Re: global real variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg22059] Re: global real variables*From*: adam_smith at my-deja.com*Date*: Fri, 11 Feb 2000 02:38:44 -0500 (EST)*References*: <87trds$5o3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Naum, What you need to do in the case of Conjugate[] is to use the command ComplexExpand[ Conjugate[ x + x * p^-1 ]] as explained in the help this assumes that all the variables are real. (You can specify a list that says that some variables are complex.) ComplexExpand[] is very useful when dealing with complex numbers of the form a + b I. The following examples are very illustrative. Note the use of TargetFunctions-> {Re,Im}. This "forces" the output in the form of a real + imaginary part. In[1]:= z = a + b I Out[1]= a + I*b In[2]:= z*Conjugate[z] Out[2]= (a + I*b)*Conjugate[a + I*b] In[3]:= ComplexExpand[z*Conjugate[z]] Out[3]= a^2 + b^2 In[7]:= z/Conjugate[z] Out[7]= (a + I*b)/Conjugate[a + I*b] In[8]:= ComplexExpand[z/Conjugate[z]] Out[8]= a^2/Abs[a + I*b]^2 + (2*I*a*b)/Abs[a + I*b]^2 - b^2/Abs[a + I*b]^2 In[6]:= ComplexExpand[z/Conjugate[z], TargetFunctions -> {Re, Im}] Out[6]= a^2/(a^2 + b^2) + (2*I*a*b)/(a^2 + b^2) - b^2/(a^2 + b^2) Adam Smith In article <87trds$5o3 at smc.vnet.net>, Naum Phleger <naum at cava.physics.ucsb.edu> wrote: > I asked a dumb question a few weeks ago about making variables real and > found that Mathematica 4 took care of this better. I have been using it > since. I still have a couple of problems with it though. First, I can have > variables be treated as real by using the assumption Element[x,Reals] in a > simplify command, but I want x to be real in all commands so I don't have to > keep using Simplify each time I want x to be recognized as real. Second, > even this doesn't seem to work quite right. Here is what I mean. > > Say I have tow var.s, x and p. Both are real so I can do this. > > Simplify[ Conjugate[ x ] , Element[ x , Reals ] ] ----> x > > amd I get the same thing for p, but it stops working if I have functions of > x and p, for instance I get > > Simplify[ Conjugate[ x + x * p^-1 ] , Element[ {x,p} , Reals ] ] ---- > > > Conjugate[ x + x * p^-1 ] > > It works if I use FullSimplify AND put p^-1 into the list of variables > that I want to have real. How can I get around this without listing every > negative power of every variable and wasting time with FullSimplify. Thanks > for any help. Thanks. > > -NAUM > > Sent via Deja.com http://www.deja.com/ Before you buy.