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>
- Reply-to: drmajorbob at yahoo.com
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. 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[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 yahoo.com
- References:
- Re: SameQ to check for simplified radical expressions... doesn't work
- From: DrMajorBob <btreat1@austin.rr.com>
- Re: SameQ to check for simplified radical expressions... doesn't work