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: 0.054000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.real) == true)	GOOD	time: 0.501000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.real) == true)	GOOD	time: 0.070000ms stack: size: 0
assert(set.integer:isSubsetOf(set.real) == true)	GOOD	time: 0.047000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.real) == true)	GOOD	time: 0.051000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.real) == true)	GOOD	time: 0.209000ms stack: size: 0
assert(set.real:isSubsetOf(set.integer) == nil)	GOOD	time: 0.235000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.029000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.integer) == nil)	GOOD	time: 0.032000ms stack: size: 0
assert(set.integer:isSubsetOf(set.integer) == true)	GOOD	time: 0.023000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.037000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.integer) == true)	GOOD	time: 0.023000ms stack: size: 0
assert(set.real:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.034000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.023000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.029000ms stack: size: 0
assert(set.integer:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.024000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.evenInteger) == true)	GOOD	time: 0.029000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.evenInteger) == nil)	GOOD	time: 0.027000ms stack: size: 0
assert(set.real:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.033000ms stack: size: 0
assert(set.positiveReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.022000ms stack: size: 0
assert(set.negativeReal:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.095000ms stack: size: 0
assert(set.integer:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.033000ms stack: size: 0
assert(set.evenInteger:isSubsetOf(set.oddInteger) == nil)	GOOD	time: 0.037000ms stack: size: 0
assert(set.oddInteger:isSubsetOf(set.oddInteger) == true)	GOOD	time: 0.027000ms stack: size: 0
realinterval
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(1, 2, true, true)) == false)	GOOD	time: 0.042000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-1, 2, true, true)) == nil)	GOOD	time: 0.254000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-2, 2, true, true)) == true)	GOOD	time: 0.037000ms stack: size: 0
assert(set.RealInterval(-2, -1, true, true):isSubsetOf(set.RealInterval(-2, 2, false, true)) == nil)	GOOD	time: 0.034000ms 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: 0.080000ms 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: 0.088000ms 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: 0.098000ms 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: 0.377000ms 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: 0.039000ms stack: size: 0
assert(set.positiveReal:contains(inf) == true)	GOOD	time: 0.199000ms stack: size: 0
assert(set.negativeReal:contains(inf) == false)	GOOD	time: 0.097000ms stack: size: 0
assert(set.nonNegativeReal:contains(inf) == true)	GOOD	time: 0.030000ms stack: size: 0
assert(set.nonPositiveReal:contains(inf) == false)	GOOD	time: 0.026000ms stack: size: 0
assert(set.positiveReal:contains(-inf) == nil)	GOOD	time: 0.312000ms stack: size: 0
assert(set.negativeReal:contains(-inf) == true)	GOOD	time: 0.566000ms stack: size: 0
assert(set.nonNegativeReal:contains(-inf) == nil)	GOOD	time: 0.072000ms stack: size: 0
assert(set.nonPositiveReal:contains(-inf) == true)	GOOD	time: 0.061000ms stack: size: 0
containing ranges of expressions
assert(set.real:contains(x))	GOOD	time: 0.035000ms 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: 0.039000ms stack: size: 0
assert(set.real:contains(sin(x)))	GOOD	time: 0.921000ms stack: size: 0
assert(set.RealSubset(-1,1,true,true):contains(sin(x)))	GOOD	time: 0.259000ms stack: size: 0
assert(not set.positiveReal:contains(abs(x)))	GOOD	time: 0.873000ms stack: size: 0
assert(set.nonNegativeReal:contains(abs(x)))	GOOD	time: 0.075000ms stack: size: 0
assert(set.complex:contains(x))	GOOD	time: 0.034000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(asin(x))) end)()	GOOD	time: 0.079000ms stack: size: 0
(function() local x = set.RealSubset(-1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.130000ms stack: size: 0
print(acos(x):getRealRange())	nil GOOD	time: 0.032000ms 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: 0.056000ms 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: 0.048000ms stack: size: 0
(function() local x = set.RealSubset(1,1,true,true):var'x' assert(set.real:contains(acos(x))) end)()	GOOD	time: 0.270000ms stack: size: 0
(function() local x = set.real:var'x' assert(abs(x)() == abs(x)) end)()	GOOD	time: 1.791000ms stack: size: 7 Init Prune Expand Prune Factor Prune Tidy
(function() local x = set.nonNegativeReal:var'x' assert(abs(x)() == x) end)()	GOOD	time: 0.841000ms 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: 1.553000ms 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: 0.082000ms stack: size: 0
assert(set.nonNegativeReal:contains(x^2))	GOOD	time: 0.069000ms stack: size: 0
assert((Constant(2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.169000ms stack: size: 0
assert((Constant(-2)^2):getRealRange() == set.RealSubset(4,4,true,true))	GOOD	time: 0.255000ms stack: size: 0
assert(set.nonNegativeReal:contains(exp(x)))	GOOD	time: 0.103000ms stack: size: 0
1/x should be disjoint
print((1/x):getRealRange())	{[-inf, -0), (0, inf]} GOOD	time: 0.099000ms stack: size: 0
assert((1/x):getRealRange():contains(0) == false)	GOOD	time: 0.074000ms stack: size: 0
assert((1/x):getRealRange():contains(1))	GOOD	time: 0.062000ms stack: size: 0
assert((1/x):getRealRange():contains(set.positiveReal))	GOOD	time: 0.072000ms 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()