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From: Torsten Schoenfeld on 7 Jun 2010 08:23
Why does FullSimplify think this equation is true even though x = -3 is
clearly a counterexample?

In[1]:= equation = Sqrt[x^2 - 1] == Sqrt[x + 1] Sqrt[x - 1]
Out[1]= Sqrt[-1 + x^2] == Sqrt[-1 + x] Sqrt[1 + x]

In[2]:= $Assumptions
Out[2]= True

In[3]:= equation // FullSimplify
Out[3]= True

In[4]:= equation /. x -> -3
Out[4]= False

(This is with Mathematica 7.0.1.0.)

From: Andrzej Kozlowski on 8 Jun 2010 07:08
It's a bug involving simplification of holonomic functions in Mathematica 7, which has already appeared a couple of times on this forum. You can avoid it by evaluating:

Unprotect[Holonomic`HolonomicFullSimplify];
Clear[Holonomic`HolonomicFullSimplify];

Andrzej Kozlowski



On 7 Jun 2010, at 21:23, Torsten Schoenfeld wrote:

> Why does FullSimplify think this equation is true even though x == -3 is
> clearly a counterexample?
>
> In[1]:== equation == Sqrt[x^2 - 1] ==== Sqrt[x + 1] Sqrt[x - 1]
> Out[1]== Sqrt[-1 + x^2] ==== Sqrt[-1 + x] Sqrt[1 + x]
>
> In[2]:== $Assumptions
> Out[2]== True
>
> In[3]:== equation // FullSimplify
> Out[3]== True
>
> In[4]:== equation /. x -> -3
> Out[4]== False
>
> (This is with Mathematica 7.0.1.0.)
>

From: Torsten Schoenfeld on 9 Jun 2010 07:20
On 08.06.10 13:08, Andrzej Kozlowski wrote:
> It's a bug involving simplification of holonomic functions in
> Mathematica 7, which has already appeared a couple of times on this
> forum. You can avoid it by evaluating:
>
> Unprotect[Holonomic`HolonomicFullSimplify];
> Clear[Holonomic`HolonomicFullSimplify];

Ah, I see. I missed the earlier threads about this. Thanks! I hope
there'll be a maintenance release to fix this soon.

By the way: why is this namespaced under "Holonomic"? What's the
relation to holonomic functions?

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