Re: simplify expr to 1
- To: mathgroup at smc.vnet.net
- Subject: [mg37953] Re: simplify expr to 1
- From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
- Date: Thu, 21 Nov 2002 00:38:31 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Jerry Blimbaum wanted to know why Mathematica doesn't simplify (f[x]/g[x])^r * (g[x]/f[x])^r --> 1 ---------------- It doesn't because it isn't always true! Some counter examples: In[1]:= x= -4; r= 1/2; x^r*(1/x)^r Out[3]= -1 In[4]:= x= -4; r= 23/7; x^r*(1/x)^r Out[6]= (-1)^(4/7) However, PowerExpand does what you were looking for. PowerExpand does transformations that aren't always true. In[7]:= Clear[x,r]; PowerExpand[x^r*(1/x)^r] Out[8] 1 Simplify knows this simplifies to 1 if (x>0), or if (r) is an integer. In[9]:= Clear[x,r]; Simplify[ x^r*(1/x)^r, x>0 ] Out[10]= 1 In[11]:= Clear[x,r]; Simplify[ x^r*(1/x)^r, r \[Element] Integers ] Out[12]= 1 But some might argue that that isn't true either because sometimes the result is 1.0 instead of the integer 1. In[13]:= x=2.3; r=1/2; x^r*(1/x)^r Out[15]= 1. In[16]:= x=2; r=0.5; x^r*(1/x)^r Out[18]= 1. ------- Regards, Ted Ersek Download my latest tricks from: http://www.verbeia.com/mathematica/tips/Tricks.html and http://www.verbeia.com/mathematica/tips/GraphicsTricks.html