       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:=
o = (Log*Cos[Pi/12] - Log*Sin[Pi/12] - 2*Cos[Pi/12] + 2*Sin[Pi/
12] + Sqrt +
2*Log[Cos[Pi/12] - Sin[Pi/12]]*Cos[Pi/12] - 2*Log[Cos[Pi/12] -
Sin[Pi/12]]*Sin[Pi/12])/
(Log*Cos[Pi/12] - Log*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=
(Sqrt + (-1 + Sqrt)/Sqrt - (1 + Sqrt)/Sqrt - ((-1 +
Sqrt)*Log)/(2*Sqrt) +
((1 + Sqrt)*Log)/(2*Sqrt) - ((-1 + Sqrt)*Log[-((-1 +
Sqrt)/(2*Sqrt)) + (1 + Sqrt)/(2*Sqrt)])/
Sqrt + ((1 + Sqrt)*Log[-((-1 + Sqrt)/(2*Sqrt)) + (1 +
Sqrt)/(2*Sqrt)])/Sqrt)/
(-(((-1 + Sqrt)*Log)/(2*Sqrt)) + ((1 + Sqrt)*Log)/
(2*Sqrt) -
((-1 + Sqrt)*Log[-((-1 + Sqrt)/(2*Sqrt)) + (1 + Sqrt)/
(2*Sqrt)])/Sqrt +
((1 + Sqrt)*Log[-((-1 + Sqrt)/(2*Sqrt)) + (1 + Sqrt)/
(2*Sqrt)])/Sqrt)

Watch now a really bad performance!

In:=
(Simplify[#1[o]] & ) /@ {Numerator, Denominator}

Out=
{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:=
Simplify[o]

Out=
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:=
RootReduce[o]

Out=
1

Dimitris

```

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