Re: Rationalizing the denominator
- To: mathgroup at smc.vnet.net
- Subject: [mg18717] Re: [mg18633] Rationalizing the denominator
- From: "Drago Ganic" <drago.ganic at in2.hr>
- Date: Sat, 17 Jul 1999 02:36:38 -0400
- Organization: HiNet
- References: <7mjtfu$flc@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Thank you both for the answers. I'm surprised that this newsgroup, unlike others, is positively oriented to newcomers questions. Drago Tomas Garza <tgarza at mail.internet.com.mx> wrote in message news:7mjtfu$flc at smc.vnet.net... > Drago Ganic [drago.ganic at in2.hr] wrote: > > > How can I get > > > > Sqrt[2]/2 > > > > instead of > > > > 1/Sqrt[2] > > > > as a result for Sin[Pi/4]. > > > > When it comes to complex numbers Mathematica never returns 1/I - > > she always > > returns -I. > > Why is the behaviour for irrationals different ? > > Hi, Drago! > > As often has been the advise in this group, look at FullForm: > > In[1]:= > 1/Sqrt[2] // FullForm > > Out[1]//FullForm= > Power[2, Rational[-1, 2]] > > You can't expect Mathematica to go back from this to the "rational" form > Sqrt[x]/x. In fact, if you write Sqrt[x]/x you'll get 1/Sqrt[x]: > > In[2]:= > Sqrt[x]/x > Out[2]= > 1/Sqrt[x] > > Of course, if you still want to "rationalize" 1/Sqrt[x] you may use a > transformation rule together with HoldForm: > > In[3]:= > Sin[Pi/4] /. > Power[x_, Rational[-1, 2]] -> > HoldForm[Power[x, Rational[1, 2]]*Power[x, -1]] > Out[3]= > Sqrt[2]/2 > > which, from the point of view of Mathematica, is a waste of time since this > last expression, if released, will be always return 1/Sqrt[2] as shown in > In[2] above: > > In[4]:= > ReleaseHold[%] > Out[4]= > 1/Sqrt[2] > > On the other hand, > > In[5]:= > 1/I // FullForm > Out[5]//FullForm= > Complex[0, -1] > > which explains why 1/I returns -I. The behavior is consistent: internally, > Mathematica has no division. > > Tomas Garza > Mexico City > >