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-- helper functions
function whatis(a)
if a == nil then
return nil
end
if a:type() == SymbolExpression then
return "Sym"
end
if a:type() == BinaryOperation then
return "BinOp"
end
if a:type() == FunctionExpression then
return "FncExp"
end
if a:type() == TrigExpression then
return "TrigExp"
end
if a:type() == Integer then
return "Int"
end
if a:type() == Rational then
return "Ratl"
end
if a:type() == DerivativeExpression then
return "DervExp"
end
if a:type() == DiffExpression then
return "DiffExp"
end
if a:type() == IntegralExpression then
return "Intgrl"
end
if a:type() == SqrtExpression then
return "Sqrt"
end
if a:type() == PolynomialRing then
return "Poly"
end
if a:type() == AbsExpression then
return "ABS"
end
if a:type() == Logarithm then
return "LOG"
end
if a:type() == RootExpression then
return "RootOf"
end
if a:type() == Equation then
return "="
end
return "No Clue"
end
function longwhatis(a)
if a == nil then
return nil
end
if a:type() == SymbolExpression then
return "SymbolExpression"
end
if a:type() == BinaryOperation then
return "BinaryOperation"
end
if a:type() == FunctionExpression then
return "FunctionExpression"
end
if a:type() == TrigExpression then
return "TrigExpression"
end
if a:type() == Integer then
return "Integer"
end
if a:type() == Rational then
return "Rational"
end
if a:type() == DerivativeExpression then
return "DerivativeExpression"
end
if a:type() == DiffExpression then
return "DiffExpression"
end
if a:type() == IntegralExpression then
return "IntegralExpression"
end
if a:type() == SqrtExpression then
return "SqrtExpression"
end
if a:type() == PolynomialRing then
return "PolynomialRing"
end
if a:type() == AbsExpression then
return "AbsExpression"
end
if a:type() == Logarithm then
return "Logarithm"
end
if a:type() == RootExpression then
return "RootExpression"
end
if a:type() == Equation then
return "Equation"
end
return "No Clue"
end
function whatring(a)
if a:getring() == Rational.makering() then
return "Rational"
end
if a:getring() == PolynomialRing.makering() then
return "PolynomialRing"
end
if a:getring() == Integer.makering() then
return "Integer"
end
if a:getring() == IntegerModN.makering() then
return "IntegerModN"
end
return "No Clue"
end
function nameof(sym)
if sym == nil then
return nil
end
if sym:type() == BinaryOperation then
local binops = {BinaryOperation.ADD,
BinaryOperation.MUL,
BinaryOperation.SUB,
BinaryOperation.DIV,
BinaryOperation.POW,
BinaryOperation.IDIV,
BinaryOperation.MOD}
local obslab = {"ADD",
"MUL",
"SUB",
"DIV",
"POW",
"IDIV",
"MOD"}
for i,j in pairs(binops) do
if sym.operation == j then
return obslab[i]
end
end
end
if sym:type() == FunctionExpression or sym:type() == TrigExpression then
return tostring(sym.name)
end
if sym:type() == SymbolExpression or sym:type() == Integer then
return tostring(sym)
end
if sym:type() == Rational then
return tostring(sym.numerator).."/"..tostring(sym.denominator)
end
if sym:type() == DerivativeExpression then
return "DD"
end
if sym:type() == DiffExpression then
return "diff"
end
if sym:type() == IntegralExpression then
return "$\\mathtt{\\int}$"
end
if sym:type() == SqrtExpression then
return "$\\mathtt{\\sqrt{\\phantom{x}}}$"
end
if sym:type() == PolynomialRing then
return "Poly"
end
if sym:type() == AbsExpression then
return "abs"
end
if sym:type() == Logarithm then
return "log"
end
if sym:type() == RootExpression then
return "RootOf"
end
if sym:type() == Equation then
return "$\\mathtt{=}$"
end
return "No Clue"
end
function Expression:getfullsubexpressionsrec()
local result = {}
for _, expression in ipairs(self:subexpressions()) do
result[#result+1] = expression
result = JoinArrays(result, expression:getfullsubexpressionsrec())
end
return result
end
function Expression:gettheshrub()
local string = ""
for index, expression in ipairs(self:subexpressions()) do
string = string.."child {node [label=-90:{expr["..tostring(index).."]}] {$\\mathtt{"..expression:tolatex().."}$}}"
end
return string
end
function Expression:getthetree()
local string = ""
for _, expression in ipairs(self:subexpressions()) do
if expression:isatomic() then
string = string.."child {node{"..nameof(expression).."}}"
else
string = string.."child {node{"..nameof(expression).."}"..expression:getthetree().."}"
end
end
return string
end
function Expression:gettheforest()
local string = ""
for _, expression in ipairs(self:subexpressions()) do
if expression:isatomic() then
string = string.." [ "..nameof(expression).." ] "
else
string = string.." [ "..nameof(expression)..expression:gettheforest().." ] "
end
end
return string
end
function Expression:getthefancyshrub()
local string = ""
if self:type() == DiffExpression then
for _, expression in ipairs(self:subexpressions()) do
string = string.." [ $\\mathtt{"..expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ] "
end
string = string.." [ $\\mathtt{\\{"
for _,symbol in ipairs(self.symbols) do
if next(self.symbols,_) == nil then
string = string .. symbol:tolatex().."\\}}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.symbols};} ] "
else
string = string .. symbol:tolatex() .. ","
end
end
return string
end
if self:type() == IntegralExpression then
string = string .. " [ $\\mathtt{"..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ] "
string = string .. "[ $\\mathtt{"..self.symbol:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.symbol};} ]"
if self:isdefinite() then
string = string .. "[ $\\mathtt{"..self.lower:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.lower};} ] "
string = string .. "[ $\\mathtt{"..self.upper:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.upper};} ] "
return string
end
return string
end
if self:type() == PolynomialRing then
string = string .. " [ $\\mathtt{\\{"
for index=0, self.degree:asnumber() do
string = string .. tostring(self.coefficients[index])
if index < self.degree:asnumber() then
string = string .. ","
end
end
string = string .. "\\} }$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.coefficients}; \\node[anchor=south west, font=\\ttfamily\\footnotesize,gray] at (.north west) {.ring "..whatring(self).."};} ]"
string = string .. " [ $\\mathtt{"..self.symbol.. "}$, tikz+={\\node[anchor=north, font=\\ttfamily\\footnotesize,gray] at (.south) {.symbol};} ]"
return string
end
if self:type() == SqrtExpression then
string = string .. " [ $\\mathtt{"..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ]"
string = string .. "[ $\\mathtt{"..self.root:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.root};} ]"
return string
end
if self:type() == TrigExpression then
string = string .. " [ $\\mathtt{"..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ]"
return string
end
if self:type() == AbsExpression then
string = string .. " [ $\\mathtt{"..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ] "
return string
end
if self:type() == Logarithm then
string = string .. " [$\\mathtt{" ..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ]"
string = string .. " [$\\mathtt{" ..self.base:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.base};} ]"
return string
end
if self:type() == RootExpression then
string = string .. "[$\\mathtt{" ..self.expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression};} ]"
return string
end
if self:type() == FunctionExpression then
local string1 = ''
local string2 = ''
local string3 = ''
for index=1, #self.variables do
string1 = string1 .. tostring(self.expressions[index])
if index < #self.variables then
string1 = string1 .. ","
end
string2 = string2 .. tostring(self.variables[index])
if index < #self.variables then
string2 = string2 .. ","
end
string3 = string3 .. tostring(self.derivatives[index])
if index < #self.variables then
string3 = string3 .. ","
end
end
string = string .. "[$\\mathtt{ \\{" .. string1 .. "\\}}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expressions};} ]"
string = string .. "[$\\mathtt{ \\{" .. string2 .. "\\}}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.variables};} ]"
string = string .. "[$\\mathtt{ \\{" .. string3 .. "\\}}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.derivatives};} ]"
return string
end
if self:type() == Equation then
string = string .. " [$\\mathtt{" ..self.lhs:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.lhs};} ]"
string = string .. " [$\\mathtt{" ..self.rhs:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.rhs};} ]"
return string
end
for index, expression in ipairs(self:subexpressions()) do
string = string.." [ $\\mathtt{"..expression:tolatex().."}$, tikz+={\\node[anchor=north,font=\\ttfamily\\footnotesize,gray] at (.south) {.expression["..index.."]};} ] "
end
return string
end
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