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Re: Re: SameQ to check for simplified radical

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  • Subject: [mg121022] Re: [mg121014] Re: SameQ to check for simplified radical
  • From: DrMajorBob <btreat1 at>
  • Date: Tue, 23 Aug 2011 05:47:46 -0400 (EDT)
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  • Reply-to: drmajorbob at

Without Simplify, we get, as you say, canonical form... 6 Sqrt[10]. My  
point was that Simplify doesn't make it any simpler, because it doesn't  
"think" Sqrt[360] is simpler.

I suppose none of us do.


On Mon, 22 Aug 2011 05:03:59 -0500, Andrzej Kozlowski <akoz at>  

> On 20 Aug 2011, at 12:15, DrMajorBob wrote:
>> The second is obviously simpler, hence Sqrt[360] is simpler than 6
>> Sqrt[10].
>> But Mathematica doesn't see it that way, and apparently, neither do you.
>> Bobby
> The point here is, however, that when Mathematica evaluates
> In[1]:= Sqrt[360]
> Out[1]= 6 Sqrt[10]
> 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[360]:
> In[2]:= LeafCount[Unevaluated[Sqrt[360]]]
> Out[2]= 2
> In[3]:= LeafCount[Sqrt[360]]
> Out[3]= 7
> Andrzej Kozlowski

DrMajorBob at

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