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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

• Follow-Ups:
  • Re: simplification of 0/0 to 1?
    • From: Murray Eisenberg <murray@math.umass.edu>