TODO do unit tests with the RealInterval / RealSubset operators
subsets
TODO don't use ":contains()" except for element testing, as in sets-of-sets
instead here use isSubsetOf
assert(set.real:isSubsetOf(set.real) == true)	GOOD	time: 0.044000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.real) == true)	GOOD	time: 0.012000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.real) == true)	GOOD	time: 0.095000ms stack: size: 0
assert(set.integer:isSubsetOf(set.real) == true)	GOOD	time: 0.011000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.real) == true)	GOOD	time: 0.007000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.real) == true)	GOOD	time: 0.006000ms stack: size: 0
assert(set.real:isSubsetOf(set.integer) == nil)	GOOD	time: 0.006000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.006000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.036000ms stack: size: 0
assert(set.integer:isSubsetOf(set.integer) == true)	GOOD	time: 0.008000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.006000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.008000ms stack: size: 0
assert(set.real:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.integer:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.evenInteger) == true)	GOOD	time: 0.005000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.035000ms stack: size: 0
assert(set.real:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.009000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.integer:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.007000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.oddInteger) == true)	GOOD	time: 0.005000ms stack: size: 0
realinterval
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(1, 2, true, true)) == false)	GOOD	time: 0.014000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-1, 2, true, true)) == nil)	GOOD	time: 0.035000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-2, 2, true, true)) == true)	GOOD	time: 0.010000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-2, 2, false, true)) == nil)	GOOD	time: 0.013000ms stack: size: 0
local A = set.RealInterval(0, 1, false, true) printbr(A, 'isSubsetOf', A) assert(A:isSubsetOf(A))	(0, 1] isSubsetOf (0, 1] GOOD	time: 0.022000ms stack: size: 0
realsubset
local A = set.RealSubset(0, 1, false, true) printbr(A, 'isSubsetOf', A) assert(A:isSubsetOf(A))	(0, 1] isSubsetOf (0, 1] GOOD	time: 0.019000ms stack: size: 0
local A = set.RealSubset(0, 1, false, true) local B = set.RealSubset{{-1, 0, true, false}, {0, 1, false, true}} printbr(A, 'isSubsetOf', B) assert(A:isSubsetOf(B))	(0, 1] isSubsetOf {[-1, 0), (0, 1]} GOOD	time: 0.228000ms stack: size: 0
assert(set.RealSubset(0, math.huge, false, true):isSubsetOf(set.RealSubset{{-math.huge, 0, true, false}, {0, math.huge, false, true}}))	GOOD	time: 0.024000ms stack: size: 0
containing constants
TODO technically that makes set.real the extended reals. should I distinguish between real and extended real? assert(set.real:contains(inf) == true)	GOOD	time: 0.065000ms stack: size: 0
assert(set.positiveReal:contains(inf) == true)	GOOD	time: 0.017000ms stack: size: 0
assert(set.negativeReal:contains(inf) == false)	GOOD	time: 0.008000ms stack: size: 0
assert(set.nonNegativeReal:contains(inf) == true)	GOOD	time: 0.006000ms stack: size: 0
assert(set.nonPositiveReal:contains(inf) == false)	GOOD	time: 0.007000ms stack: size: 0
assert(set.positiveReal:contains(-inf) == nil)	GOOD	time: 0.075000ms stack: size: 0
assert(set.negativeReal:contains(-inf) == true)	GOOD	time: 0.089000ms stack: size: 0
assert(set.nonNegativeReal:contains(-inf) == nil)	GOOD	time: 0.107000ms stack: size: 0
assert(set.nonPositiveReal:contains(-inf) == true)	GOOD	time: 0.111000ms stack: size: 0
containing ranges of expressions
assert(set.real:contains(x))	GOOD	time: 0.014000ms stack: size: 0
x is in (-inf, inf).
is x in (0, inf)?
maybe.
not certainly yes (subset).
not certainly no (complement intersection / set subtraction is empty).
so return nil
if x's set is a subset of this set then return true
if x's set is an intersection of this set then return nil
if x's set does not intersect this set then return false
assert(set.positiveReal:contains(x) == nil)	GOOD	time: 0.024000ms stack: size: 0
assert(set.real:contains(sin(x)))	GOOD	time: 0.078000ms stack: size: 0
assert(set.RealSubset(-1,1,true,true):contains(sin(x)))	GOOD	time: 0.205000ms stack: size: 0
assert(not set.positiveReal:contains(abs(x)))	GOOD	time: 0.219000ms stack: size: 0
assert(set.nonNegativeReal:contains(abs(x)))	GOOD	time: 0.023000ms stack: size: 0
assert(set.complex:contains(x))	GOOD	time: 0.062000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(asin(x))) end)()	GOOD	time: 0.061000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.197000ms stack: size: 0
print(acos(x):getRealRange())	nil GOOD	time: 0.013000ms stack: size: 0
TODO eventually return uncertain / touches but not contains (function() local x = set.RealSubset(1,math.huge,true,true):var'x' assert(not set.real:contains(acos(x))) end)()	GOOD	time: 0.021000ms stack: size: 0
TODO return definitely false (function() local x = set.RealSubset(1,math.huge,false,true):var'x' assert(not set.real:contains(acos(x))) end)()	GOOD	time: 0.016000ms stack: size: 0
(function() local x = set.RealSubset(1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.115000ms stack: size: 0
(function() local x = set.real:var'x' assert(abs(x)() == abs(x)) end)()	GOOD	time: 0.365000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
(function() local x = set.nonNegativeReal:var'x' assert(abs(x)() == x) end)()	GOOD	time: 0.162000ms stack: size: 8 Init abs:Prune:apply Prune Expand Prune Factor Prune Tidy
(function() local x = set.nonNegativeReal:var'x' assert(abs(sinh(x))() == sinh(x)) end)()	GOOD	time: 0.606000ms stack: size: 8 Init abs:Prune:apply Prune Expand Prune Factor Prune Tidy
x^2 should be positive
assert((x^2):getRealRange() == set.nonNegativeReal)	GOOD	time: 0.112000ms stack: size: 0
assert(set.nonNegativeReal:contains(x^2))	GOOD	time: 0.191000ms stack: size: 0
assert((Constant(2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.047000ms stack: size: 0
assert((Constant(-2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.150000ms stack: size: 0
assert(set.nonNegativeReal:contains(exp(x)))	GOOD	time: 0.265000ms stack: size: 0
1/x should be disjoint
print((1/x):getRealRange())	{[-inf, -0), (0, inf]} GOOD	time: 0.142000ms stack: size: 0
assert((1/x):getRealRange():contains(0) == false)	GOOD	time: 0.155000ms stack: size: 0
assert((1/x):getRealRange():contains(1))	GOOD	time: 0.074000ms stack: size: 0
assert((1/x):getRealRange():contains(set.positiveReal))	GOOD	time: 0.060000ms stack: size: 0
../../sin.lua:function sin:getRealRange()
../../sin.lua: local Is = self[1]:getRealRange()
../../asinh.lua:asinh.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_inc
../../atan.lua:atan.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_inc
../../cosh.lua:cosh.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_evenIncreasing
../../acos.lua:function acos:getRealRange()
../../acos.lua: local Is = self[1]:getRealRange()
../../tanh.lua:tanh.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_inc
../../asin.lua:asin.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_pmOneInc
../../sqrt.lua:sqrt.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_posInc_negIm
../../log.lua:log.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_posInc_negIm
../../acosh.lua:function acosh:getRealRange()
../../acosh.lua: local Is = x[1]:getRealRange()
../../atanh.lua:atanh.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_pmOneInc
../../tan.lua:function tan:getRealRange()
../../tan.lua: local Is = self[1]:getRealRange()
../../cos.lua:function cos:getRealRange()
../../cos.lua: local Is = self[1]:getRealRange()
../../cos.lua: -- here I'm going to add pi/2 and then just copy the sin:getRealRange() code
../../sinh.lua:sinh.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_inc
../../abs.lua:abs.getRealRange = require 'symmath.set.RealSubset'.getRealDomain_evenIncreasing
../../Constant.lua:function Constant:getRealRange()
../../Expression.lua:function Expression:getRealRange()
../../Variable.lua:function Variable:getRealRange()
../../op/mul.lua:function mul:getRealRange()
../../op/mul.lua: local I = self[1]:getRealRange()
../../op/mul.lua: local I2 = self[i]:getRealRange()
../../op/div.lua:function div:getRealRange()
../../op/div.lua: local I = self[1]:getRealRange()
../../op/div.lua: local I2 = self[2]:getRealRange()
../../op/sub.lua:function sub:getRealRange()
../../op/sub.lua: local I = self[1]:getRealRange()
../../op/sub.lua: local I2 = self[i]:getRealRange()
../../op/add.lua:function add:getRealRange()
../../op/add.lua: local I = self[1]:getRealRange()
../../op/add.lua: local I2 = self[i]:getRealRange()
../../op/pow.lua:function pow:getRealRange()
../../op/pow.lua: local I = self[1]:getRealRange()
../../op/pow.lua: local I2 = self[2]:getRealRange()
../../op/unm.lua:function unm:getRealRange()
../../op/unm.lua: local I = self[1]:getRealRange()
../../set/RealSubset.lua:-- commonly used versions of the Expression:getRealRange function
../../set/RealSubset.lua:function RealSubset.getRealDomain_evenIncreasing(x)
../../set/RealSubset.lua: local Is = x[1]:getRealRange()
../../set/RealSubset.lua:function RealSubset.getRealDomain_posInc_negIm(x)
../../set/RealSubset.lua: local Is = x[1]:getRealRange()
../../set/RealSubset.lua:function RealSubset.getRealDomain_pmOneInc(x)
../../set/RealSubset.lua: local Is = x[1]:getRealRange()
../../set/RealSubset.lua:function RealSubset.getRealDomain_inc(x)
../../set/RealSubset.lua: local Is = x[1]:getRealRange()
../../set/RealInterval.lua: local I = x:getRealRange()