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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
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