Re: Re: Assumptions in Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg20594] Re: [mg20579] Re: [mg20562] Assumptions in Integrate
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Tue, 2 Nov 1999 02:35:29 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Looking at this again I noticed another problem. The answer given by Mathematica isn't true for n=0, so there is a bug in Simplify. The correct command should have been: In[39]:= Simplify[Integrate[Cos[n x], {x, -Pi, Pi}, Assumptions -> Element[n, Integers]], Element[n, Integers] && n != 0] Out[39]= 0 Note however that the following does not work, though it should: In[40]:= Integrate[Cos[n x], {x, -Pi, Pi}, Assumptions -> Element[n, Integers] && n != 0] Out[40]= 2 2 Sin[Sqrt[n ] Pi] ------------------ 2 Sqrt[n ] -- > From: Andrzej Kozlowski <andrzej at tuins.ac.jp> > Date: Sat, 30 Oct 1999 14:54:54 -0400 > To: mathgroup at smc.vnet.net > Subject: [mg20594] [mg20579] Re: [mg20562] Assumptions in Integrate > > I also think the Assumptions mechanism in Integrate leaves a lot to be > desired. Probably the best thing one can do right now is something like: > > In[45]:= > Simplify[Integrate[Cos[n x], {x, -Pi, Pi}, > Assumptions -> Element[n, Integers]], Element[n, Integers]] > > Out[45]= > 0 > -- > > >> From: Julian Aguirre Estibalez <mtpagesj at lg.ehu.es> To: mathgroup at smc.vnet.net >> Organization: Universidad del Pais Vasco/Euskal Herriko Unibertsitatea >> Date: Sat, 30 Oct 1999 00:14:09 -0400 >> To: mathgroup at smc.vnet.net >> Subject: [mg20594] [mg20579] [mg20562] Assumptions in Integrate >> >> Dear Math Group, >> >> I find the results of using assumptions in Integrate somewhat >> stranege. For instance, >> >> In[21]:= Integrate[Cos[n x], {x, -Pi, Pi}] >> >> Out[21]= 2 Sin[n Pi] >> ----------- >> n >> >> In[22]:= Integrate[Cos[n x], {x, -Pi, Pi}, >> Assumptions -> Element[n, Integers]] >> >> Out[22]= >> 2 >> 2 Sin[Sqrt[n ] Pi] >> ------------------ >> 2 >> Sqrt[n ] >> >> In[23]:= $Version >> >> Out[23]= "4.0 for Power Macintosh (July 20, 1999)" >> >> I know I can define my own transformation rules, but one would >> think that Mathematica should do it directly. >> >> Julian Aguirre | Voice: +34 946012659 >> Departamento de Matematicas | Fax: +34 944648500 >> Universidad del Pais Vasco | Postal: Aptdo. 644, 48080 Bilbao, Spain >> | email: mtpagesj at lg.ehu.es >> >> > >