dimension + +-- make the table callable +setmetatable(Dimension, { + __call = function(class, ...) + return Dimension.new(...) + end +}) + +-- index for the dimension names +Dimension._index = {} + +-- registry for base dimensions +Dimension._base = {} + + +-- constructor +function Dimension.new(d) + + -- string + if type(d) == "string" then + return Dimension._index[d] + end + + local e = {} + setmetatable(e, Dimension) + + -- copy constructor + if getmetatable(d) == Dimension then + for i=1, #Dimension._base do + e[i] = d[i] or 0 + end + + -- create zero dimension + else + for i=1, #Dimension._base do + e[i] = 0 + end + end + + return e +end + + +-- define a base new dimension +function Dimension.defineBase(symbol, name) + + local index = Dimension._index + + if index[name] ~= nil then + error("Error: Base dimension '"..name.."' does already exist.") + + elseif index[symbol] ~= nil then + error("Error: Base dimension '"..symbol.."' does already exist.") + + end + + -- create new dimension + local base = Dimension._base + + local n = #base + 1 + local d = Dimension.new() + d[n] = 1 + d.symbol = symbol + + -- add to registry + base[n] = d + + -- resize all other base dimension vectors + for i=1, n-1 do + base[i][n] = 0 + end + + -- update index + index[symbol] = d + index[name] = d + + return d +end + + +-- define a new derived dimension +function Dimension.define(name, o) + + local index = Dimension._index + + if index[name] ~= nil then + error("Error. Dimension '"..name.."' is already defined.") + + elseif getmetatable(o) ~= Dimension then + error("Error. Object in definition of '"..name.."' is no dimension.") + + end + + index[name] = o + + return o +end + + +-- check if the dimension vector has length zero +function Dimension.iszero(o) + for i=1,#Dimension._base do + if o[i] ~= 0 then + return false + end + end + + return true +end + + +-- test if two dimensions are equal +function Dimension.__eq(d1, d2) + for i=1, #Dimension._base do + if d1[i] ~= d2[i] then + return false + end + end + + return true +end + + +-- add two dimensions +function Dimension.__add(d1,d2) + error("Error: Cannot add dimension objects.") +end + + +-- subtract two dimensions +function Dimension.__sub(d1,d2) + error("Error: Cannot subtract dimension objects.") +end + + +-- multiply two dimensions +function Dimension.__mul(d1,d2) + local d = Dimension.new(d1) + + for i=1, #Dimension._base do + d[i] = d1[i] + d2[i] + end + + return d +end + + +-- divide two dimensions +function Dimension.__div(d1,d2) + local d = Dimension.new(d1) + + if type(d1) == "number" then + for i=1, #Dimension._base do + d[i] = 0 - d2[i] + end + else + for i=1, #Dimension._base do + d[i] = d1[i] - d2[i] + end + end + + return d +end + + +-- raise a dimension to the power +function Dimension:__pow(n) + if type(n) ~= "number" then + error("Error: The exponent of the power operation has to be a number.") + end + + local d = Dimension.new() + + for i=1, #Dimension._base do + d[i] = self[i] * n + end + + return d +end + + +-- convert dimension to a string +function Dimension:__tostring() + + local result = {} + + -- search for the name of the dimension + for name,d in pairs(Dimension._index) do + if d == self then + result[#result + 1] = name + end + end + + if #result ~= 0 then + return "["..table.concat(result,",").."]" + end + + -- assemble dimension from base dimensions + local base = Dimension._base + for i=1,#base do + if self[i] ~= 0 then + local dim = "["..base[i].symbol.."]" + + if self[i] ~= 1 then + dim = dim.."^"..self[i] + end + + result[#result + 1]= dim + end + end + + return table.concat(result," ") + +end + +return Dimension
\ No newline at end of file diff --git a/Master/texmf-dist/scripts/lua-physical/physical-init.lua b/Master/texmf-dist/scripts/lua-physical/physical-init.lua new file mode 100644 index 00000000000..fa2e9eceb11 --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-init.lua @@ -0,0 +1,53 @@ +--[[ + +lua-physical + +Author: Thomas Jenni +Version: 1.0.1 +Date: 2020-09-05 + +License: MIT + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +local current_folder = (...):gsub('%.physical%-init$', '') + +-- Source: http://kiki.to/blog/2014/04/12/rule-5-beware-of-multiple-files/ + +local Dimension = require(current_folder .. '.physical-dimension') +local Unit = require(current_folder .. '.physical-unit') +local Quantity = require(current_folder .. '.physical-quantity') +local Number = require(current_folder .. '.physical-number') + +require(current_folder .. '.physical-definition') + +local Data = require(current_folder .. '.physical-data') + +local m = { + Dimension = Dimension, + Unit = Unit, + Number = Number, + Quantity = Quantity, + Data = Data +} + +return m
\ No newline at end of file diff --git a/Master/texmf-dist/scripts/lua-physical/physical-isotope.lua b/Master/texmf-dist/scripts/lua-physical/physical-isotope.lua new file mode 100644 index 00000000000..0ec85f1a5eb --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-isotope.lua @@ -0,0 +1,3564 @@ +local Isotopes = {} +Isotopes.symbols = {"n","H","He","Li","Be","B","C","N","O","F","Ne","Na","Mg","Al","Si","P","S","Cl","Ar","K","Ca","Sc","Ti","V","Cr","Mn","Fe","Co","Ni","Cu","Zn","Ga","Ge","As","Se","Br","Kr","Rb","Sr","Y","Zr","Nb","Mo","Tc","Ru","Rh","Pd","Ag","Cd","In","Sn","Sb","Te","I","Xe","Cs","Ba","La","Ce","Pr","Nd","Pm","Sm","Eu","Gd","Tb","Dy","Ho","Er","Tm","Yb","Lu","Hf","Ta","W","Re","Os","Ir","Pt","Au","Hg","Tl","Pb","Bi","Po","At","Rn","Fr","Ra","Ac","Th","Pa","U","Np","Pu","Am","Cm","Bk","Cf","Es","Fm","Md","No","Lr","Rf","Db","Sg","Bh","Hs","Mt","Ds","Rg","Cn","Ed","Fl","Ef","Lv","Eh","Ei",["Ge"]=32,["Fe"]=26,["La"]=57,["He"]=2,["Li"]=3,["Pm"]=61,["Ni"]=28,["Ga"]=31,["C"]=6,["Tm"]=69,["F"]=9,["Ti"]=22,["Be"]=4,["B"]=5,["K"]=19,["Eu"]=63,["N"]=7,["Am"]=95,["H"]=1,["I"]=53,["S"]=16,["Ne"]=10,["Ta"]=73,["V"]=23,["Se"]=34,["P"]=15,["Au"]=79,["Te"]=52,["Rh"]=45,["Gd"]=64,["Md"]=101,["Ei"]=118,["Mt"]=109,["Tl"]=81,["Np"]=93,["Pt"]=78,["Ed"]=113,["Ac"]=89,["Cd"]=48,["Sm"]=62,["Bh"]=107,["Ef"]=115,["Fl"]=114,["Na"]=11,["Cl"]=17,["Ce"]=58,["Al"]=13,["Pd"]=46,["Ds"]=110,["Nd"]=60,["Hs"]=108,["Eh"]=117,["At"]=85,["Db"]=105,["O"]=8,["Rg"]=111,["U"]=92,["Fm"]=100,["Es"]=99,["Ca"]=20,["Mg"]=12,["Bk"]=97,["Cm"]=96,["Po"]=84,["Pu"]=94,["No"]=102,["Mo"]=42,["Pa"]=91,["Th"]=90,["Os"]=76,["Sg"]=106,["Ho"]=67,["Ag"]=47,["Cs"]=55,["Ra"]=88,["Cu"]=29,["Co"]=27,["Rn"]=86,["Bi"]=83,["In"]=49,["Ba"]=56,["Hg"]=80,["Re"]=75,["As"]=33,["Tc"]=43,["Sc"]=21,["Si"]=14,["Lu"]=71,["Mn"]=25,["Hf"]=72,["Yb"]=70,["W"]=74,["Zr"]=40,["Sr"]=38,["Sn"]=50,["Y"]=39,["Ru"]=44,["Lv"]=116,["Pr"]=59,["Ir"]=77,["Cf"]=98,["Zn"]=30,["Lr"]=103,["Er"]=68,["Fr"]=87,["Xe"]=54,["n"]=0,["Ar"]=18,["Br"]=35,["Cr"]=24,["Cn"]=112,["Dy"]=66,["Rb"]=37,["Sb"]=51,["Tb"]=65,["Rf"]=104,["Nb"]=41,["Kr"]=36,["Pb"]=82} +Isotopes.names = {"Neutronium","Hydrogen","Helium","Lithium","Beryllium","Boron","Carbon","Nitrogen","Oxygen","Fluorine","Neon","Sodium","Magnesium","Aluminium","Silicon","Phosphorus","Sulfur","Chlorine","Argon","Potassium","Calcium","Scandium","Titanium","Vanadium","Chromium","Manganese","Iron","Cobalt","Nickel","Copper","Zinc","Gallium","Germanium","Arsenic","Selenium","Bromine","Krypton","Rubidium","Strontium","Yttrium","Zirconium","Niobium","Molybdenum","Technetium","Ruthenium","Rhodium","Palladium","Silver","Cadmium","Indium","Tin","Antimony","Tellurium","Iodine","Xenon","Caesium","Barium","Lanthanum","Cerium","Praseodymium","Neodymium","Promethium","Samarium","Europium","Gadolinium","Terbium","Dysprosium","Holmium","Erbium","Thulium","Ytterbium","Lutetium","Hafnium","Tantalum","Tungsten","Rhenium","Osmium","Iridium","Platinum","Gold","Mercury","Thallium","Lead","Bismuth","Polonium","Astatine","Radon","Francium","Radium","Actinium","Thorium","Protactinium","Uranium","Neptunium","Plutonium","Americium","Curium","Berkelium","Californium","Einsteinium","Fermium","Mendelevium","Nobelium","Lawrencium","Rutherfordium","Dubnium","Seaborgium","Bohrium","Hassium","Meitnerium","Darmstadtium","Roentgenium","Copernicium","Nihonium","Flerovium","Moscovium","Livermorium","Tennessine","Oganesson",["Terbium"]=65,["Dysprosium"]=66,["Yttrium"]=39,["Nihonium"]=113,["Neptunium"]=93,["Promethium"]=61,["Copper"]=29,["Hassium"]=108,["Tennessine"]=117,["Antimony"]=51,["Neon"]=10,["Caesium"]=55,["Palladium"]=46,["Tin"]=50,["Cobalt"]=27,["Sodium"]=11,["Boron"]=5,["Rubidium"]=37,["Americium"]=95,["Potassium"]=19,["Ytterbium"]=70,["Calcium"]=20,["Molybdenum"]=42,["Iodine"]=53,["Mendelevium"]=101,["Bismuth"]=83,["Oganesson"]=118,["Nitrogen"]=7,["Selenium"]=34,["Bohrium"]=107,["Tellurium"]=52,["Carbon"]=6,["Cadmium"]=48,["Scandium"]=21,["Moscovium"]=115,["Meitnerium"]=109,["Flerovium"]=114,["Copernicium"]=112,["Silicon"]=14,["Roentgenium"]=111,["Darmstadtium"]=110,["Magnesium"]=12,["Hydrogen"]=1,["Hafnium"]=72,["Seaborgium"]=106,["Europium"]=63,["Thorium"]=90,["Lutetium"]=71,["Phosphorus"]=15,["Vanadium"]=23,["Livermorium"]=116,["Gadolinium"]=64,["Fermium"]=100,["Einsteinium"]=99,["Californium"]=98,["Gallium"]=31,["Actinium"]=89,["Tantalum"]=73,["Oxygen"]=8,["Lithium"]=3,["Polonium"]=84,["Tungsten"]=74,["Gold"]=79,["Curium"]=96,["Zirconium"]=40,["Sulfur"]=16,["Uranium"]=92,["Nickel"]=28,["Protactinium"]=91,["Chlorine"]=17,["Rutherfordium"]=104,["Radium"]=88,["Xenon"]=54,["Francium"]=87,["Argon"]=18,["Zinc"]=30,["Radon"]=86,["Astatine"]=85,["Plutonium"]=94,["Thallium"]=81,["Indium"]=49,["Niobium"]=41,["Platinum"]=78,["Iridium"]=77,["Osmium"]=76,["Lanthanum"]=57,["Holmium"]=67,["Erbium"]=68,["Strontium"]=38,["Thulium"]=69,["Lead"]=82,["Nobelium"]=102,["Helium"]=2,["Bromine"]=35,["Technetium"]=43,["Dubnium"]=105,["Mercury"]=80,["Rhenium"]=75,["Samarium"]=62,["Manganese"]=25,["Rhodium"]=45,["Iron"]=26,["Neodymium"]=60,["Krypton"]=36,["Barium"]=56,["Germanium"]=32,["Chromium"]=24,["Aluminium"]=13,["Lawrencium"]=103,["Praseodymium"]=59,["Ruthenium"]=44,["Titanium"]=22,["Silver"]=47,["Beryllium"]=4,["Cerium"]=58,["Berkelium"]=97,["Arsenic"]=33,["Fluorine"]=9} 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+,{160,169,178,187,196,206,215,225,235,245,255,266,276,287,298,309,320,332,343,355,367,379,391,404} +,{179,188,197,207,216,226,236,246,256,267,277,288,299,310,321,333,344,356,368,380,392,405,417,429} +,{198,208,217,227,237,247,257,268,278,289,300,311,322,334,345,357,369,381,393,406,418,430,441,453} +,{218,228,238,248,258,269,279,290,301,312,323,335,346,358,370,382,394,407,419,431,442,454,465,477,489} +,{239,249,259,270,280,291,302,313,324,336,347,359,371,383,395,408,420,432,443,455,466,478,490,502,514} +,{260,271,281,292,303,314,325,337,348,360,372,384,396,409,421,433,444,456,467,479,491,503,515,527,539,552} +,{282,293,304,315,326,338,349,361,373,385,397,410,422,434,445,457,468,480,492,504,516,528,540,553,565,577,589} +,{305,316,327,339,350,362,374,386,398,411,423,435,446,458,469,481,493,505,517,529,541,554,566,578,590,602,614,626} +,{328,340,351,363,375,387,399,412,424,436,447,459,470,482,494,506,518,530,542,555,567,579,591,603,615,627,639,651,664} +,{352,364,376,388,400,413,425,437,448,460,471,483,495,507,519,531,543,556,568,580,592,604,616,628,640,652,665,677,690} +,{365,377,389,401,414,426,438,449,461,472,484,496,508,520,532,544,557,569,581,593,605,617,629,641,653,666,678,691,703,716,729} +,{390,402,415,427,439,450,462,473,485,497,509,521,533,545,558,570,582,594,606,618,630,642,654,667,679,692,704,717,730,743,756} +,{403,416,428,440,451,463,474,486,498,510,522,534,546,559,571,583,595,607,619,631,643,655,668,680,693,705,718,731,744,757,770,783,797} +,{452,464,475,487,499,511,523,535,547,560,572,584,596,608,620,632,644,656,669,681,694,706,719,732,745,758,771,784,798,811,825} +,{476,488,500,512,524,536,548,561,573,585,597,609,621,633,645,657,670,682,695,707,720,733,746,759,772,785,799,812,826,839,853,867} +,{501,513,525,537,549,562,574,586,598,610,622,634,646,658,671,683,696,708,721,734,747,760,773,786,800,813,827,840,854,868,882,896} +,{526,538,550,563,575,587,599,611,623,635,647,659,672,684,697,709,722,735,748,761,774,787,801,814,828,841,855,869,883,897,910,924,938} +,{551,564,576,588,600,612,624,636,648,660,673,685,698,710,723,736,749,762,775,788,802,815,829,842,856,870,884,898,911,925,939,953,967} +,{601,613,625,637,649,661,674,686,699,711,724,737,750,763,776,789,803,816,830,843,857,871,885,899,912,926,940,954,968,982,996,1011} +,{638,650,662,675,687,700,712,725,738,751,764,777,790,804,817,831,844,858,872,886,900,913,927,941,955,969,983,997,1012,1026,1041,1056} +,{663,676,688,701,713,726,739,752,765,778,791,805,818,832,845,859,873,887,901,914,928,942,956,970,984,998,1013,1027,1042,1057,1071,1086,1101} +,{689,702,714,727,740,753,766,779,792,806,819,833,846,860,874,888,902,915,929,943,957,971,985,999,1014,1028,1043,1058,1072,1087,1102,1116,1130} +,{715,728,741,754,767,780,793,807,820,834,847,861,875,889,903,916,930,944,958,972,986,1000,1015,1029,1044,1059,1073,1088,1103,1117,1131,1145,1159,1174,1189} +,{742,755,768,781,794,808,821,835,848,862,876,890,904,917,931,945,959,973,987,1001,1016,1030,1045,1060,1074,1089,1104,1118,1132,1146,1160,1175,1190,1205,1220} +,{769,782,795,809,822,836,849,863,877,891,905,918,932,946,960,974,988,1002,1017,1031,1046,1061,1075,1090,1105,1119,1133,1147,1161,1176,1191,1206,1221,1236,1251,1267} +,{796,810,823,837,850,864,878,892,906,919,933,947,961,975,989,1003,1018,1032,1047,1062,1076,1091,1106,1120,1134,1148,1162,1177,1192,1207,1222,1237,1252,1268,1283,1299,1315} +,{824,838,851,865,879,893,907,920,934,948,962,976,990,1004,1019,1033,1048,1063,1077,1092,1107,1121,1135,1149,1163,1178,1193,1208,1223,1238,1253,1269,1284,1300,1316,1331,1347,1363} +,{852,866,880,894,908,921,935,949,963,977,991,1005,1020,1034,1049,1064,1078,1093,1108,1122,1136,1150,1164,1179,1194,1209,1224,1239,1254,1270,1285,1301,1317,1332,1348,1364,1379,1395,1411} +,{881,895,909,922,936,950,964,978,992,1006,1021,1035,1050,1065,1079,1094,1109,1123,1137,1151,1165,1180,1195,1210,1225,1240,1255,1271,1286,1302,1318,1333,1349,1365,1380,1396,1412,1428,1444,1460} +,{923,937,951,965,979,993,1007,1022,1036,1051,1066,1080,1095,1110,1124,1138,1152,1166,1181,1196,1211,1226,1241,1256,1272,1287,1303,1319,1334,1350,1366,1381,1397,1413,1429,1445,1461,1477,1493,1510} +,{952,966,980,994,1008,1023,1037,1052,1067,1081,1096,1111,1125,1139,1153,1167,1182,1197,1212,1227,1242,1257,1273,1288,1304,1320,1335,1351,1367,1382,1398,1414,1430,1446,1462,1478,1494,1511,1527,1544} +,{981,995,1009,1024,1038,1053,1068,1082,1097,1112,1126,1140,1154,1168,1183,1198,1213,1228,1243,1258,1274,1289,1305,1321,1336,1352,1368,1383,1399,1415,1431,1447,1463,1479,1495,1512,1528,1545,1561,1578,1595} +,{1010,1025,1039,1054,1069,1083,1098,1113,1127,1141,1155,1169,1184,1199,1214,1229,1244,1259,1275,1290,1306,1322,1337,1353,1369,1384,1400,1416,1432,1448,1464,1480,1496,1513,1529,1546,1562,1579,1596,1612,1629} +,{1040,1055,1070,1084,1099,1114,1128,1142,1156,1170,1185,1200,1215,1230,1245,1260,1276,1291,1307,1323,1338,1354,1370,1385,1401,1417,1433,1449,1465,1481,1497,1514,1530,1547,1563,1580,1597,1613,1630,1646,1663,1680} +,{1085,1100,1115,1129,1143,1157,1171,1186,1201,1216,1231,1246,1261,1277,1292,1308,1324,1339,1355,1371,1386,1402,1418,1434,1450,1466,1482,1498,1515,1531,1548,1564,1581,1598,1614,1631,1647,1664,1681,1697,1714} +,{1144,1158,1172,1187,1202,1217,1232,1247,1262,1278,1293,1309,1325,1340,1356,1372,1387,1403,1419,1435,1451,1467,1483,1499,1516,1532,1549,1565,1582,1599,1615,1632,1648,1665,1682,1698,1715,1731,1748} 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\ No newline at end of file diff --git a/Master/texmf-dist/scripts/lua-physical/physical-number.lua b/Master/texmf-dist/scripts/lua-physical/physical-number.lua new file mode 100644 index 00000000000..8c278aacfee --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-number.lua @@ -0,0 +1,755 @@ +--[[ +This file contains the number class which allows to do +calculations with uncertainties. + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +-- Number class +local Number = {} +Number.__index = Number + +-- make the table callable +setmetatable(Number, { + __call = function(class, ...) + return Number.new(...) + end +}) + + +-- If a number is given as a string and it has no uncertainty defined, this options +-- allows to set a default uncertainty, i.e. (5.6) will become (5.60 +/- 0.05) +Number.defaultUncertainty = 0.5 + +-- Switch for writing uncertainty or not +Number.omitUncertainty = false + +-- If true, the plus-minus notation will be used, otherwise the uncertainty +-- will be appended to the value in parentheses. +Number.seperateUncertainty = false + +-- number format "decimal" or "scientific" +Number.DECIMAL = 0 +Number.SCIENTIFIC = 1 + +Number.format = Number.SCIENTIFIC + +-- The rounding function uses this value to determine the rounding method +-- if it is set to 0.5 the rounding method is "towards nearest, ties to even". +Number.half = 0.5 + + + +-- constructor +function Number.new(x, dx) + + local n = {} + setmetatable(n, Number) + + -- pure number without uncertainty + if type(x) == "number" then + n._x = x + n._dx = dx or 0 + + return n + + -- copy constructor + elseif type(x) == "table" and getmetatable(x) == Number then + n._x = x._x + n._dx = x._dx + + return n + + -- number from string + elseif type(x) == "string" then + + -- parse string of the form "3.4e-3" + local m = tonumber(x) + if m ~= nil then + n._x = m + + local m1, m2, e = string.match(x,"^([^%s%.]*)%.?([^%seE]*)[eE]?([^%s]*)$") + + -- get exponent + if e ~= "" then + e = tonumber(e) + else + e = 0 + end + + -- calculate uncertainty + n._dx = Number.defaultUncertainty * 10^e + if m2 ~= "" then + n._dx = n._dx * 10^(-string.len(m2)) + end + + return n + end + + -- parse string of the form "5.4e-3 +/- 2.4e-6" + local m1, m2 = string.match(x,"^([^%s]*)%s*%+%/%-%s*([^%s]*)$") + if m1 ~= nil and m2 ~= nil then + n._x = tonumber(m1) + n._dx = tonumber(m2) + + return n + end + + -- parse string of the form "5.45(7)e-23" + local m1, m2, u, e = string.match(x,"^([^%s%.]*)%.?([^%seE]*)%(([0-9]+)%)[eE]?([^%s]*)$") + if m1 ~= nil then + + n._x = tonumber(m1.."."..m2) + n._dx = u * 10^(-string.len(m2)) + + -- exponent + if e ~= "" then + n._x = n._x * 10^e + n._dx = n._dx * 10^e + end + + return n + end + + print("Error: The string '"..tostring(_x).."' cannot be converted to a physical.Number.") + + return nil + + -- default + else + n._x = 0 + n._dx = 0 + + return n + end + +end + +-- return the mean value +function Number:mean() + return self._x +end + +-- return the uncertainty +function Number:uncertainty() + return self._dx +end + +-- get mantissa and exponent in scientific notation +function Number._frexp(x) + if x == 0 then + return 0,0 + end + + local s = (x < 0 and -1) or 1 + local m = s * x + local exp = math.floor(math.log(m,10)) + m = s * m * 10^(-exp) + + return m, exp +end + +-- round a number x to a precision n +function Number._round(x,n) + local m = math.pow(10.0, n) + local y = x * m + + if y >= 0 then + y = math.floor(y + Number.half) + else + y = math.ceil(y - Number.half) + end + + return y / m +end + + +-- convert number to string +-- x: number +-- n: decimal places +function Number._flt2str(x,n) + return string.format("%."..math.max(n,0).."f", Number._round(x,n) ) +end + +-- convert number to a number +function Number:__tonumber() + return self._x +end + + +-- plus minus notation, i.e. (5.040 +/- 0.001) +function Number:toPlusMinusNotation(format) + + if format == nil then + format = Number.format + end + + local m, e = self._frexp(self._x) + local dm, de = self._frexp(self._dx) + + -- if the first digit of the uncetainty is a 1, give two digits of the uncertainty + local udigit = 0 + if math.floor(dm) == 1 then + udigit = 1 + end + + local str + + -- In the decimal format, the numbers are given as decimals, i.e. (0.02 +/- 0.001) + if format == Number.DECIMAL then + if de - udigit >= 0 then + str = self._flt2str(self._x, 0).." +/- "..self._flt2str(self._dx, 0) + else + local digits = math.abs(-de + udigit) + str = self._flt2str(self._x, digits).." +/- "..self._flt2str(self._dx, digits) + end + + str = "("..str..")" + + -- In the scientific format, the numbers are written with powers of ten, i.e. (2.0 +/- 0.1) e-2 + elseif format == Number.SCIENTIFIC then + + -- the uncertainty should have the same exponent as the value + dm = dm * 10^(de-e) + de = de - e + + if de >= 0 then + str = self._flt2str(m, 0).." +/- "..self._flt2str(dm, 0) + else + local digits = math.abs(-de + udigit) + str = self._flt2str(m, digits).." +/- "..self._flt2str(dm, digits) + end + + str = "("..str..")" + + if e ~= 0 then + str = str.."e"..e + end + else + error("Unknown number format: '"..format.."'") + end + + return str +end + + +-- generate a string representation in parenthesis notation, i.e. i.e. 5.45(7)e-23 +-- Source: http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html +function Number:toParenthesisNotation(format) + + if format == nil then + format = Number.format + end + + local m, e = self._frexp(self._x) + local dm, de = self._frexp(self._dx) + + -- if the first digit of the uncetainty is a 1, give two digits of the uncertainty + local udigit = 0 + if self._round(dm, 0) == 1 then + udigit = 1 + dm = dm * 10 + de = de - 1 + end + + local str + + -- In the decimal format, the numbers are given as decimals, i.e. 0.00343(12) + if format == Number.DECIMAL then + if de - udigit >= 0 then + str = self._flt2str(self._x, 0).."(".. self._flt2str(dm*10^de, 0) ..")" + else + str = self._flt2str(self._x, math.abs(de)).."(".. self._flt2str(dm, 0) ..")" + end + + -- In the scientific format, the numbers are written with powers of ten, i.e. 3.43(12)e-3 + elseif format == Number.SCIENTIFIC then + str = self._flt2str(m, math.abs(de-e)).."("..self._flt2str(dm, 0)..")" + + if e ~= 0 then + str = str.."e"..e + end + + else + error("Unknown number format: '"..format.."'") + end + + return str +end + + + +function Number:toOmitUncertaintyNotation(format) + + local m, e = self._frexp(self._x) + local dm, de = self._frexp(self._dx) + + local str = "" + + if Number.format == Number.DECIMAL then + str = self._flt2str(self._x, math.abs(de + 1)) + + elseif Number.format == Number.SCIENTIFIC then + str = self._flt2str(m, math.abs(de + 1 - e)) + + if e ~= 0 then + str = str.."e"..e + end + + else + error("Unknown number format: '"..format.."'") + end + + return str +end + + +-- convert number to a string +function Number:__tostring() + + if self._dx == 0 then + return tostring(self._x) + + elseif Number.omitUncertainty then + return self:toOmitUncertaintyNotation() + + elseif Number.seperateUncertainty then + return self:toPlusMinusNotation() + + else + return self:toParenthesisNotation() + end + +end + + +-- equal +-- Two physical numbers are equal if they have the same value and uncertainty +function Number.__eq(n1,n2) + return n1._x == n2._x and n1._dx == n2._dx +end + +-- less than +function Number.__lt(n1,n2) + if getmetatable(n1) ~= Number then + return n1 < n2._x + + elseif getmetatable(n2) ~= Number then + return n1._x < n2 + + else + return n1._x < n2._x + end +end + +-- less equal +function Number.__le(n1,n2) + + if getmetatable(n1) ~= Number then + return n1 <= n2._x + + elseif getmetatable(n2) ~= Number then + return n1._x <= n2 + + else + return n1._x <= n2._x + end + +end + + +-- add two numbers +function Number.__add(n1,n2) + local m = Number.new() + + if type(n1) == "number" then + m._x = n1 + n2._x + m._dx = n2._dx + + elseif type(n2) == "number" then + m._x = n1._x + n2 + m._dx = n1._dx + + -- n1 an object + elseif getmetatable(n1) ~= Number then + return n1.__add(n1,n2) + + -- n2 an object + elseif getmetatable(n2) ~= Number then + return n2.__add(n1,n2) + + else + m._x = n1._x + n2._x + m._dx = (n1._dx^2 + n2._dx^2)^0.5 + end + + return m +end + + +-- subtract two numbers +function Number.__sub(n1,n2) + local m = Number.new() + + if type(n1) == "number" then + m._x = n1 - n2._x + m._dx = n2._dx + + elseif type(n2) == "number" then + m._x = n1._x - n2 + m._dx = n1._dx + + -- n1 an object + elseif getmetatable(n1) ~= Number then + return n1.__sub(n1,n2) + + -- n2 an object + elseif getmetatable(n2) ~= Number then + return n2.__sub(n1,n2) + + else + m._x = n1._x - n2._x + m._dx = (n1._dx^2 + n2._dx^2)^0.5 + end + + return m +end + + +-- unary minus +function Number.__unm(n1) + local m = Number.new() + + m._x = -n1._x + m._dx = n1._dx + + return m +end + + +-- multiplication +function Number.__mul(n1,n2) + local m = Number.new() + + -- n1 float , n2 number + if type(n1) == "number" then + m._x = n1 * n2._x + m._dx = n1 * n2._dx + + -- n1 number , o2 float + elseif type(n2) == "number" then + m._x = n1._x * n2 + m._dx = n1._dx * n2 + + -- n1 is an object + elseif getmetatable(n1) ~= Number then + return n1.__mul(n1,n2) + + -- n2 is an object + elseif getmetatable(n2) ~= Number then + return n2.__mul(n1,n2) + + -- o1 number , o2 number + else + m._x = n1._x * n2._x + + local dx = 0 + if n1._x ~= 0 then + dx = (n1._dx/n1._x)^2 + end + if n2._x ~= 0 then + dx = dx + (n2._dx/n2._x)^2 + end + + m._dx = m._x * dx^0.5 + end + + return m +end + + +-- division +function Number.__div(n1,n2) + local m = Number.new() + + -- n1 float , n2 number + if type(n1) == "number" then + m._x = n1 / n2._x + m._dx = n2._dx * n1 / n2._x^2 + + -- n1 number , o2 float + elseif type(n2) == "number" then + m._x = n1._x / n2 + m._dx = n1._dx / n2 + + -- n1 an object + elseif getmetatable(n1) ~= Number then + return n1.__div(n1,n2) + + -- n2 an object + elseif getmetatable(n2) ~= Number then + return n2.__div(n1,n2) + + -- o1 number , o2 number + else + m._x = n1._x / n2._x + + local dx = 0 + if n1._x ~= 0 then + dx = (n1._dx/n1._x)^2 + end + if n2._x ~= 0 then + dx = dx + (n2._dx/n2._x)^2 + end + + m._dx = m._x * dx^0.5 + end + + return m +end + + +-- exponentiation +function Number.__pow(n1,n2) + local m = Number.new() + + -- n1 float , n2 number + if type(n1) == "number" then + m._x = n1^n2._x + m._dx = n2._dx * math.abs(math.log(n1)*n1^n2._x) + + -- n1 number , o2 float + elseif type(n2) == "number" then + m._x = n1._x^n2 + m._dx = n1._dx * math.abs(n2 * n1._x^(n2-1)) + + -- n1 an object + elseif getmetatable(n1) ~= Number then + return n1.__pow(n1,n2) + + -- n2 an object + elseif getmetatable(n2) ~= Number then + return n2.__pow(n1,n2) + + -- o1 number , o2 number + else + m._x = n1._x^n2._x + m._dx = n1._dx*math.abs(n2._x*n1._x^(n2._x-1)) + n2._dx*math.abs(math.log(n1._x)*n1._x^n2._x) + end + + return m +end + + + + + + +-- calculate the absolute value +function Number.abs(n) + local m = Number.new() + + m._x = math.abs(n._x) + m._dx = n._dx + + return m +end + +-- calculate the square root +function Number.sqrt(n) + local m = Number.new() + + m._x = math.sqrt(n._x) + m._dx = n._dx / (2*math.sqrt(n._x)) + + return m +end + +-- calculate the natural logarithm +function Number.log(n,base) + local m = Number.new() + + if base == nil then + m._x = math.log(n._x) + m._dx = n._dx / math.abs(n._x) + else + m._x = math.log(n._x,base) + m._dx = n._dx / math.abs(n._x*math.log(base)) + end + + return m +end + + +-- calculate the exponential function +function Number.exp(n) + local m = Number.new() + + m._x = math.exp(n._x) + m._dx = n._dx * math.exp(n._x) + + return m +end + + +-- TRIGONOMETRIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Trigonometric_functions + +-- sine +function Number.sin(n) + local m = Number.new() + + m._x = math.sin(n._x) + m._dx = n._dx * math.abs(math.cos(n._x)) + + return m +end + +-- cosine +function Number.cos(n) + local m = Number.new() + + m._x = math.cos(n._x) + m._dx = n._dx * math.abs(math.sin(n._x)) + + return m +end + +-- tangent +function Number.tan(n) + local m = Number.new() + + m._x = math.tan(n._x) + m._dx = n._dx * math.abs(1/math.cos(n._x)^2) + + return m +end + + +-- INVERS TRIGONOMETRIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#arctan + +-- invers sine +function Number.asin(n) + local m = Number.new() + + m._x = math.asin(n._x) + m._dx = n._dx * 1 / math.sqrt(1 - n._x^2) + + return m +end + +-- inverse cosine +function Number.acos(n) + local m = Number.new() + + m._x = math.acos(n._x) + m._dx = n._dx * 1 / math.sqrt(1 - n._x^2) + + return m +end + +-- inverse tangent +function Number.atan(n) + local m = Number.new() + + m._x = math.atan(n._x) + m._dx = n._dx / (1 + n._x^2) + + return m +end + + +-- HYPERBOLIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Hyperbolic_function + +-- hyperbolic sine +function Number.sinh(n) + local m = Number.new() + + m._x = 0.5 * math.exp(n._x) - 0.5 / math.exp(n._x) + m._dx = n._dx * (0.5 * math.exp(n._x) + 0.5 / math.exp(n._x)) + + return m +end + +-- hyperbolic cosine +function Number.cosh(n) + local m = Number.new() + + m._x = 0.5 * math.exp(n._x) + 0.5 / math.exp(n._x) + m._dx = n._dx * (0.5 * math.exp(n._x) - 0.5 / math.exp(n._x)) + + return m +end + +-- hyperbolic tangent +function Number.tanh(n) + local m = Number.new() + + m._x = (math.exp(n._x) - math.exp(-n._x)) / (math.exp(n._x) + math.exp(-n._x)) + m._dx = n._dx / (0.5 * math.exp(n._x) + 0.5 / math.exp(n._x))^2 + + return m +end + + +-- INVERS HYPERBOLIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Inverse_hyperbolic_function + +-- inverse hyperbolic sine +-- (-inf < n < +inf) +function Number.asinh(n) + local m = Number.new() + + m._x = math.log(n._x + math.sqrt(n._x^2 + 1)) + m._dx = n._dx / math.sqrt(n._x^2 + 1) + + return m +end + +-- inverse hyperbolic cosine +-- (1 < n) +function Number.acosh(n) + local m = Number.new() + + m._x = math.log(n._x + math.sqrt(n._x^2 - 1)) + m._dx = n._dx / math.sqrt(n._x^2 - 1) + + return m +end + +-- inverse hyperbolic tangent +-- (-1 < n < 1) +function Number.atanh(n) + local m = Number.new() + + m._x = 0.5 * math.log((1 + n._x)/(1 - n._x)) + m._dx = n._dx / math.abs(n._x^2 - 1) + + return m +end + + + +return Number + + diff --git a/Master/texmf-dist/scripts/lua-physical/physical-quantity.lua b/Master/texmf-dist/scripts/lua-physical/physical-quantity.lua new file mode 100644 index 00000000000..47a02063c5d --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-quantity.lua @@ -0,0 +1,839 @@ +--[[ +This file contains the quantity class + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +local prefix = ... and (...):match '(.-%.?)[^%.]+$' or '' +local D = require(prefix..'physical-dimension') +local U = require(prefix..'physical-unit') +local N = require(prefix..'physical-number') + +-- Quantity class +local Quantity = {} +Quantity.__index = Quantity + +-- make Quantity table callable +setmetatable(Quantity, { + __call = function(class, ...) + return Quantity.new(...) + end +}) + + +-- registry for base units +Quantity._base = {} + +-- registry for prefixes +Quantity._prefixes = {} + +-- modes for the function tosiunitx() +Quantity.siunitx_SI = 0 +Quantity.siunitx_num = 1 +Quantity.siunitx_si = 2 + + +-- constructor +function Quantity.new(q) + + local p = {} + setmetatable(p, Quantity) + + -- copy constructor + if getmetatable(q) == Quantity then + p.dimension = q.dimension + p.value = q.value + p.basefactor = q.basefactor + p.unit = U(q.unit) + + -- create a dimensionless Quantity + else + p.dimension = D.new() + p.value = q or 1 + p.basefactor = 1 + p.unit = U() + end + + return p +end + + +-- create base quantities +function Quantity.defineBase(symbol,name,dimension) + + if rawget(_G,"_"..symbol) ~= nil then + error("Error: Quantity '_"..symbol.."' does already exist.") + end + + local p = Quantity.new() + p.value = 1 + p.dimension = dimension + p.unit = U.new(symbol,name) + + table.insert(Quantity._base,p) + + rawset(_G, "_"..symbol, p) + + return p +end + + +-- create derived quantities +function Quantity.define(symbol, name, q) + + -- check if quantity does already exist + if rawget(_G,"_"..symbol) ~= nil then + error("Error: Quantity '_"..symbol.."' does already exist.") + end + + -- check if given value is a quantity + if getmetatable(q) ~= Quantity then + error("Error: No quantity given in the definition of '"..name.."'.") + end + + local p = Quantity.new(q) + + if name ~= nil then + p.value = 1 + p.basefactor = q.basefactor * q.value + p.unit = U.new(symbol, name) + else + local p = Quantity.new(q) + end + + rawset(_G, "_"..symbol, p) + + return p +end + + +-- define a prefix +function Quantity.definePrefix(symbol,name,factor) + + -- check if prefix does already exist + if Quantity._prefixes[symbol] ~= nil then + error("Error: Prefix '"..symbol.."' does already exist.") + end + + -- append prefix to the _prefixes table + Quantity._prefixes[symbol] = { + symbol=symbol, + name=name, + factor=factor + } +end + + +-- create prefixed versions of the given units +function Quantity.addPrefix(prefixes, qs) + + -- todo: what if prefixes and units are no lists? + + for i=1,#prefixes do + local prefix = Quantity._prefixes[prefixes[i]] + + for j=1,#qs do + local q = qs[j] + + local p = Quantity.new(q) + p.unit = U.new(q.unit.symbol, q.unit.name, prefix.symbol, prefix.name) + p.basefactor = p.basefactor*prefix.factor + + -- assert that unit does not exist + local symbol = "_"..prefix.symbol..q.unit.symbol + if rawget(_G,symbol) ~= nil then + error("Error: Cannot create prefixed Quantity, because '"..symbol.."' does already exist.") + end + + -- set unit as a global variable + rawset(_G, symbol, p) + end + end +end + + +-- Add two quantities +function Quantity.__add(q1, q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + if q1.dimension ~= q2.dimension then + error("Error: Cannot add '"..tostring(q1).."' to '"..tostring(q2).."', because they have different dimensions.") + end + + -- convert o1 to q2 units + local p = q1:to(q2) + p.value = p.value + q2.value + + return p +end + + +-- subtract a dimension from another one +function Quantity.__sub(q1, q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + if q1.dimension ~= q2.dimension then + error("Error: Cannot subtract '"..tostring(q2).."' from '"..tostring(q1).."', because they have different dimensions.") + end + + -- convert q1 to q2 units + local p = q1:to(q2) + p.value = p.value - q2.value + + return p +end + + +-- unary minus +function Quantity.__unm(q) + local p = Quantity.new(q) + p.value = -p.value + return p +end + + +-- multiply a dimension by a number +function Quantity.__mul(q1, q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + local p = Quantity.new() + + p.dimension = q1.dimension * q2.dimension + p.value = q1.value * q2.value + p.basefactor = q1.basefactor * q2.basefactor + p.unit = q1.unit * q2.unit + + return p +end + + +-- divide a quantity / number by a quantity / number +function Quantity.__div(q1, q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + local p = Quantity.new() + + p.dimension = q1.dimension / q2.dimension + p.value = q1.value / q2.value + p.basefactor = q1.basefactor / q2.basefactor + p.unit = q1.unit / q2.unit + + return p +end + +-- power +function Quantity.__pow(q1,q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + if not q2.dimension:iszero() then + error("Error: Cannot take the power of '"..tostring(q1).."', because the exponent '"..tostring(q2).."' is not dimensionless.") + end + + local p = Quantity.new() + local e = q2:to() + + p.value = q1.value^e.value + + e = e:__tonumber() + p.dimension = q1.dimension^e + p.basefactor = q1.basefactor^e + p.unit = q1.unit^e + + return p +end + +-- test if two quantities are equal +function Quantity.__eq(q1,q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + local p = q1:to(q2) + + if p.value ~= q2.value then + return false + elseif p.dimension ~= q2.dimension then + return false + elseif p.basefactor ~= q2.basefactor then + return false + end + + return true +end + +-- check if this quantity is less than another one +function Quantity.__lt(q1,q2) + + if getmetatable(q1) ~= Quantity then + q1 = Quantity.new(q1) + end + if getmetatable(q2) ~= Quantity then + q2 = Quantity.new(q2) + end + + if q1.dimension ~= q2.dimension then + error("Error: Cannot compare '"..tostring(q1).."' to '"..tostring(q2).."', because they have different dimensions.") + end + + return q1:to().value < q2:to().value +end + +-- check if this quantity is close to another one. r is the maximal relative deviation. +function Quantity:isclose(q, r) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if getmetatable(r) ~= Quantity then + r = Quantity.new(r) + end + + if self.dimension ~= q.dimension then + error("Error: Cannot compare '"..tostring(self).."' to '"..tostring(q)..", because they have different dimensions.") + end + if not r.dimension:iszero() then + error("Error. The argument '"..tostring(r).."' of the isclose function is not unitless.") + end + + local q1 = self:to():__tonumber() + local q2 = q:to():__tonumber() + local r = r:to():__tonumber() + + local delta = math.abs(q1 - q2) + local min = math.min(math.abs(q1),math.abs(q2)) + return (delta / min) <= r +end + + +-- convert quantity to another unit +function Quantity:to(q) + + local p = Quantity.new() + + -- convert to base units + p.dimension = self.dimension + p.value = self.value * self.basefactor + + -- convert to target units + if q ~= nil then + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if self.dimension ~= q.dimension then + error("Error: Cannot convert '"..tostring(self).."' to '"..tostring(q).."', because they have different dimensions.") + end + + p.value = p.value / q.basefactor + p.basefactor = q.basefactor + p.unit = U(q.unit) + + -- convert to base units + else + local unit = U.new() + local base = Quantity._base + + for i=1,#base do + unit = unit * base[i].unit^self.dimension[i] + end + + p.unit = unit + end + + return p +end + + +-- convert quantity to a number +function Quantity:__tonumber() + if type(self.value) == "number" then + return self.value + else + return self.value:__tonumber() + end +end + + +-- convert quantity to a string +function Quantity:__tostring() + return tostring(self.value)..tostring(self.unit) +end + + +-- convert quantity to an siunitx expression +function Quantity:tosiunitx(param,mode) + + mode = mode or self.siunitx_SI + param = param or "" + + if param ~= "" then + param = "["..param.."]" + end + + if mode == Quantity.siunitx_SI then + return "\\SI"..param.."{"..tostring(self.value).."}".."{"..self.unit:tosiunitx().."}" + + elseif mode == Quantity.siunitx_num then + return "\\num"..param.."{"..tostring(self.value).."}" + + elseif mode == Quantity.siunitx_si then + return "\\si"..param.."{"..self.unit:tosiunitx().."}" + + else + error("Error: Unknown mode '"..tostring(mode).."'.") + end + +end + + +-- minimum value +function Quantity.min(q,...) + + for _,p in ipairs({...}) do + if p < q then + q = p + end + end + + return Quantity.new(q) +end + + +-- maximum value +function Quantity.max(q,...) + + for _,p in ipairs({...}) do + if p > q then + q = p + end + end + + return Quantity.new(q) +end + + +-- absolute value +function Quantity.abs(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if q.value < 0 then + return -q + else + return q + end +end + + +-- square root +function Quantity.sqrt(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + return q^0.5 +end + + +-- logarithm +function Quantity.log(q, base) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the logarithm function is not unitless.") + end + + + local b = nil + if base ~= nil then + if getmetatable(base) ~= Quantity then + base = Quantity.new(base) + end + + b = base:to():__tonumber() + end + + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.log(q:to().value, b) + else + p.value = q:to().value:log(b) + end + + return p +end + + +-- exponential function +function Quantity.exp(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the exponential function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.exp(q:to().value) + else + p.value = q:to().value:exp() + end + + return p +end + + +-- TRIGONOMETRIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Trigonometric_functions + +-- sine +function Quantity.sin(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the sine function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.sin(q:to().value) + else + p.value = q:to().value:sin() + end + + return p +end + + +-- cosine +function Quantity.cos(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the cosine function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.cos(q:to().value) + else + p.value = q:to().value:cos() + end + + return p +end + + +-- tangent +function Quantity.tan(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the tangent function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.tan(q:to().value) + else + p.value = q:to().value:tan() + end + + return p +end + + +-- arcus sine +function Quantity.asin(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the arcus sine function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.asin(q:to().value) + else + p.value = q:to().value:asin() + end + + return p +end + + +-- arcus cosine +function Quantity.acos(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the arcus cosine function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.acos(q:to().value) + else + p.value = q:to().value:acos() + end + + return p +end + + +-- arcus tangent +function Quantity.atan(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the arcus tangent function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.atan(q:to().value) + else + p.value = q:to().value:atan() + end + + return p +end + + +-- HYPERBOLIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Hyperbolic_function + +-- hyperbolic sine +function Quantity.sinh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the sine hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = 0.5 * math.exp(q.value) - 0.5 / math.exp(q.value) + else + p.value = q:to().value:sinh() + end + + return p +end + + +-- hyperbolic cosine +function Quantity.cosh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the cosine hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = 0.5 * math.exp(q.value) + 0.5 / math.exp(q.value) + else + p.value = q:to().value:cosh() + end + + return p +end + + +-- hyperbolic tangent +function Quantity.tanh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the tangent hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = (math.exp(q.value) - math.exp(-q.value)) / (math.exp(q.value) + math.exp(-q.value)) + else + p.value = q:to().value:tanh() + end + + return p +end + + +-- INVERS HYPERBOLIC FUNCTIONS +-- https://en.wikipedia.org/wiki/Inverse_hyperbolic_function + +-- inverse hyperbolic sine +-- (-inf < q < +inf) +function Quantity.asinh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the inverse sine hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.log(q.value + math.sqrt(q.value^2 + 1)) + else + p.value = q:to().value:asinh() + end + + return p +end + + +-- inverse hyperbolic cosine +-- (1 < q) +function Quantity.acosh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the inverse cosine hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = math.log(q.value + math.sqrt(q.value^2 - 1)) + else + p.value = q:to().value:acosh() + end + + return p +end + + +-- inverse hyperbolic tangent +-- (-1 < q < 1) +function Quantity.atanh(q) + + if getmetatable(q) ~= Quantity then + q = Quantity.new(q) + end + + if not q.dimension:iszero() then + error("Error. The argument '"..tostring(q).."' of the inverse tangent hyperbolicus function is not unitless.") + end + + local p = Quantity.new() + + if type(q.value) == "number" then + p.value = 0.5 * math.log((1 + q.value)/(1 - q.value)) + else + p.value = q:to().value:atanh() + end + + return p +end + + +return Quantity
\ No newline at end of file diff --git a/Master/texmf-dist/scripts/lua-physical/physical-unit.lua b/Master/texmf-dist/scripts/lua-physical/physical-unit.lua new file mode 100644 index 00000000000..65c016449b0 --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical-unit.lua @@ -0,0 +1,245 @@ +--[[ +This file contains the unit class. It task is keeping +track of the unit terms. + +Copyright (c) 2020 Thomas Jenni + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. +]]-- + +local prefix = ... and (...):match '(.-%.?)[^%.]+$' or '' + +-- Unit class +local Unit = {} +Unit.__index = Unit + +-- make Unit callable +setmetatable(Unit, { + __call = function(class, ...) + return Unit.new(...) + end +}) + +-- constructor +function Unit.new(...) + local arg = {...} + + local u = {} + setmetatable(u, Unit) + + -- Unit.new() + if #arg == 0 then + u._term = {{},{}} + u.prefixsymbol = nil + u.prefixname = nil + + -- copy constructor + elseif #arg == 1 then + local o = arg[1] + + -- check if given object is a unit + if getmetatable(o) ~= Unit then + error("Error: Cannot create a copy of the object, because it's not a unit.") + end + + u.prefixsymbol = o.prefixsymbol + u.prefixname = o.prefixname + u._term = o._term + + -- Unit.new(symbol, name) + elseif #arg == 2 then + u.symbol = arg[1] + u.name = arg[2] + u._term = {{{u,1}},{}} + + -- Unit.new(symbol, name, prefixsymbol, prefixname) + elseif #arg == 4 then + u.symbol = arg[1] + u.name = arg[2] + u.prefixsymbol = arg[3] + u.prefixname = arg[4] + u._term = {{{u,1}},{}} + + else + error("Wrong number of arguments. Cannot create the unit.") + + end + + return u +end + +function Unit.__mul(o1,o2) + local u = Unit.new() + + u:_append(o1) + u:_append(o2) + + return u +end + +function Unit.__div(o1,o2) + local u = Unit.new() + + u:_append(o1) + u:_append(o2, true) + + return u +end + +function Unit.__pow(o,n) + local u = Unit.new() + + -- invert the term + if n < 0 then + u:_append(o,true) + n = -n + else + u:_append(o) + end + + -- multiply term by factor n + for i=1,2 do + local part = u._term[i] + for j=1,#part do + part[j][2] = part[j][2] * n + end + end + + return u +end + +--copy units from an other quantity +function Unit:_append(u, inversed) + + local s = {1,2} + if inversed then + s = {2,1} + end + + for i=1,2 do + local part = u._term[s[i]] + local term = self._term[i] + + for j=1,#part do + local unit = part[j][1] + local exponent = part[j][2] + + term[#term + 1] = {unit, exponent} + end + end +end + +-- convert quantity to a string +function Unit:__tostring() + + -- assemble unit strings + local u = {{},{}} + + for i=1,2 do + local units = self._term[i] + + for j=1,#units do + local unit = units[j] + local exponent = unit[2] + + if exponent ~= 0 then + local symbol = unit[1].symbol + + local s = "_" + + if unit[1].prefixsymbol ~= nil then + s = s..unit[1].prefixsymbol + end + + if symbol ~= nil then + s = s..symbol + end + + if exponent ~= 1 then + s = s.."^"..exponent + end + + table.insert(u[i], s) + end + end + end + + local str = "" + + -- write enumerator + if #u[1] > 0 then + str = str.." * "..table.concat(u[1], " * ") + end + + -- write division sign + if #u[2] > 0 then + str = str.." / " + end + + -- write denominator + if #u[2] > 1 then + str = str.."("..table.concat(u[2], " * ")..")" + else + str = str..table.concat(u[2], " * ") + end + + return str +end + +-- convert the unit to a unit string which can be read from the latex package siunitx. +function Unit:tosiunitx() + + local s = "" + + for i=1,2 do + local units = self._term[i] + + for j=1,#units do + local unit = units[j] + local e = unit[2] + + if e ~= 0 then + + if i == 2 then + s = s.."\\per" + end + + if unit[1].prefixname ~= nil then + s = s.."\\"..unit[1].prefixname + end + + s = s.."\\"..unit[1].name + + if e ~= 1 then + s = s.."\\tothe{"..e.."}" + end + end + end + end + + return s +end + + +return Unit + + + + + diff --git a/Master/texmf-dist/scripts/lua-physical/physical.lua b/Master/texmf-dist/scripts/lua-physical/physical.lua new file mode 100755 index 00000000000..3bbbc00efe4 --- /dev/null +++ b/Master/texmf-dist/scripts/lua-physical/physical.lua @@ -0,0 +1 @@ +return require((...) .. '.physical-init')
\ No newline at end of file |