Re: Ordering of output question

*To*: mathgroup at smc.vnet.net*Subject*: [mg28269] Re: Ordering of output question*From*: johntodd at fake.com (John Todd)*Date*: Sat, 7 Apr 2001 03:44:28 -0400 (EDT)*References*: <200104050700.DAA26439@smc.vnet.net> <9ajns1$sg2@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 6 Apr 2001 02:31:29 -0400, Tomas Garza <tgarza01 at prodigy.net.mx> wrote: >Evaluation of your code below gave > >f(z) = f[z] >Let z = x + I y >f(x + I*y) = f[x + I*y] = Re[f[x + I*y]] + I* Im[f[x + I*y]]. >The real part of f(z) = I + I*z is Re[f[x + I*y]] and the imaginary part is >Im[f[x + I*y]]. Sorry about that, I posted a correction (too late obviously)... >so I imagine some kind of assignment or rule saying that z = x + I*y was >lost somewhere. Now, I guess you are mainly concerned with *displaying* a >complex number in the form a + I b. Forcing Mathematica to change the order >in which expressions are internally handled would be difficult and, in the >end, useless. If a canonical order is used to internally handle expressions, >then so be it. For example, if we were to use variables {w, v, u} (in that >precise order), w and v real, in your example, then I'm not particularly interested in changing the way expressions are handled internally, rather I want a way to take what Mathematica returns and make it conform to a particular format. >In[2]:= >ComplexExpand[I + I*u /. u -> w + I*v] >Out[2]= >-v + I*(1 + w) > >which is the way you would like a complex number to be displayed, and this >is because v comes before w in canonical order. However, if you want only an >*external* way of displaying a result, i.e., only for visual purposes, you >needn't go into so much trouble. I think defining one fCZ and one fCXY is >unnecesary, since a single function f, say, can handle its argument either >in the form z or in the form x +I y. Thus, if you define f as follows, and >then extract the real and imaginary parts I agree with you, I actually defined one as fCZ := and one as fCXY = and the reason I did that, is that I figured rather than continually evaluating ComplexExpand[fCZ[x + iy]] everytime I needed that form, I would simply store it for future use. The more I use Mathematica, the more I realize the need for code organization and that is the reason for my perhaps arcane function and variable names. I'm basically trying to come up with a Hungarian notation for my Mathematica code/notebooks. So, for example fCZ means a function that takes a complex operand z and fCXY means that that is the form in which I did the Complex expand on fCZ. Since, I'm treating fCXY as a variable, I actually need to prepend it with a g, which is what I'm using to denote globally declared variables. >In[3]:= >f[z_] := I + I z >In[4]:= >reim = #[ComplexExpand[f[z] /. z -> x + I y]] & /@ {Re, Im} >Out[4]= >{-y, 1 + x} > >you can then print something like > >In[5]:= >Print["The real part of f(z) = ", f[z], " is ", reim[[1]], > " and the imaginary part is ", reim[[2]], > ", where z = x + I y\n so that ", f[z], "= ", reim[[1]], " + I (", > reim[[2]], ")."]; >"The real part of f(z) = "I + > I*z" is "-y" and the imaginary part is "1 + > x", where z = x + I y so that "I + > I*z"= "-y" + I ("1 + x")." > >BTW, in your original print statement, I think saying Print["f(z) = ", >f[z]]; could be misleading. f(z) is *not* equal to f[z]. You might say >something like "In Mathematica the function f(z) is written as f[z], because >round parentheses are only used for grouping purposes", or something like >that. The only reason I use the f(z) in the Print statement is for output purposes, because others not familiar with Mathematica will be seeing some of the output and I want it to appear as mathematically 'familiar' as possible, which is also the reason for my wanting to be able to show the output in a particular manner .. >Tomas Garza >Mexico City Thanks for your help, especially the code because it's helped me to learn yet more about setting up expressions in Mathematica... JT

**References**:**Ordering of output question***From:*johntodd@fake.com (John Todd)

**Re: A universal simulation interface: database, input/output, plotting and visualization**

**Removing Audio "Clicking"**

**Re: Ordering of output question**

**Re: Ordering of output question**