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Re: Re: Re: Radicals simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg106415] Re: [mg106411] Re: [mg106386] Re: Radicals simplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 12 Jan 2010 04:46:59 -0500 (EST)
• References: <hic37h$5ef$1@smc.vnet.net> <201001111030.FAA23508@smc.vnet.net> <201001112354.SAA21089@smc.vnet.net>

Yes, but Adam Strzebonski has already posted here the default 
CoplexityFunction in the past, and knowing it really wont help you much:


SimplifyCount[p_] :=
If[Head[p]===Symbol, 1,
   If[IntegerQ[p],
      If[p==0, 1, Floor[N[Log[2, Abs[p]]/Log[2, 10]]]+If[p>0, 1, 
2]],
      If[Head[p]===Rational,
         SimplifyCount[Numerator[p]]+SimplifyCount[Denominator[p]]+1,
         If[Head[p]===Complex,
            SimplifyCount[Re[p]]+SimplifyCount[Im[p]]+1,
            If[NumberQ[p], 2,
	       SimplifyCount[Head[p]]+If[Length[p]==0, 0,
	       Plus@@(SimplifyCount/@(List@@p))]]]]]]

Would it be helpful to have this in the Documentation? Or is it more 
helpful to know that most of the time (but not always) this agrees with 
LeafCount?
I think a very large percentage of complaints about the documentation 
reduce to this sort of issues.

Andrzej Kozlowski


On 12 Jan 2010, at 08:54, Murray Eisenberg wrote:

> Mathematica 7 documentation does NOT say that LeafCount is the 
criterion
> for determining simplicity, that is, the default value of
> ComplexityFunction.  Rather it says:
>
>   "The default ComplexityFunction counts the subexpressions and digits

> of integers."
>
> But it does not even say how it combines the counts of the number of

> subexpressions and digits of integers!
>
> On 1/11/2010 5:30 AM, dh wrote:
>> Hi,
>>
>> why do you think x(x^2 y^3)^(1/4) is simpler than (x^6 y^3)^(1/4)?
>>
>> Mathematica needs some criterion for this decision. The default 
criterion is the
>>
>> "LeafCount[..]". If that does not suit you, you must define another
>>
>> criterion.
>>
>> Daniel
>>
>>
>>
>> francix wrote:
>>
>>> Hi,
>>
>>> I am using Matematica 7 and need some help with Radicals.
>>
>>>
>>
>>> If I do
>>
>>> Simplify[(x^4 y^3)^(1/4), x>= 0] I correctly have
>>
>>>
>>
>>> x (y^3)^(1/4)
>>
>>>
>>
>>> But If I do
>>
>>>
>>
>>> Simplify[(x^6 y^3)^(1/4), x>= 0] I get
>>
>>>
>>
>>> (x^6 y^3)^(1/4) and not the correct answer  x(x^2 y^3)^(1/4)
>>
>>>
>>
>>> Thanks in advanced.
>>
>>>
>>
>>>
>>
>>>
>>
>>>
>>
>>>
>>
>>>
>>
>>>
>>
>>
>>
>
> --
> Murray Eisenberg                     murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305
>

• Follow-Ups:
  • Re: Re: Re: Re: Radicals simplify
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Re: Radicals simplify
    • From: dh <dh@metrohm.com>
  • Re: Re: Radicals simplify
    • From: Murray Eisenberg <murray@math.umass.edu>