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Re: simplification of 0/0 to 1?

• To: mathgroup at smc.vnet.net
• Subject: [mg77543] Re: [mg77510] simplification of 0/0 to 1?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Tue, 12 Jun 2007 01:27:38 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200706110822.EAA20741@smc.vnet.net>
• Reply-to: murray at math.umass.edu

The issue of what a piece of software should do about 0/0 -- even when 
it arises in precisely that form, without any CAS first simplifying 
algebraic expressions to reach that form -- is a sticky one.  The issue 
was a mildly hot one many years ago in connection with the programming 
language APL (from which parts of the Mathematica language are 
descended).  Aside from the possibility of signaling an error, there are 
two other "good" possibilities for 0/0: 0 and 1.  So I proposed in APL 
that the handling be user-specifiable.

The simple answer is that there is no good way to handle 0/0 that will 
satisfy everyone.

dimitris wrote:
> Hi fellas.
> This appeared in another forum as part of a question
> what another CAS does.
> Just of curiosity I check Mathematica's performance (5.2).
> The result was poor!
> 
> Here is the expression
> 
> 
> In[16]:=
> o = (Log[2]*Cos[Pi/12] - Log[2]*Sin[Pi/12] - 2*Cos[Pi/12] + 2*Sin[Pi/
> 12] + Sqrt[2] +
>     2*Log[Cos[Pi/12] - Sin[Pi/12]]*Cos[Pi/12] - 2*Log[Cos[Pi/12] -
> Sin[Pi/12]]*Sin[Pi/12])/
>    (Log[2]*Cos[Pi/12] - Log[2]*Sin[Pi/12] + 2*Log[Cos[Pi/12] -
> Sin[Pi/
> 12]]*Cos[Pi/12] -
>     2*Log[Cos[Pi/12] - Sin[Pi/12]]*Sin[Pi/12])
> 
> 
> Out[16]=
> (Sqrt[2] + (-1 + Sqrt[3])/Sqrt[2] - (1 + Sqrt[3])/Sqrt[2] - ((-1 +
> Sqrt[3])*Log[2])/(2*Sqrt[2]) +
>    ((1 + Sqrt[3])*Log[2])/(2*Sqrt[2]) - ((-1 + Sqrt[3])*Log[-((-1 +
> Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/(2*Sqrt[2])])/
>     Sqrt[2] + ((1 + Sqrt[3])*Log[-((-1 + Sqrt[3])/(2*Sqrt[2])) + (1 +
> Sqrt[3])/(2*Sqrt[2])])/Sqrt[2])/
>   (-(((-1 + Sqrt[3])*Log[2])/(2*Sqrt[2])) + ((1 + Sqrt[3])*Log[2])/
> (2*Sqrt[2]) -
>    ((-1 + Sqrt[3])*Log[-((-1 + Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/
> (2*Sqrt[2])])/Sqrt[2] +
>    ((1 + Sqrt[3])*Log[-((-1 + Sqrt[3])/(2*Sqrt[2])) + (1 + Sqrt[3])/
> (2*Sqrt[2])])/Sqrt[2])
> 
> Watch now a really bad performance!
> 
> In[17]:=
> (Simplify[#1[o]] & ) /@ {Numerator, Denominator}
> 
> Out[17]=
> {0, 0}
> 
> That is Mathematica simplifies succesfully both the numerator
> and denominator to zero. So, you wonder what goes wrong?
> 
> Try now to simplify the whole expression!
> 
> In[19]:=
> Simplify[o]
> 
> Out[19]=
> 1
> 
> A very weird result to my opinion!
> Simplification of 0/0 to 1?
> I think no simplification or some
> warning messages would be much better
> than 1!
> 
> Note also that
> 
> In[20]:=
> RootReduce[o]
> 
> Out[20]=
> 1
> 
> Dimitris
> 
> 

-- 
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: simplification of 0/0 to 1?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• References:
  • simplification of 0/0 to 1?
    • From: dimitris <dimmechan@yahoo.com>