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-- The luafractions module
-- Authors: Chetan Shirore and Ajit Kumar
-- version 1.2, Date=21-Aug-2023
-- Licensed under LaTeX Project Public License v1.3c or later. The complete license text is available at http://www.latex-project.org/lppl.txt.
M = {} -- the module
frac_mt = {} -- the metatable
function M.new (n, d, mode)
mode = mode or 'fracs'
if mode == 'nofracs' then
return (n/d)
end
if mode == 'fracs' then
if n~=math.floor(n) or d~=math.floor(d) then
error('Only integers are expected.')
end
if d == 0 then
error('Invalid fraction')
end
local fr = {}
local g = M.lgcd(n,d)
fr = {n=n/g, d=d/g}
return setmetatable(fr,frac_mt)
end
end
lfrac = M.new
function M.lgcd (a, b)
local r
while (b ~= 0) do
r = a % b
a = b
b = r
end
return a
end
function M.simp (num)
local cf = gcd(num[1], num[2])
return M.new(num[1] / cf, num2[2] / cf)
end
function M.toFnumber(c)
return c.n / c.d
end
function M.toFrac(x)
if type(x) == "number" then
if x==math.floor(x) then
return M.new(math.floor(x),1)
else
return x
end
end
return x
end
function addFracs (c1, c2)
return M.new(c1.n * c2.d + c1.d * c2.n, c1.d*c2.d)
end
function subFracs (c1, c2)
return M.new(c1.n * c2.d - c1.d * c2.n, c1.d*c2.d)
end
function mulFracs (c1, c2)
return M.new(c1.n * c2.n, c1.d*c2.d)
end
function divFracs (c1, c2)
return M.new(c1.n * c2.d, c1.d*c2.n)
end
function minusFracs (c1)
return M.new(-c1.n,c1.d)
end
function powerFracs (c1,m)
return M.new((c1.n)^m,(c1.d)^m)
end
function M.add(a, b)
if type(a) == "number" then
if a==math.floor(a) then
return addFracs(M.new(a,1),b)
else
return a + M.toFnumber(b)
end
end
if type(b) == "number" then
if b==math.floor(b) then
return addFracs(a,M.new(b,1))
else
return M.toFnumber(a) + b
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( a ) == frac_mt and getmetatable( b ) == complex_meta then
return setmetatable( { a+b[1], b[2] }, complex_meta )
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( b ) == frac_mt and getmetatable( a ) == complex_meta then
return setmetatable( { b+a[1], a[2] }, complex_meta )
end
end
return addFracs(a, b)
end
function M.sub(a, b)
if type(a) == "number" then
if a==math.floor(a) then
return subFracs(M.new(a,1),b)
else
return a - M.toFnumber(b)
end
end
if type(b) == "number" then
if b==math.floor(b) then
return subFracs(a,M.new(b,1))
else
return M.toFnumber(a) - b
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( a ) == frac_mt and getmetatable( b ) == complex_meta then
return setmetatable( { a-b[1], -b[2] }, complex_meta )
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( b ) == frac_mt and getmetatable( a ) == complex_meta then
return setmetatable( { a[1]-b, a[2] }, complex_meta )
end
end
return subFracs(a, b)
end
function M.mul(a, b)
if type(a) == "number" then
if a==math.floor(a) then
return mulFracs(M.new(a,1),b)
else
return a * M.toFnumber(b)
end
end
if type(b) == "number" then
if b==math.floor(b) then
return mulFracs(a,M.new(b,1))
else
return M.toFnumber(a) * b
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( a ) == frac_mt and getmetatable( b ) == complex_meta then
return setmetatable( { a*b[1], a*b[2] }, complex_meta )
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( b ) == frac_mt and getmetatable( a ) == complex_meta then
return setmetatable( { b*a[1], b*a[2] }, complex_meta )
end
end
return mulFracs(a, b)
end
function M.div(a, b)
if type(a) == "number" then
if a==math.floor(a) then
return divFracs(M.new(a,1),b)
else
return a / M.toFnumber(b)
end
end
if type(b) == "number" then
if b==math.floor(b) then
return divFracs(a,M.new(b,1))
else
return M.toFnumber(a) / b
end
end
if type( a ) == "table" and type(b) =="table" then
if getmetatable( a ) == frac_mt and getmetatable( b ) == complex_meta then
b= setmetatable( { M.toFrac(b[1]), M.toFrac(b[2]) }, complex_meta )
return a*(1/b)
end
end
return divFracs(a, b)
end
function M.tostring (c)
if c.n == 0 then
return string.format("%g",0)
end
if c.d == 1 then
return string.format("%g",c.n)
end
if c.d == -1 then
return string.format("%g",-c.n)
end
return string.format("\\frac{%g}{%g}", c.n, c.d)
end
--Setting Metatable operations.
frac_mt.__add = M.add
frac_mt.__sub = M.sub
frac_mt.__mul = M.mul
frac_mt.__div = M.div
frac_mt.__unm = minusFracs
frac_mt.__pow = powerFracs
frac_mt.__tostring = M.tostring
return M
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