       Re: Re: SameQ to check for simplified radical

• To: mathgroup at smc.vnet.net
• Subject: [mg121022] Re: [mg121014] Re: SameQ to check for simplified radical
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Tue, 23 Aug 2011 05:47:46 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108201015.GAA04919@smc.vnet.net>

```Without Simplify, we get, as you say, canonical form... 6 Sqrt. My
point was that Simplify doesn't make it any simpler, because it doesn't
"think" Sqrt is simpler.

I suppose none of us do.

Bobby

On Mon, 22 Aug 2011 05:03:59 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl>
wrote:

>
> On 20 Aug 2011, at 12:15, DrMajorBob wrote:
>
>> The second is obviously simpler, hence Sqrt is simpler than 6
>> Sqrt.
>>
>> But Mathematica doesn't see it that way, and apparently, neither do you.
>>
>> Bobby
>
>
> The point here is, however, that when Mathematica evaluates
>
> In:= Sqrt
> Out= 6 Sqrt
>
> it is not really "simplifying" the expression but putting it into a
> "canonical form". Simplification depends on a complexity function but
> canonical form do not. They are necessary, because if expressions were
> not put into these canonical forms, certain cancellations would not take
> place because under a given complexity function two equivalent
> expressions might never be transformed into the same expression (so that
> cancellation can take place). So you really need these canonical forms
> to be independent of any complexity function. Because expressions are
> put into a canonical form before Simplify is applied, sometimes you will
> never be able to get an answer that has the lowest complexity (for a
> given ComplexityFunction). In this case the lowest complexity is, if
> course, possessed by Sqrt:
>
> In:= LeafCount[Unevaluated[Sqrt]]
>
> Out= 2
>
> In:= LeafCount[Sqrt]
>
> Out= 7
>
> Andrzej Kozlowski
>
>
>

--
DrMajorBob at yahoo.com

```

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