跳转到内容

模組:Complex Number

添加链接
本页使用了标题或全文手工转换
被永久保护的模块
维基百科，自由的百科全书

这是本页的一个历史版本，由A2569875​（留言 | 贡献）在2018年11月4日 (日) 16:42 （Special:Diff/51900590）编辑。这可能和当前版本存在着巨大的差异。

(差异) ←上一修订 | 最后版本 (差异) | 下一修订→ (差异)

local p = { PrimeTable = {} }
local numlib = require("Module:Number")
local numdata = require("Module:Number/data")

p.cmath = {
	abs=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		if imag == 0 then return math.abs(real) end
		return math.sqrt(real * real, imag * imag)
	end,
	is_prime=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		if imag == 0 and real == 0 then return false end
		if not numdata._is_integer(imag) or not numdata._is_integer(real) then return false end
		if imag == 0 then 
			if numdata._is_integer((real - 3.0) / 4.0) then
				if p.PrimeTable.table_max == nil then p.PrimeTable = require('Module:Factorization') end
				p.PrimeTable.primeIndexOf({real+2})
				return p.PrimeTable.lists[real] ~= nil
			end
		end
		local value = imag*imag + real*real
		if p.PrimeTable.table_max == nil then p.PrimeTable = require('Module:Factorization') end
		p.PrimeTable.primeIndexOf({value+2})
		return p.PrimeTable.lists[value] ~= nil
	end,
	sqrt=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		local argument = 0
		local length = math.sqrt( real * real + imag * imag )
		if imag ~= 0 then
			argument = 2.0 * math.atan(imag / (length + real))
		else
			if real > 0 then argument = 0.0 
			else argument = math.pi end
		end
		local sq_len = math.sqrt(length)
		return p.cmath.getComplexNumber(sq_len * math.cos(argument/2.0), sq_len * math.sin(argument/2.0)):clean()
	end,
	cos=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		return p.cmath.getComplexNumber(math.cos(real) * math.cosh(imag), -math.sin(real) * math.sinh(imag)) 
	end,
	sin=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		return p.cmath.getComplexNumber(math.sin(real) * math.cosh(imag), math.cos(real) * math.sinh(imag)) 
	end,
	cis=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		local hyp = 1
		if imag ~= 0 then hyp = math.cosh(imag) - math.sinh(imag) end
		return p.cmath.getComplexNumber(math.cos(real) * hyp, math.sin(real) * hyp)
	end,
	exp=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		local cis_r, cis_i, exp_r = 1, 0, math.exp(real)
		if imag ~= 0 then cis_r, cis_i = math.cos(imag), math.sin(imag) end
		return p.cmath.getComplexNumber(exp_r * cis_r, exp_r * cis_i)
	end,
	log=function(z)
		local real, imag = tonumber(z) or z.real, (tonumber(z) and 0) or z.imag
		local argument = 0
		local length = math.sqrt( real * real + imag * imag )
		if imag ~= 0 then
			argument = 2.0 * math.atan(imag / (length + real))
		else
			if real > 0 then argument = 0.0 
			else argument = math.pi end
		end
		return p.cmath.getComplexNumber(math.log(length), argument)
	end,
	pow=function(op1,op2)
		--a ^ z
		local a = p.cmath.getComplexNumber( tonumber(op1) or op1.real, (tonumber(op1) and 0) or op1.imag )
		local z = p.cmath.getComplexNumber( tonumber(op2) or op2.real, (tonumber(op2) and 0) or op2.imag )
		return p.cmath.exp(z * p.cmath.log(a)):clean()
	end,
	ComplexNumberMeta = {
		__add = function (op1, op2) 
			local real1, real2 = tonumber(op1) or op1.real, tonumber(op2) or op2.real
			local imag1, imag2 = (tonumber(op1) and 0) or op1.imag, (tonumber(op2) and 0) or op2.imag
			return p.cmath.getComplexNumber(real1 + real2, imag1 + imag2) 
		end,
		__sub = function (op1, op2) 
			local real1, real2 = tonumber(op1) or op1.real, tonumber(op2) or op2.real
			local imag1, imag2 = (tonumber(op1) and 0) or op1.imag, (tonumber(op2) and 0) or op2.imag
			return p.cmath.getComplexNumber(real1 - real2, imag1 - imag2) 
		end,
		__mul = function (op1, op2) 
			local a, c = tonumber(op1) or op1.real, tonumber(op2) or op2.real
			local b, d = (tonumber(op1) and 0) or op1.imag, (tonumber(op2) and 0) or op2.imag
			return p.cmath.getComplexNumber(a * c - b * d, b * c + a * d) 
		end,
		__div = function (op1, op2) 
			local a, c = tonumber(op1) or op1.real, tonumber(op2) or op2.real
			local b, d = (tonumber(op1) and 0) or op1.imag, (tonumber(op2) and 0) or op2.imag
			local op1_d, op2_d = a*a + b*b, c*c + d*d
			if op2_d <= 0 then return op1_d / op2_d end
			return p.cmath.getComplexNumber((a * c + b * d) / op2_d, (b * c - a * d) / op2_d) 
		end,
		__tostring = function (this) 
			local body = ''
			if this.real ~= 0 then body = tostring(this.real) end
			if this.imag ~= 0 then 
				if body ~= '' and this.imag > 0 then body = body .. '+' end
				if this.imag == -1 then  body = body .. '-' end
				if math.abs(this.imag) ~= 1 then body = body .. tostring(this.imag) end
				body = body .. 'i'
			end
			if body == '' then body = '0' end
			return body
		end,
		__unm = function (this)
			return p.cmath.getComplexNumber(-this.real, -this.imag) 
		end,
		__eq = function (op1, op2)
			local diff_real = math.abs( (tonumber(op1) or op1.real) - (tonumber(op2) or op2.real) )
			local diff_imag1 = math.abs( ( (tonumber(op1) and 0) or op1.imag) - ( (tonumber(op2) and 0) or op2.imag) )
			return diff_real < 1e-12 and diff_imag1 < 1e-12
		end,
	},
	getComplexNumber = function(real,imag)
		ComplexNumber = {}
		setmetatable(ComplexNumber,p.cmath.ComplexNumberMeta) 
		function ComplexNumber:update()
			self.argument = 0
			self.length = math.sqrt( self.real * self.real + self.imag * self.imag )
			if self.imag ~= 0 then
				self.argument = 2.0 * math.atan(self.imag / (self.length + self.real))
			else
				if self.real > 0 then self.argument = 0.0 
				else self.argument = math.pi end
			end
		end
		function ComplexNumber:clean()
			if math.abs(self.real) <= 1e-12 then self.real = 0 end
			if math.abs(self.imag) <= 1e-12 then self.imag = 0 end
			if math.abs(self.real - math.floor(self.real)) <= 1e-12 then self.real = math.floor(self.real) end
			if math.abs(self.imag - math.floor(self.imag)) <= 1e-12 then self.imag = math.floor(self.imag) end
			return self
		end
		ComplexNumber.real, ComplexNumber.imag = real, imag
		return ComplexNumber
	end,
	toComplexNumber = function(num_str)
		local real, imag = p.cmath.toComplexNumberPart(num_str)
		if real == nil or imag == nil then return nil end
		return p.cmath.getComplexNumber(real, imag)
	end,
	toComplexNumberPart = function(num_str)
		local body = ''
		local real, imag = 0, 0
		local split_str = mw.text.split(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(
				num_str or '',
			'%s+',''),'%++([%d%.])',',+%1'),'%++([ij])',',+1%1'),'%-+([%d%.])',',-%1'),'%-+([ij])',',-1%1'),'%*+([%d%.])',',*%1'),'%*+([ij])',',*1%1'),'%/+([%d%.])',',/%1'),'%/+([ij])',',/1%1'),',')
		local first = true
		local continue = false
		
		for k,v in pairs(split_str) do
			continue = false
			local val = mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.ustring.gsub(mw.text.trim(v),'[ij]+','i'),'^(%.)','0%1'),'^([%d%.])','+%1'),'([%+%-])([%d%.])','%1\48%2'),'^([ij])','+1%1')
			if mw.ustring.find(val,"%/") or mw.ustring.find(val,"%*") then return end
			if val == nil or val == '' then if first == true then first = false continue = true else return end end
			if not continue then
				local num_text = mw.ustring.match(val,"[%+%-][%d%.]+i?")
				if num_text ~= val then return end
				local num_part = tonumber(mw.ustring.match(num_text,"[%+%-][%d%.]+"))
				if num_part == nil then return end
				if mw.ustring.find(num_text,"i") then
					imag = imag + num_part
				else
					real = real + num_part
				end
			end
		end
		return real, imag
	end,
	init = function()
		p.cmath.pi = p.cmath.getComplexNumber(math.pi, 0) 
		p.cmath.zero = p.cmath.getComplexNumber(0, 0) 
		p.cmath.one = p.cmath.getComplexNumber(1, 0) 
		p.cmath[-1] = p.cmath.getComplexNumber(-1, 0) 
		p.cmath.i = p.cmath.getComplexNumber(0, 1) 
		p.cmath[0],p.cmath[1] = p.cmath.zero,p.cmath.one
		return p.cmath
	end
}

return p
检索自“https://zh.wikipedia.org/w/index.php?title=Module:Complex_Number&oldid=51900619”