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simplification of 0/0 to 1?
 To: mathgroup at smc.vnet.net
 Subject: [mg77510] simplification of 0/0 to 1?
 From: dimitris <dimmechan at yahoo.com>
 Date: Mon, 11 Jun 2007 04:22:48 0400 (EDT)
Hi fellas.
This appeared in another forum as part of a question
what another CAS does.
Just of curiosity I check Mathematica's performance (5.2).
The result was poor!
Here is the expression
In[16]:=
o = (Log[2]*Cos[Pi/12]  Log[2]*Sin[Pi/12]  2*Cos[Pi/12] + 2*Sin[Pi/
12] + Sqrt[2] +
2*Log[Cos[Pi/12]  Sin[Pi/12]]*Cos[Pi/12]  2*Log[Cos[Pi/12] 
Sin[Pi/12]]*Sin[Pi/12])/
(Log[2]*Cos[Pi/12]  Log[2]*Sin[Pi/12] + 2*Log[Cos[Pi/12] 
Sin[Pi/
12]]*Cos[Pi/12] 
2*Log[Cos[Pi/12]  Sin[Pi/12]]*Sin[Pi/12])
Out[16]=
(Sqrt[2] + (1 + Sqrt[3])/Sqrt[2]  (1 + Sqrt[3])/Sqrt[2]  ((1 +
Sqrt[3])*Log[2])/(2*Sqrt[2]) +
((1 + Sqrt[3])*Log[2])/(2*Sqrt[2])  ((1 + Sqrt[3])*Log[((1 +
Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/(2*Sqrt[2])])/
Sqrt[2] + ((1 + Sqrt[3])*Log[((1 + Sqrt[3])/(2*Sqrt[2])) + (1 +
Sqrt[3])/(2*Sqrt[2])])/Sqrt[2])/
((((1 + Sqrt[3])*Log[2])/(2*Sqrt[2])) + ((1 + Sqrt[3])*Log[2])/
(2*Sqrt[2]) 
((1 + Sqrt[3])*Log[((1 + Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/
(2*Sqrt[2])])/Sqrt[2] +
((1 + Sqrt[3])*Log[((1 + Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/
(2*Sqrt[2])])/Sqrt[2])
Watch now a really bad performance!
In[17]:=
(Simplify[#1[o]] & ) /@ {Numerator, Denominator}
Out[17]=
{0, 0}
That is Mathematica simplifies succesfully both the numerator
and denominator to zero. So, you wonder what goes wrong?
Try now to simplify the whole expression!
In[19]:=
Simplify[o]
Out[19]=
1
A very weird result to my opinion!
Simplification of 0/0 to 1?
I think no simplification or some
warning messages would be much better
than 1!
Note also that
In[20]:=
RootReduce[o]
Out[20]=
1
Dimitris
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