newcomparison_test.sj

 ClearAll(a,b,c,d,x)

T 1 == 1
T !(1 != 1)
T !(1 > 1)
T !(1 < 1)
T 1 >= 1
T 1 <= 1
T 1 == 1.0
T 1 < 2
T 2 > 1
T !( 1 > 2)
T !( 2 < 1)
T !( 2 == 1)
T  2 != 1
T  2 >= 1
T  1 <= 2
T  !( 1 >= 2 )
T  !( 2 <= 1 )
T  1 < 2 < 3
T  3 > 2 > 1
T  !( 3 < 2 < 1)
T  1 < 2 < 3 < 4
T  1 < 2.0 < 3 < 4.0

T  (1 < 2 < b) == (2 < b)

T ((1 < 2 < b < c == c < 4 < 10)) == ((2 < b) && (b < c) && (c < 4))

# FIXME: do we want this ?
# T ( (a < c/d) != True )

ClearAll(b,c)
#  1 < x < 1  --> 1 < x && x < 1).   FIXME. this should return false.

# This, at least, works.
T  Apply(List, 1 < 2 < b < c == c < 4 < 10) == [2 < b,b < c,c < 4]

# Agrees with Mma
T  (1 < x >  1) == ( 1 < x && (x > 1) )

## FIXME: for older method
# T Apply(List, b>2) == [b,>,2]
# T Apply(List, 2>b) == [2,>,b]
# T Apply(List, a < b) == List(a, < , b)
# T Apply(List, a <= b) == List(a, <= , b)
# T Apply(List, a >= b) == List(a, >= , b)
# T Apply(List, a < 1) == List(a, < , 1)
# T Apply(List, a == 1) == List(a, == , 1)
# T Apply(List, f(a) < 1) == List(f(a), < , 1)
# T Apply(List, f(a) < 1.0) == List(f(a), < , 1.0)

T (a == a ) == True
T (a != a) == False

## FIXME: reinstate this ?
# T (a <= a) == True
# T (a >= a) == True

T (a < 1) == (a < 1)

## FIXME: reimplement this. we used maybe_N
# T Sqrt(2) > 0
# T -Sqrt(2) < 0
# T  3 < Pi < 4
# T  2 < E < 3
# T  0 < EulerGamma < 1

#### Infinity

## FIXME: reimpement this.
# T  1 != Infinity
# T  Not(1 == Infinity)
# T  1.0 != Infinity
# T  Not(1.0 == Infinity)

#### Not

T Not(a != a) == True
T Not(a == a) == False

## Mma evaluates this to true with FullSimplify but not Simplify
## FullSimplify(b >= b)
T Head(b >= b) == GreaterEqual
T Head(b <= b) == LessEqual
T Head(b < b) == Less
T Head(b > b) == Greater
T b == b
T Not(b != b)

## Mma does evaluates these immediately
T Not(a < b) == (a >= b)
T Not(a >= b) == (a < b)
T Not(a > b) == (a <= b)
T Not(a <= b) == (a > b)
T Not(a == b) == (a != b)
T Not(a != b) == (a == b)
## This is not distributed automatically
T Head(Not( (a == b) && ( c == d))) == Not

T Head(Not(3)) == Not

#### Or

T Or() == False
T Or(1) == 1
T Or(True) == True
T Or(True,False) == True
T Or(False,False) == False
T Or(True,True) == True
T Or(False,True) == True
T Or(True,False,False) == True

# Test flatten with Or
T Args(a || b || c || d ) == [a,b,c,d]

#### And

T And() == True
T And(1) == 1
T And(True) == True
T And(False,True) == False
T And(True,False) == False
T And(True,True) == True
T And(False,False) == False
T And(True,True,True) == True

# Test flatten with And
T Args(a && b && c && d ) == [a,b,c,d]

 ClearAll(a,b,c,d,f,x)

#### Refine

# This belongs elsewhere

ClearAll(aaa)

Assume(aaa,Positive)
T Refine(Abs(aaa)) == aaa

ClearAll(aaa,a)

### String

T Head(f(x) == "cat") == Equal

### SameQ

T SameQ(a,a)
T Not(SameQ(a,b))
T Not(SameQ(3,3.0))
T SameQ(3,3)
T SameQ("cat", "cat")

### Equal

T Equal() == True
T Equal(3,3)
T Equal(3,3.0)
T Head(Equal(x,y)) == Equal
T Equal(x,x)
#T Equal(2,bf"2")  # probably want to get rid of bf and bi
T Equal(2,big"2")
#T Equal(2.0,bf"2")
T Equal(2.0,big"2")

T Not(Unequal(3,3))
T Not(Unequal(3,3.0))
T Not(Unequal(y,y))
T Head(Unequal(x,y)) == Unequal

T (Undefined == 3) === Undefined
T (3 == Undefined) === Undefined
T (Undefined == a) === Undefined
T (a == Undefined) === Undefined
T (a + b == Undefined) === Undefined
T ( Undefined == a + b) === Undefined
T (Undefined != 3) === Undefined
T (3 != Undefined) === Undefined
T (Undefined != a) === Undefined
T (a != Undefined) === Undefined
T (a + b != Undefined) === Undefined

ClearAll(f,x)
Apply(ClearAll,UserSyms())