WolframLang: Equality Test

Tip on equality test

• Use SameQ when you can. It always return True or False.
• Use Equal when you have numbers with decimal point.

SameQ[expr1, expr2]

(short syntax: ===)

return True if two expressions are symbolically identical, else False.

examples:

• {a,b,c} === {a,b,c} return True because they are the same expression term-by-term.
• 3 === 3.0 return False because one is exact number while the other is approx.
• 3 === xyz return False because xyz is a symbol. (unless it has a value of 3)

SameQ

x = 3;
y = 3.0;
x === y
(* False *)

Equal[expr1, expr2]

(short syntax: ==)

• return True if two expressions are semantically equal. (e.g. 3 vs 3.0)
• return False if two expressions are not semantically equal.
• return whole expression as is, if semantic equality cannot be determined easily or WolframLang quirk.

Equal

3 == 3
(* True *)

3 == 3.0
(* True *)

{3} == {3.0}
(* True *)

WARNING. Equal does not return True or False even for obvious cases.

{} == 2
(* return expression as is *)

(* using Reduce makes it true *)
Reduce[ {} == 2 ] === True

(* WARNING *)
{{1}} == {2}
(* return expression as is *)

{{1.0}} == {2.0}
(* return expression as is *)

x == 3
(* return as is *)

ReplaceAll[ x == 3 , x -> 3 ]
(* True *)

Inequality

UnsameQ

(short syntax: =!=)
Same as Not[SameQ[x, y]] . UnsameQ

Unequal

(short syntax: !=)
Same as Not[Equal[x, y]]. Unequal