Re: Uniform design

*To*: mathgroup at smc.vnet.net*Subject*: [mg48107] Re: Uniform design*From*: ab_def at prontomail.com (Maxim)*Date*: Thu, 13 May 2004 00:08:47 -0400 (EDT)*References*: <c7nnc7$dm5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here's a couple of more 'mathematical' examples along the same lines: In[1]:= 0*Interval[{0, Infinity}] Infinity*Interval[{0, Infinity}] Interval[{0, 0}]*Interval[{0, Infinity}] Interval[{0, Infinity}]*Interval[{0, Infinity}] Infinity::indet: Indeterminate expression 0*Infinity encountered. Out[1]= Interval[{0, Indeterminate}] Out[2]= Interval[{0, Infinity}] Infinity::indet: Indeterminate expression 0*Infinity encountered. Out[3]= Interval[{0, Indeterminate}] Out[4]= Interval[{0, Infinity}] This also leads to the more general question of whether we need to distinguish between open and closed intervals or the endpoints can simply be neglected. But in any case there should be one uniform convention for dealing with such issues, otherwise we won't be able to get consistent results: In[5]:= Interval[{0, Infinity}]*(x*Interval[{0, Infinity}] + 1) // D[#, x]& Interval[{0, Infinity}]*(x*Interval[{0, Infinity}] + 1) // Expand // D[#, x]& Infinity::indet: Indeterminate expression 0*Infinity encountered. Out[5]= x*Interval[{0, Indeterminate}] + Interval[{0, Infinity}] Out[6]= Interval[{0, Infinity}] Also, it's strange that Solve accepts intervals (Mathematica Help for Interval even gives such an example), but doesn't really support them: In[7]:= Solve[1/(x - 1) == Interval[{-1, 1}]] Out[7]= {{x -> Interval[{-Infinity, Infinity}]}} Not much point in treating this equation as Solve[1/(x-1)==a,x] and giving incorrect result. Another question is related to Laplace transform. Mathematica mixes the use of generalized functions with formulas like L[f']=p*F(p)-f(0), which are only valid for ordinary functions. Because of this, we get results like the following: In[8]:= LaplaceTransform[f'[t], t, p] /. f -> UnitStep Out[8]= 0 Maxim Rytin m.r at prontomail.com

**Follow-Ups**:**Re: Re: Uniform design***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>