Set of real numbers: Difference between revisions

=={{header|Lua}}==

{{trans|}}

<lang lua>function createSet(low,high,rt)

local l,h = tonumber(low), tonumber(high)

if l and h then

local t = {low=l, high=h}

if type(rt) == "string" then

if rt == "open" then

t.contains = function(d) return low< d and d< high end

elseif rt == "closed" then

t.contains = function(d) return low<=d and d<=high end

elseif rt == "left" then

t.contains = function(d) return low< d and d<=high end

elseif rt == "right" then

t.contains = function(d) return low<=d and d< high end

else

error("Unknown range type: "..rt)

end

elseif type(rt) == "function" then

t.contains = rt

else

error("Unable to find a range type or predicate")

end

t.union = function(o)

local l2 = math.min(l, o.low)

local h2 = math.min(h, o.high)

local p = function(d) return t.contains(d) or o.contains(d) end

return createSet(l2, h2, p)

end

t.intersect = function(o)

local l2 = math.min(l, o.low)

local h2 = math.min(h, o.high)

local p = function(d) return t.contains(d) and o.contains(d) end

return createSet(l2, h2, p)

end

t.subtract = function(o)

local l2 = math.min(l, o.low)

local h2 = math.min(h, o.high)

local p = function(d) return t.contains(d) and not o.contains(d) end

return createSet(l2, h2, p)

end

t.length = function()

if h <= l then return 0.0 end

local p = l

local count = 0

local interval = 0.00001

repeat

if t.contains(p) then count = count + 1 end

p = p + interval

until p>=high

return count * interval

end

t.empty = function()

if l == h then

return not t.contains(low)

end

return t.length() == 0.0

end

return t

else

error("Either '"..low.."' or '"..high.."' is not a number")

end

end

local a = createSet(0.0, 1.0, "left")

local b = createSet(0.0, 2.0, "right")

local c = createSet(1.0, 2.0, "left")

local d = createSet(0.0, 3.0, "right")

local e = createSet(0.0, 1.0, "open")

local f = createSet(0.0, 1.0, "closed")

local g = createSet(0.0, 0.0, "closed")

for i=0,2 do

print("(0, 1] union [0, 2) contains "..i.." is "..tostring(a.union(b).contains(i)))

print("[0, 2) intersect (1, 2] contains "..i.." is "..tostring(b.intersect(c).contains(i)))

print("[0, 3) - (0, 1) contains "..i.." is "..tostring(d.subtract(e).contains(i)))

print("[0, 3) - [0, 1] contains "..i.." is "..tostring(d.subtract(f).contains(i)))

print()

end

print("[0, 0] is empty is "..tostring(g.empty()))

print()

local aa = createSet(

0.0, 10.0,

function(x) return (0.0<x and x<10.0) and math.abs(math.sin(math.pi * x * x)) > 0.5 end

)

local bb = createSet(

0.0, 10.0,

function(x) return (0.0<x and x<10.0) and math.abs(math.sin(math.pi * x)) > 0.5 end

)

local cc = aa.subtract(bb)

print("Approx length of A - B is "..cc.length())</lang>

{{out}}

<pre>(0, 1] union [0, 2) contains 0 is true

[0, 2) intersect (1, 2] contains 0 is false

[0, 3) - (0, 1) contains 0 is true

[0, 3) - [0, 1] contains 0 is false

(0, 1] union [0, 2) contains 1 is true

[0, 2) intersect (1, 2] contains 1 is false

[0, 3) - (0, 1) contains 1 is true

[0, 3) - [0, 1] contains 1 is false

(0, 1] union [0, 2) contains 2 is false

[0, 2) intersect (1, 2] contains 2 is false

[0, 3) - (0, 1) contains 2 is true

[0, 3) - [0, 1] contains 2 is true

[0, 0] is empty is false

Approx length of A - B is 2.07587</pre>