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--- @class DiffExpression
--- An expression for a multi-variable higher-order derivatives of an expression.
--- @field symbols SymbolExpression
--- @field expression Expression
DiffExpression = {}
__DiffExpression = {}
----------------------------
-- Instance functionality --
----------------------------
-- Creates a new derivative operation with the given symbols and expression.
--- @param expression Expression
--- @param symbols table<number, Symbol>
--- @return DiffExpression
function DiffExpression:new(expression,symbols)
local o = {}
local __o = Copy(__ExpressionOperations)
o.symbols = Copy(symbols)
o.degree = #o.symbols
o.expression = Copy(expression)
__o.__tostring = function(a)
local varlist = '(d'
if a.degree == 1 then
varlist = varlist .. '/d' .. tostring(a.symbols[1]) .. " " .. tostring(a.expression) .. ')'
end
if a.degree > 1 then
varlist = varlist .. '^' .. tostring(a.degree) .. '/'
local varnum = 1
for index = 1, #a.symbols do
local var = a.symbols[#a.symbols-index+1]
if a.symbols[#a.symbols-index] == var then
varnum = varnum + 1
goto nextvar
end
if a.symbols[#a.symbols-index] ~=var then
if varnum == 1 then
varlist = varlist .. 'd' .. tostring(var)
else
varlist = varlist .. 'd' .. tostring(var) .. '^' .. tostring(varnum)
end
varnum = 1
end
::nextvar::
end
varlist = varlist .. " " .. tostring(a.expression) .. ')'
end
return varlist
end
__o.__index = DiffExpression
__o.__eq = function(a, b)
-- This shouldn't be needed, since __eq should only fire if both metamethods have the same function, but for some reason Lua always rungs this anyway
if not b:type() == DiffExpression then
return false
end
if a.expression ~= b.expression then
return false
end
local loc = 1
while a.symbols[loc] or b.symbols[loc] do
if not a.symbols[loc] or not b.symbols[loc] or
(a.symbols[loc] ~= b.symbols[loc]) then
return false
end
loc = loc + 1
end
return true
end
o = setmetatable(o, __o)
return o
end
--- @return Expression
function DiffExpression:evaluate()
local exp = self.expression
for _,var in ipairs(self.symbols) do
exp = DerivativeExpression(exp,var):evaluate()
end
return exp
end
--- @return Expression
function DiffExpression:autosimplify()
return DiffExpression(self.expression:autosimplify(), self.symbols):evaluate()
end
--- @return table<number, Expression>
function DiffExpression:subexpressions()
return {self.expression}
end
--- @param subexpressions table<number, Expression>
--- @return DiffExpression
function DiffExpression:setsubexpressions(subexpressions)
return DiffExpression(subexpressions[1], self.symbols)
end
--- @param other Expression
--- @return boolean
function DiffExpression:order(other)
if other:type() == IntegralExpression then
return true
end
if other:type() ~= DiffExpression then
return false
end
if self.degree > other.degree then
return false
end
if self.degree < other.degree then
return true
end
return self.expression:order(other.expression)
end
--- @return string
function DiffExpression:tolatex()
local varlist = '\\frac{'
if self.degree == 1 then
varlist = varlist .. 'd}{d' .. self.symbols[1]:tolatex() .. '}\\left(' .. self.expression:tolatex() .. '\\right)'
end
if self.degree > 1 then
local cvarlist = {}
local count = 1
for index, var in ipairs(self.symbols) do
if var == self.symbols[index+1] then
count = count + 1
else
table.insert(cvarlist,{var,count})
count = 1
end
end
if #cvarlist == 1 then
varlist = varlist .. 'd^{' .. self.degree .. '}}{' .. 'd' .. cvarlist[1][1]:tolatex() .. '^{' .. self.degree .. '}'
end
if #cvarlist > 1 then
varlist = varlist .. '\\partial^{' .. self.degree .. '}}{'
for index, varnum in ipairs(cvarlist) do
var = cvarlist[#cvarlist - index+1][1]
num = cvarlist[#cvarlist - index+1][2]
if num == 1 then
varlist = varlist .. '\\partial ' .. var:tolatex()
else
varlist = varlist .. '\\partial ' .. var:tolatex() .. '^{' .. num .. '}'
end
end
end
varlist = varlist .. '} \\left(' .. self.expression:tolatex() .. '\\right)'
end
return varlist
end
-----------------
-- Inheritance --
-----------------
__DiffExpression.__index = CompoundExpression
__DiffExpression.__call = DiffExpression.new
DiffExpression = setmetatable(DiffExpression, __DiffExpression)
----------------------
-- Static constants --
----------------------
diff = function(expression,...)
local symbols = {}
for i = 1, select("#",...) do
local var = select(i,...)
if #var == 0 then
table.insert(symbols,var)
end
if #var > 0 then
for index=1, RR(var[2]) do
table.insert(symbols,var[1])
end
end
end
return DiffExpression(expression,symbols)
end
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