Re: Re: Re: Bug in Simplify?

• To: mathgroup at smc.vnet.net
• Subject: [mg33292] Re: [mg33265] Re: [mg33216] Re: Bug in Simplify?
• From: Gianluca Gorni <gorni at dimi.uniud.it>
• Date: Thu, 14 Mar 2002 02:21:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```
> As best I can tell, however, nothing that you said explains why
> we should expect Simplify[x/y, x==0 && y==0] to yield 0. This
> still puzzles me.
>
> Regards,
> David
>

It seems that Simplify will not look at denominators to see when
they vanish. For example

Simplify[x/y == 1 && y == 0]

will return the argument unevaluated. Also Solve has the same problem:
Solve[x/y == 1] will not warn you that x=y=0 is not a solution.

A function that cares for vanishing denominators is Reduce:

Reduce[x/y == 1 && y == 0] gives False

Also, Reduce[x/y == 1] gives x == y && y != 0

I don't know how relevant it is, but 2 years ago Adam Strzebonski,
in response to why Simplify[Sqrt[x^2], x == 1 + Sqrt[2]] did not
return x, wrote:

> I am not convinced that Simplify should be
> optimized for assumptions of the form x==constant. I would
> expect that in most cases what one really wants is
> Simplify[expr/.x->constant]
> rather than
> Simplify[expr, x==constant].

Best regards,

Gianluca Gorni

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```

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