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-- Seperates the various binary operations into their own files for readability
--- Automatic simplification of multiplication expressions.
--- @return BinaryOperation
function BinaryOperation:simplifyproduct()
if not self.expressions[1] then
error("Execution error: attempted to simplify empty product")
end
if not self.expressions[2] then
return self.expressions[1]
end
-- Uses the property that x*0=0
for _, expression in ipairs(self.expressions) do
if expression:isconstant() and expression == expression:zero() then
return expression:zero()
end
end
local result = self:simplifyproductrec()
-- We don't really know what ring we are working in here, so just assume the integer ring
if not result.expressions[1] then
return Integer.one()
end
if not result.expressions[2] then
return result.expressions[1]
end
return result
end
function BinaryOperation:simplifyproductrec()
local term1 = self.expressions[1]
local term2 = self.expressions[2]
if not self.expressions[3] then
if (term1:isconstant() or not (term1.operation == BinaryOperation.MUL)) and
(term2:isconstant() or not (term2.operation == BinaryOperation.MUL)) then
if term1:isconstant() and term2:isconstant() then
local result = self:evaluate()
if result == result:one() then
return BinaryOperation(BinaryOperation.MUL, {})
end
return BinaryOperation(BinaryOperation.MUL, {result})
end
-- Uses the property that x*1 = x
if term1:isconstant() and term1 == term1:one() then
return BinaryOperation(BinaryOperation.MUL, {term2})
end
if term2:isconstant() and term2 == term2:one() then
return BinaryOperation(BinaryOperation.MUL, {term1})
end
-- Distributes constants if the other term is a sum expression.
if term1:isconstant() and term2.operation == BinaryOperation.ADD then
local distributed = BinaryOperation(BinaryOperation.ADD, {})
for i, exp in ipairs(term2:subexpressions()) do
distributed.expressions[i] = term1 * exp
end
return BinaryOperation(BinaryOperation.MUL, {distributed:autosimplify()})
end
if term2:isconstant() and term1.operation == BinaryOperation.ADD then
local distributed = BinaryOperation(BinaryOperation.ADD, {})
for i, exp in ipairs(term1:subexpressions()) do
distributed.expressions[i] = term2 * exp
end
return BinaryOperation(BinaryOperation.MUL, {distributed:autosimplify()})
end
-- Uses the property that sqrt(a,r)*sqrt(b,r) = sqrt(a*b,r) if a,r are positive integers
if term1:type() == SqrtExpression and term2:type() == SqrtExpression and term1.expression:isconstant() and term2.expression:isconstant() and term1.root:type() == Integer then
if term1.root == term2.root and term1.expression > Integer.zero() then
local expression = term1.expression*term2.expression
local result = SqrtExpression(expression,term1.root):autosimplify()
if result == Integer.one() then
return BinaryOperation(BinaryOperation.MUL,{})
else
return BinaryOperation(BinaryOperation.MUL,{result})
end
end
end
--if term1.operation == BinaryOperation.POW and term2.operation == BinaryOperation.POW and term1.expressions[1]:type() == SqrtExpression and term2.expressions[1]:type() == SqrtExpression and term1.expressions[2]:type() == Integer and term2.expressions[2]:type() == Integer and term1.expressions[2] < Integer.zero() and term2.expressions[2] < Integer.zero() and term1.expressions[1].root == term2.expressions[1].root then
-- local expo1 = term1.expressions[2]:neg()
-- local expo2 = term2.expressions[2]:neg()
-- local root = term1.expressions[1].root
-- local expr1 = term1.expressions[1].expression
-- local expr2 = term2.expressions[1].expression
-- local result1 = BinaryOperation(BinaryOperation.POW,{SqrtExpression(expr1,root),expo1}):simplifypower()
-- local result2 = BinaryOperation(BinaryOperation.POW,{SqrtExpression(expr2,root),expo2}):simplifypower()
-- local result = BinaryOperation(BinaryOperation.MUL,{result1,result2}):autosimplify()
-- if result == Integer.one() then
-- return BinaryOperation(BinaryOperation.MUL,{})
-- end
-- if result:type() == Integer then
-- return BinaryOperation(BinaryOperation.MUL,{Rational(Integer.one(),result)})
-- end
-- return BinaryOperation(BinaryOperation.MUL,{BinaryOperation(BinaryOperation.POW, {result,Integer(-1)})}):autosimplify()
--end
-- Uses the property that x^a*x^b=x^(a+b)
local revertterm1 = false
local revertterm2 = false
if term1.operation ~= BinaryOperation.POW then
term1 = BinaryOperation(BinaryOperation.POW, {term1, Integer.one()})
revertterm1 = true
end
if term2.operation ~= BinaryOperation.POW then
term2 = BinaryOperation(BinaryOperation.POW, {term2, Integer.one()})
revertterm2 = true
end
if term1.expressions[1] == term2.expressions[1]
--and not
-- (term1.expressions[1]:type() == Integer and
-- term1.expressions[2]:type() ~= term2.--expressions[2]:type())
then
local result = BinaryOperation(BinaryOperation.POW,
{term1.expressions[1],
BinaryOperation(BinaryOperation.ADD,
{term1.expressions[2], term2.expressions[2]}):autosimplify()}):autosimplify()
if result:isconstant() and result == result:one() then
return BinaryOperation(BinaryOperation.MUL, {})
end
return BinaryOperation(BinaryOperation.MUL, {result})
end
if revertterm1 then
term1 = term1.expressions[1]
end
if revertterm2 then
term2 = term2.expressions[1]
end
if term2:order(term1) then
return BinaryOperation(BinaryOperation.MUL, {term2, term1})
end
return self
end
if term1.operation == BinaryOperation.MUL and not (term2.operation == BinaryOperation.MUL) then
return term1:mergeproducts(BinaryOperation(BinaryOperation.MUL, {term2}))
end
if not (term1.operation == BinaryOperation.MUL) and term2.operation == BinaryOperation.MUL then
return BinaryOperation(BinaryOperation.MUL, {term1}):mergeproducts(term2)
end
return term1:mergeproducts(term2)
end
local rest = {}
for index, expression in ipairs(self.expressions) do
if index > 1 then
rest[index - 1] = expression
end
end
local result = BinaryOperation(BinaryOperation.MUL, rest):simplifyproductrec()
if term1.operation ~= BinaryOperation.MUL then
term1 = BinaryOperation(BinaryOperation.MUL, {term1})
end
if result.operation ~= BinaryOperation.MUL then
result = BinaryOperation(BinaryOperation.MUL, {result})
end
return term1:mergeproducts(result)
end
-- Merges two lists of products
function BinaryOperation:mergeproducts(other)
if not self.expressions[1] then
return other
end
if not other.expressions[1] then
return self
end
local first = BinaryOperation(BinaryOperation.MUL, {self.expressions[1], other.expressions[1]}):simplifyproductrec()
local selfrest = {}
for index, expression in ipairs(self.expressions) do
if index > 1 then
selfrest[index - 1] = expression
end
end
local otherrest = {}
for index, expression in ipairs(other.expressions) do
if index > 1 then
otherrest[index - 1] = expression
end
end
if first.operation ~= BinaryOperation.MUL or not first.expressions[2] then
local result = BinaryOperation(self.operation, selfrest):mergeproducts(BinaryOperation(other.operation, otherrest))
if not first.expressions[1] then
return result
end
table.insert(result.expressions, 1, first.expressions[1])
if result.operation == BinaryOperation.MUL and not result.expressions[3] and result.expressions[1] and result.expressions[2] then
if result.expressions[1]:isconstant() and result.expressions[2]:isconstant() then
return result:simplifyproductrec()
end
end
return result
end
local result
if first.expressions[1] == self.expressions[1] then
result = BinaryOperation(self.operation, selfrest):mergeproducts(other)
else
result = self:mergeproducts(BinaryOperation(other.operation, otherrest))
end
table.insert(result.expressions, 1, first.expressions[1])
if result.operation == BinaryOperation.MUL and not result.expressions[3] and result.expressions[1] and result.expressions[2] then
if result.expressions[1]:isconstant() and result.expressions[2]:isconstant() then
return result:simplifyproductrec()
end
end
return result
end
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