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>