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Re: Re: TraditionForm Appears to be Inconsistent

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99635] Re: [mg99606] Re: TraditionForm Appears to be Inconsistent
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sun, 10 May 2009 05:13:41 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <9293149.1241693402776.JavaMail.root@n11> <gu0bal$fsj$1@smc.vnet.net> <200905090720.DAA29931@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Because 1/Sin[x] has Depth 3, whereas Csc[x] has Depth 2?

AES wrote:
> In article <gu0bal$fsj$1 at smc.vnet.net>,
>  "David Park" <djmpark at comcast.net> wrote:
> 
>> One just has to get used to what simplifications Mathematica automatically
>> does and which ones it doesn't do. Some of the automatic ones are annoying,
>> such as 1/Sin[x] -> Csc[x].
>>
> 
> This particular one has always been particularly puzzling for me.  In my 
> experience at least, more or less everyone uses Sin and Cos in writing 
> out any expressions containing these functions, and practically no one 
> ever uses Sec and Csc.  
> 
> Moreover, I'd make a small bet that if you took a large random sample of 
> science and engineering professionals, approaching half of them would 
> get the relationships between Sin and Cos, and Sec and Csc, wrong.  
> ("Let's see -- it's COsine and COsecant, and then Sin and Secant -- 
> right?")
> 
> Is there some fundamental mathematical or logical reason behind 
> Mathematica's choice?  Or some strongly embedded or historical 
> convention in the field of symbolic algebra that leads to this being 
> done?
> 

-- 
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


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