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--- @class BinaryOperation
--- Represents a binary operation with two inputs and one output.
--- Represents a generic function that takes zero or more expressions as inputs.
--- @field name string
--- @field operation function
--- @field expressions table<number, Expression>
BinaryOperation = {}
__BinaryOperation = {}
----------------------------
-- Instance functionality --
----------------------------
--- Creates a new binary operation with the given operation.
--- @param operation function
--- @param expressions table<number, Expression>
--- @return BinaryOperation
function BinaryOperation:new(operation, expressions)
local o = {}
local __o = Copy(__ExpressionOperations)
if type(operation) ~= "function" then
error("Sent parameter of wrong type: operation must be a function")
end
if type(expressions) ~= "table" then
error("Sent parameter of wrong type: expressions must be an array")
end
o.name = BinaryOperation.DEFAULT_NAMES[operation]
o.operation = operation
o.expressions = Copy(expressions)
if BinaryOperation.COMMUTATIVITY[operation] then
function o:iscommutative()
return true
end
else
function o:iscommutative()
return false
end
end
if not o:iscommutative() and o.operation ~= BinaryOperation.SUB and #o.expressions ~= 2 then
error("Sent parameter of wrong type: noncommutative operations cannot have an arbitrary number of paramaters")
end
__o.__index = BinaryOperation
__o.__tostring = function(a)
local expressionnames = ''
for index, expression in ipairs(a.expressions) do
if index == 1 and not a.expressions[index + 1] then
expressionnames = expressionnames .. a.name .. ' '
end
if index > 1 then
expressionnames = expressionnames .. ' '
end
if expression:isatomic() and not (a.operation == BinaryOperation.POW and expression:type() == Rational) then
expressionnames = expressionnames .. tostring(expression)
else
expressionnames = expressionnames .. '(' .. tostring(expression) .. ')'
end
if a.expressions[index + 1] then
expressionnames = expressionnames .. ' ' .. a.name
end
end
return expressionnames
end
__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 runs this anyway
if not a.operation or not b.operation then
return false
end
local loc = 1
while a.expressions[loc] or b.expressions[loc] do
if not a.expressions[loc] or not b.expressions[loc] or
(a.expressions[loc] ~= b.expressions[loc]) then
return false
end
loc = loc + 1
end
return a.operation == b.operation
end
o = setmetatable(o, __o)
return o
end
--- @return Expression
function BinaryOperation:evaluate()
local results = {}
local reducible = true
for index, expression in ipairs(self:subexpressions()) do
results[index] = expression:evaluate()
if not results[index]:isconstant() then
reducible = false
end
end
if not reducible then
return BinaryOperation(self.operation, results)
end
if not self.expressions[1] then
error("Execution error: cannot perform binary operation on zero expressions")
end
local result = results[1]
for index, expression in ipairs(results) do
if not (index == 1) then
result = self.operation(result, expression)
end
end
return result
end
--- @return Expression
function BinaryOperation:autosimplify()
local results = {}
for index, expression in ipairs(self:subexpressions()) do
results[index] = expression:autosimplify()
end
local simplified = BinaryOperation(self.operation, results)
if simplified.operation == BinaryOperation.POW then
return simplified:simplifypower()
end
if simplified.operation == BinaryOperation.MUL then
return simplified:simplifyproduct()
end
if simplified.operation == BinaryOperation.ADD then
return simplified:simplifysum()
end
if simplified.operation == BinaryOperation.DIV then
return simplified:simplifyquotient()
end
if simplified.operation == BinaryOperation.SUB then
return simplified:simplifydifference()
end
return simplified
end
--- @return table<number, Expression>
function BinaryOperation:subexpressions()
return self.expressions
end
--- @param subexpressions table<number, Expression>
--- @return BinaryOperation
function BinaryOperation:setsubexpressions(subexpressions)
return BinaryOperation(self.operation, subexpressions)
end
--- @return Expression
function BinaryOperation:expand()
local results = {}
for index, expression in ipairs(self:subexpressions()) do
results[index] = expression:expand()
end
local expanded = BinaryOperation(self.operation, results)
if expanded.operation == BinaryOperation.MUL then
local allsums = BinaryOperation(BinaryOperation.ADD, {Integer.one()})
for _, expression in ipairs(expanded.expressions) do
allsums = allsums:expand2(expression)
end
return allsums:autosimplify()
end
if expanded.operation == BinaryOperation.POW and expanded.expressions[2]:type() == Integer then
if expanded.expressions[1]:type() ~= BinaryOperation then
return expanded:autosimplify()
end
local exp = BinaryOperation.MULEXP({Integer.one()})
local pow = expanded.expressions[2]:asnumber()
for _ = 1, math.abs(pow) do
exp = exp:expand2(expanded.expressions[1])
if _ > 1 then
exp = exp:autosimplify()
end
end
if pow < 0 then
exp = exp^Integer(-1)
end
return exp
end
if expanded.operation == BinaryOperation.POW and expanded.expressions[2].operation == BinaryOperation.ADD then
local exp = {}
for i = 1, #expanded.expressions[2].expressions do
exp[#exp+1] = (expanded.expressions[1]^expanded.expressions[2].expressions[i]):autosimplify()
end
return BinaryOperation.MULEXP(exp)
end
return expanded:autosimplify()
end
--- Helper for expand - multiplies two addition expressions.
--- @return Expression
function BinaryOperation:expand2(other)
local result = {}
for _, expression in ipairs(self:subexpressions()) do
if other:type() == BinaryOperation and other.operation == BinaryOperation.ADD then
for _, expression2 in ipairs(other.expressions) do
result[#result+1] = expression * expression2
end
else
result[#result+1] = expression * other
end
end
return BinaryOperation(BinaryOperation.ADD, result)
end
--- @return Expression
function BinaryOperation:factor()
local results = {}
-- Recursively factors sub-expressions
for index, expression in ipairs(self:subexpressions()) do
results[index] = expression:factor()
end
-- Attempts to factor expressions as monovariate polynomials
local factoredsubs = BinaryOperation(self.operation, results)
local subs = factoredsubs:getsubexpressionsrec()
for index, sub in ipairs(subs) do
local substituted = factoredsubs:substitute({[sub]=SymbolExpression("_")}):autosimplify()
local polynomial, result = substituted:topolynomial()
if result then
local factored = polynomial:factor():autosimplify()
if factored ~= substituted then
return factored:substitute({[SymbolExpression("_")]=sub})
end
end
end
-- Pulls common sub-expressions out of sum expressions
if self.operation == BinaryOperation.ADD then
local gcf
for _, expression in ipairs(factoredsubs:subexpressions()) do
if expression.operation ~= BinaryOperation.MUL then
expression = BinaryOperation.MULEXP({expression})
end
if not gcf then
gcf = expression
else
local newgcf = Integer.one()
for _, gcfterm in ipairs(gcf:subexpressions()) do
local gcfpower = Integer.one()
if gcfterm:type() == BinaryOperation and gcfterm.operation == BinaryOperation.POW and gcfterm.expressions[2]:type() == Integer then
gcfpower = gcfterm.expressions[2]
gcfterm = gcfterm.expressions[1]
end
for _, term in ipairs(expression:subexpressions()) do
local power = Integer.one()
if term:type() == BinaryOperation and term.operation == BinaryOperation.POW and term.expressions[2]:type() == Integer then
power = term.expressions[2]
term = term.expressions[1]
end
if term == gcfterm then
newgcf = newgcf * term^Integer.min(power, gcfpower)
end
end
end
gcf = newgcf
end
end
if gcf:type() ~= Integer then
local out = Integer.zero()
for _, expression in ipairs(factoredsubs:subexpressions()) do
out = out + expression/gcf
end
out = gcf*(out:autosimplify():factor())
return out:autosimplify()
end
end
return factoredsubs
end
--- @return Expression
function BinaryOperation:combine()
local den, num, aux, mul, input = {}, {}, {}, {}, self:autosimplify():expand()
if input.operation ~= BinaryOperation.ADD then
return input
end
for _, expr in ipairs(input.expressions) do
local numpart, denpart = Integer.one(), Integer.one()
if expr.operation == BinaryOperation.POW and expr.expressions[2]:type() == Integer and expr.expressions[2] < Integer.zero() then
denpart = denpart*expr.expressions[1] ^ expr.expressions[2]:neg()
for index,term in ipairs(den) do
if expr.expressions[1] == den[index] then
if expr.expressions[2]:neg() > mul[index] then
mul[index] = expr.expressions[2]:neg()
goto continue
else
goto continue
end
end
end
table.insert(den,expr.expressions[1])
table.insert(mul,expr.expressions[2]:neg())
::continue::
end
if expr.operation == BinaryOperation.MUL then
for _,subexpr in ipairs(expr.expressions) do
if subexpr.operation == BinaryOperation.POW and subexpr.expressions[2]:type() == Integer and subexpr.expressions[2] < Integer.zero() then
denpart = denpart*subexpr.expressions[1] ^ subexpr.expressions[2]:neg()
for index,term in ipairs(den) do
if subexpr.expressions[1] == den[index] then
if subexpr.expressions[2]:neg() > mul[index] then
mul[index] = subexpr.expressions[2]:neg()
goto continue
else
goto continue
end
end
end
table.insert(den,subexpr.expressions[1])
table.insert(mul,subexpr.expressions[2]:neg())
::continue::
else
numpart = numpart*subexpr
end
end
end
if expr.operation ~= BinaryOperation.POW and expr.operation ~= BinaryOperation.MUL then
numpart = expr
end
table.insert(num,numpart)
table.insert(aux,denpart)
end
local denominator = Integer.one()
local numerator = Integer.zero()
for index,expr in ipairs(den) do
denominator = denominator*den[index] ^ mul[index]
end
denominator = denominator:autosimplify()
for index,expr in ipairs(num) do
local uncommon = denominator/aux[index]
uncommon = uncommon:factor():simplify()
numerator = numerator + expr*uncommon
end
numerator = numerator:simplify():factor()
if denominator == Integer.one() then
return numerator
else
return numerator/denominator
end
end
--- @param collect Expression
--- @return Expression
function BinaryOperation:collect(collect)
-- Constant expressions cannot be collected
if collect:isconstant() then
return self
end
-- Recusively collect subexpressions
local results = {}
for index, expression in ipairs(self:subexpressions()) do
results[index] = expression:collect(collect)
end
local collected = BinaryOperation(self.operation, results)
if not (collected.operation == BinaryOperation.ADD) then
return collected:autosimplify()
end
local coefficients = {}
-- TODO: Add an expression map class
setmetatable(coefficients, {__index =
function(table, key)
local out = rawget(table, tostring(key))
return out or Integer.zero()
end,
__newindex =
function (table, key, value)
rawset(table, tostring(key), value)
end
})
-- Finds all instances of a constant power of the expression to be collected, and maps each power to all terms it is multiplied by
for _, expression in ipairs(collected:subexpressions()) do
if expression == collect then
coefficients[Integer.one()] = coefficients[Integer.one()] + Integer.one()
elseif expression.operation == BinaryOperation.POW and expression:subexpressions()[1] == collect and expression:subexpressions()[2]:isconstant() then
coefficients[expression:subexpressions()[2]] = coefficients[expression:subexpressions()[2]] + Integer.one()
elseif collect:type() == BinaryOperation and collect.operation == BinaryOperation.POW and
expression.operation == BinaryOperation.POW and expression:subexpressions()[1] == collect:subexpressions()[1] then
-- Handle the fact that autosimplify turns (a^x^n -> a^(xn)), this is needed if the term to collect is itself an exponential
local power = (expression:subexpressions()[2] / collect:subexpressions()[2]):autosimplify()
if power:isconstant() then
coefficients[power] = coefficients[power] + Integer.one()
else
coefficients[Integer.zero()] = coefficients[Integer.zero()] + expression
end
elseif expression.operation == BinaryOperation.MUL then
local varpart
local coeffpart = Integer.one()
for _, term in ipairs(expression:subexpressions()) do
if term == collect then
varpart = Integer.one()
elseif (term.operation == BinaryOperation.POW and term:subexpressions()[1] == collect and term:subexpressions()[2]:isconstant()) then
varpart = term:subexpressions()[2]
elseif collect:type() == BinaryOperation and collect.operation == BinaryOperation.POW and
term.operation == BinaryOperation.POW and term:subexpressions()[1] == collect:subexpressions()[1] then
local power = (term:subexpressions()[2] / collect:subexpressions()[2]):autosimplify()
if power:isconstant() then
varpart = power
end
else
coeffpart = coeffpart * term
end
end
if varpart then
coefficients[varpart] = coefficients[varpart] + coeffpart
else
coefficients[Integer.zero()] = coefficients[Integer.zero()] + expression
end
else
coefficients[Integer.zero()] = coefficients[Integer.zero()] + expression
end
end
local out = Integer.zero()
for index, value in pairs(coefficients) do
out = out + collect ^ Rational.fromstring(index) * value
end
return out:autosimplify()
end
--- @param other Expression
--- @return boolean
function BinaryOperation:order(other)
if other:isconstant() then
return false
end
if other:isatomic() then
if self.operation == BinaryOperation.POW then
return self:order(BinaryOperation(BinaryOperation.POW, {other, Integer.one()}))
end
if self.operation == BinaryOperation.MUL then
return self:order(BinaryOperation(BinaryOperation.MUL, {other}))
end
if self.operation == BinaryOperation.ADD then
return self:order(BinaryOperation(BinaryOperation.ADD, {other}))
end
end
if self.operation == BinaryOperation.POW and other.operation == BinaryOperation.POW then
if self.expressions[1] ~= other.expressions[1] then
return self.expressions[1]:order(other.expressions[1])
end
return self.expressions[2]:order(other.expressions[2])
end
if (self.operation == BinaryOperation.MUL and other.operation == BinaryOperation.MUL) or
(self.operation == BinaryOperation.ADD and other.operation == BinaryOperation.ADD) then
local k = 0
while #self.expressions - k > 0 and #other.expressions - k > 0 do
if self.expressions[#self.expressions - k] ~= other.expressions[#other.expressions - k] then
return self.expressions[#self.expressions - k]:order(other.expressions[#other.expressions - k])
end
k = k + 1
end
return #self.expressions < #other.expressions
end
if (self.operation == BinaryOperation.MUL) and (other.operation == BinaryOperation.POW or other.operation == BinaryOperation.ADD) then
return self:order(BinaryOperation(BinaryOperation.MUL, {other}))
end
if (self.operation == BinaryOperation.POW) and (other.operation == BinaryOperation.MUL) then
return BinaryOperation(BinaryOperation.MUL, {self}):order(other)
end
if (self.operation == BinaryOperation.POW) and (other.operation == BinaryOperation.ADD) then
return self:order(BinaryOperation(BinaryOperation.POW, {other, Integer.one()}))
end
if (self.operation == BinaryOperation.ADD) and (other.operation == BinaryOperation.MUL) then
return BinaryOperation(BinaryOperation.MUL, {self}):order(other)
end
if (self.operation == BinaryOperation.ADD) and (other.operation == BinaryOperation.POW) then
return BinaryOperation(BinaryOperation.POW, {self, Integer.one()}):order(other)
end
if other:type() == FunctionExpression or other:type() == TrigExpression or other:type() == Logarithm then
if self.operation == BinaryOperation.ADD or self.operation == BinaryOperation.MUL then
return self:order(BinaryOperation(self.operation, {other}))
end
if self.operation == BinaryOperation.POW then
return self:order(other^Integer.one())
end
end
return true
end
--- Returns whether the binary operation is commutative.
--- @return boolean
function BinaryOperation:iscommutative()
error("Called unimplemented method: iscommutative()")
end
--- @return PolynomialRing, boolean
function BinaryOperation:topolynomial()
local addexp = self
if not self.operation or self.operation ~= BinaryOperation.ADD then
addexp = BinaryOperation(BinaryOperation.ADD, {self})
end
local poly = {}
local degree = 0
local symbol
for _, expression in ipairs(addexp.expressions) do
local coefficient
local sym
local power
-- Expressions of the form c
if expression:isconstant() then
coefficient = expression
power = 0
-- Expressions of the form x
elseif expression:type() == SymbolExpression then
coefficient = Integer.one()
sym = expression.symbol
power = 1
-- Expressions of the form c*x
elseif expression.operation and expression.operation == BinaryOperation.MUL and #expression.expressions == 2
and expression.expressions[1]:isconstant() and expression.expressions[2]:type() == SymbolExpression then
coefficient = expression.expressions[1]
sym = expression.expressions[2].symbol
power = 1
-- Expressions of the form c*x^n (totally not confusing)
elseif expression.operation and expression.operation == BinaryOperation.MUL and #expression.expressions == 2
and expression.expressions[1]:isconstant() and expression.expressions[2].operation and
expression.expressions[2].operation == BinaryOperation.POW and #expression.expressions[2].expressions == 2
and expression.expressions[2].expressions[1]:type() == SymbolExpression and expression.expressions[2].expressions[2].getring
and expression.expressions[2].expressions[2]:getring() == Integer.getring() and expression.expressions[2].expressions[2] > Integer.zero() then
coefficient = expression.expressions[1]
sym = expression.expressions[2].expressions[1].symbol
power = expression.expressions[2].expressions[2]:asnumber()
-- Expressions of the form x^n
elseif expression.operation and expression.operation == BinaryOperation.POW and #expression.expressions == 2
and expression.expressions[1]:type() == SymbolExpression and expression.expressions[2].getring
and expression.expressions[2]:getring() == Integer.getring() and expression.expressions[2] > Integer.zero() then
coefficient = Integer.one()
sym = expression.expressions[1].symbol
power = expression.expressions[2]:asnumber()
else
return self, false
end
if symbol and sym and symbol ~= sym then
return self, false
end
if not symbol then
symbol = sym
end
poly[power + 1] = coefficient
if power > degree then
degree = power
end
end
for i = 1,degree+1 do
poly[i] = poly[i] or Integer.zero()
end
return PolynomialRing(poly, symbol), true
end
function BinaryOperation:tolatex()
if self.operation == BinaryOperation.POW then
if self.expressions[2]:type() == Integer and self.expressions[2] < Integer.zero() then
local base = self.expressions[1]
local exponent = self.expressions[2]
if exponent == Integer(-1) then
return "\\frac{1}{" .. base:tolatex() .. "}"
else
if base:isatomic() then
return "\\frac{1}{" .. base:tolatex() .. "^{" .. exponent:neg():tolatex() .. "}}"
else
return "\\frac{1}{\\left(" .. base:tolatex() .. "\\right)^{" .. exponent:neg():tolatex() .. "}}"
end
end
end
if self.expressions[1]:isatomic() then
if self.expressions[2]:isconstant() and self.expressions[2]:getring() == Rational:getring() and self.expressions[2].numerator == Integer.one() then
if self.expressions[2].denominator == Integer(2) then
return "\\sqrt{" .. self.expressions[1]:tolatex() .. '}'
end
return "\\sqrt[" .. self.expressions[2].denominator:tolatex() .. ']{' .. self.expressions[1]:tolatex() .. '}'
end
return self.expressions[1]:tolatex() .. '^{' .. self.expressions[2]:tolatex() .. '}'
else
if self.expressions[2]:isconstant() and self.expressions[2]:getring() == Rational:getring() and self.expressions[2].numerator == Integer.one() then
if self.expressions[2].denominator == Integer(2) then
return "\\sqrt{" .. self.expressions[1]:tolatex() .. '}'
end
return "\\sqrt[" .. self.expressions[2].denominator:tolatex() .. ']{' .. self.expressions[1]:tolatex() .. '}'
end
return "\\left(" .. self.expressions[1]:tolatex() .. "\\right)" .. '^{' .. self.expressions[2]:tolatex() .. '}'
end
end
if self.operation == BinaryOperation.MUL then
local sign = ''
local out = ''
local denom = ''
if self:autosimplify():isconstant() then
for index, expression in ipairs(self.expressions) do
if index == 1 then
out = out .. expression:tolatex()
else
out = out .. "\\cdot " .. expression:tolatex()
end
end
return out
end
if #self.expressions == 2 and self.expressions[2]:type() == BinaryOperation and self.expressions[2].operation == BinaryOperation.POW and self.expressions[2].expressions[2] == -Integer.one() then
out = '\\frac{' .. self.expressions[1]:tolatex() .. '}{' .. self.expressions[2].expressions[1]:tolatex() .. '}'
return out
end
for _, expression in ipairs(self.expressions) do
if expression:type() == BinaryOperation then
if expression.operation == BinaryOperation.POW and expression.expressions[2]:isconstant() and expression.expressions[2] < Integer.zero() then
local reversed = (Integer.one() / expression):autosimplify()
if reversed.operation == BinaryOperation.ADD or expression.operation == BinaryOperation.SUB then
denom = denom .. '\\left('.. reversed:tolatex() .. '\\right)'
else
denom = denom .. reversed:tolatex()
end
elseif expression.operation == BinaryOperation.ADD or expression.operation == BinaryOperation.SUB then
out = out .. '\\left(' .. expression:tolatex() .. '\\right)'
else
out = out .. expression:tolatex()
end
else
if expression == Integer(-1) then
out = out .. '-'
elseif expression:type() == Rational and expression.numerator == Integer.one() then
denom = denom .. expression.denominator:tolatex()
elseif expression:type() == Rational and expression.numerator == Integer(-1) then
out = out .. '-'
denom = denom .. expression.denominator:tolatex()
elseif expression:type() == Rational then
out = out .. expression.numerator:tolatex()
denom = denom .. expression.denominator:tolatex()
else
out = out .. expression:tolatex()
end
end
end
if string.sub(out,1,1) == '-' then
sign = '-'
out = string.sub(out,2,-1)
end
if denom ~= '' and out == '' then
return sign .. '\\frac{' .. '1' .. '}{' .. denom .. '}'
end
if denom ~= '' then
return sign .. '\\frac{' .. out .. '}{' .. denom .. '}'
end
return sign..out
end
if self.operation == BinaryOperation.ADD then
local out = ''
for index, expression in ipairs(self.expressions) do
out = out .. expression:tolatex()
if self.expressions[index + 1] and string.sub(self.expressions[index + 1]:tolatex(), 1, 1) ~= "-" then
out = out .. '+'
end
end
return out
end
if self.operation == BinaryOperation.DIV then
return '\\frac{' .. self.expressions[1]:tolatex() .. '}{' .. self.expressions[2]:tolatex() .. '}'
end
if self.operation == BinaryOperation.SUB then
local out = ''
if not self.expressions[2] then
if not self.expressions[1]:isatomic() then
out = '-\\left(' .. self.expressions[1]:tolatex() .. '\\right)'
else
out = '-' .. self.expressions[1]:tolatex()
end
else
for index, expression in ipairs(self.expressions) do
if expression.operation and (expression.operation == BinaryOperation.ADD or expression.operation == BinaryOperation.SUB) and index >1 then
out = out .. "\\left(" .. expression:tolatex() .. "\\right)"
else
out = out .. expression:tolatex()
end
if self.expressions[index + 1] then
out = out .. '-'
end
end
end
return out
end
return self
end
-----------------
-- Inheritance --
-----------------
__BinaryOperation.__index = CompoundExpression
__BinaryOperation.__call = BinaryOperation.new
BinaryOperation = setmetatable(BinaryOperation, __BinaryOperation)
----------------------
-- Static constants --
----------------------
BinaryOperation.ADD = function(a, b)
return a + b
end
BinaryOperation.SUB = function(a, b)
return a - b
end
BinaryOperation.MUL = function(a, b)
return a * b
end
BinaryOperation.DIV = function(a, b)
return a / b
end
BinaryOperation.IDIV = function(a, b)
return a // b
end
BinaryOperation.MOD = function(a, b)
return a % b
end
BinaryOperation.POW = function(a, b)
return a ^ b
end
BinaryOperation.DEFAULT_NAMES = {
[BinaryOperation.ADD] = "+",
[BinaryOperation.SUB] = "-",
[BinaryOperation.MUL] = "*",
[BinaryOperation.DIV] = "/",
[BinaryOperation.IDIV] = "//",
[BinaryOperation.MOD] = "%",
[BinaryOperation.POW] = "^"
}
BinaryOperation.COMMUTATIVITY = {
[BinaryOperation.ADD] = true,
[BinaryOperation.SUB] = false,
[BinaryOperation.MUL] = true,
[BinaryOperation.DIV] = false,
[BinaryOperation.IDIV] = false,
[BinaryOperation.MOD] = false,
[BinaryOperation.POW] = false
}
BinaryOperation.ADDEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.ADD, expressions, name)
end
BinaryOperation.SUBEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.SUB, expressions, name)
end
BinaryOperation.MULEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.MUL, expressions, name)
end
BinaryOperation.DIVEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.DIV, expressions, name)
end
BinaryOperation.IDIVEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.IDIV, expressions, name)
end
BinaryOperation.MODEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.MOD, expressions, name)
end
BinaryOperation.POWEXP = function(expressions, name)
return BinaryOperation(BinaryOperation.POW, expressions, name)
end
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