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: 0.011000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.real) == true)	GOOD	time: 0.118000ms stack: size: 0
assert(set.integer:isSubsetOf(set.real) == true)	GOOD	time: 0.008000ms 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: 0.005000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.004000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.040000ms stack: size: 0
assert(set.integer:isSubsetOf(set.integer) == true)	GOOD	time: 0.006000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.005000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.005000ms 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: 0.008000ms 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: 0.010000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.039000ms stack: size: 0
assert(set.real:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.006000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.004000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.004000ms stack: size: 0
assert(set.integer:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.005000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.016000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.oddInteger) == true)	GOOD	time: 0.006000ms stack: size: 0
realinterval
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(1, 2, true, true)) == false)	GOOD	time: 0.027000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-1, 2, true, true)) == nil)	GOOD	time: 0.008000ms 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: 0.007000ms 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: 0.015000ms 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: 0.020000ms 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: 0.025000ms 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: 0.059000ms 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: 0.010000ms stack: size: 0
assert(set.positiveReal:contains(inf) == true)	GOOD	time: 0.006000ms stack: size: 0
assert(set.negativeReal:contains(inf) == false)	GOOD	time: 0.013000ms stack: size: 0
assert(set.nonNegativeReal:contains(inf) == true)	GOOD	time: 0.064000ms stack: size: 0
assert(set.nonPositiveReal:contains(inf) == false)	GOOD	time: 0.005000ms stack: size: 0
assert(set.positiveReal:contains(-inf) == nil)	GOOD	time: 0.240000ms stack: size: 0
assert(set.negativeReal:contains(-inf) == true)	GOOD	time: 0.071000ms stack: size: 0
assert(set.nonNegativeReal:contains(-inf) == nil)	GOOD	time: 0.068000ms stack: size: 0
assert(set.nonPositiveReal:contains(-inf) == true)	GOOD	time: 0.191000ms stack: size: 0
containing ranges of expressions
assert(set.real:contains(x))	GOOD	time: 0.008000ms 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: 0.137000ms stack: size: 0
assert(set.real:contains(sin(x)))	GOOD	time: 0.069000ms stack: size: 0
assert(set.RealSubset(-1,1,true,true):contains(sin(x)))	GOOD	time: 0.030000ms stack: size: 0
assert(not set.positiveReal:contains(abs(x)))	GOOD	time: 0.125000ms stack: size: 0
assert(set.nonNegativeReal:contains(abs(x)))	GOOD	time: 0.111000ms stack: size: 0
assert(set.complex:contains(x))	GOOD	time: 0.046000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(asin(x))) end)()	GOOD	time: 0.184000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.175000ms stack: size: 0
print(acos(x):getRealRange())	nil GOOD	time: 0.018000ms 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: 0.018000ms 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: 0.011000ms stack: size: 0
(function() local x = set.RealSubset(1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.045000ms stack: size: 0
(function() local x = set.real:var'x' assert(abs(x)() == abs(x)) end)()	GOOD	time: 0.326000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
(function() local x = set.nonNegativeReal:var'x' assert(abs(x)() == x) end)()	GOOD	time: 0.465000ms 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: 0.628000ms 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: 0.123000ms stack: size: 0
assert(set.nonNegativeReal:contains(x^2))	GOOD	time: 0.061000ms stack: size: 0
assert((Constant(2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.024000ms stack: size: 0
assert((Constant(-2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.020000ms stack: size: 0
assert(set.nonNegativeReal:contains(exp(x)))	GOOD	time: 0.091000ms stack: size: 0
1/x should be disjoint
print((1/x):getRealRange())	{[-inf, -0), (0, inf]} GOOD	time: 0.067000ms stack: size: 0
assert((1/x):getRealRange():contains(0) == false)	GOOD	time: 0.077000ms stack: size: 0
assert((1/x):getRealRange():contains(1))	GOOD	time: 0.111000ms stack: size: 0
assert((1/x):getRealRange():contains(set.positiveReal))	GOOD	time: 0.195000ms 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()