> Here's the same sort of thing in Mathematica.
>
> In[3]:= 12 == 2
>
> Out[3]= False
>
> In[4]:= 1 == 1
>
> Out[4]= True
>
> In[5]:= AcrSin[x] == 2 ArcTan[x/(1+Sqrt[1+x^2])]
>
>                                     x
> Out[5]= AcrSin[x] == 2 ArcTan[----------------]
>                                            2
>                              1 + Sqrt[1 + x ]
>
>
> In[7]:= x^3 == x x^2
>
> Out[7]= True
>
> As you can see, when Mathematica does not know if the expression is
> true or false, it returns the expression, not "True" or "False".

Here's the same thing in Sage:

sage: 12 == 2
False
sage: 1 == 1
True
sage: arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2)))
arcsin(x) == 2*arctan(x/(sqrt(-x^2 + 1) + 1))
sage: x^3 == x*x^2
x^3 == x^3

As you see, Sage does the exact same thing; although, it doesn't even
try to determine if x^3 is equal x^3.  But, the user is _explicitly_
asking to return either a True or False value -- that's what "bool"
does in Python.

--Mike

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