Re: Rationalizing the denominator

*To*: mathgroup at smc.vnet.net*Subject*: [mg18671] Re: [mg18633] Rationalizing the denominator*From*: "Tomas Garza" <tgarza at mail.internet.com.mx>*Date*: Thu, 15 Jul 1999 01:45:55 -0400*Sender*: owner-wri-mathgroup at wolfram.com

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