On 6 December 2010 19:33, Mike Hansen <[email protected]> wrote:
>> 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
Oh, I missed that - it is similar, but not identical to Mathematica's
TrueQ[]. Again, I personally prefer the MMA behavior.
In[9]:= ?TrueQ
TrueQ[expr] yields True if expr is True, and yields False otherwise.
In[10]:= True[ AcrSin[x] == 2 ArcTan[x/(1+Sqrt[1+x^2])]]
x
Out[10]= True[AcrSin[x] == 2 ArcTan[----------------]]
2
1 + Sqrt[1 + x ]
Sage's documentation is reasonably clear, though gives no hint it
could claim something to be false when in fact it's true.
Dave
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