Re: Ordering of output question

*To*: mathgroup at smc.vnet.net*Subject*: [mg28263] Re: [mg28226] Ordering of output question*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Fri, 6 Apr 2001 01:53:12 -0400 (EDT)*References*: <200104050700.DAA26439@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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]]. 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 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 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. Tomas Garza Mexico City -----Original Message ----- From: "John Todd" <johntodd at fake.com> To: mathgroup at smc.vnet.net Subject: [mg28263] [mg28226] Ordering of output question > Hello, > I'm trying to get the output of the following to be in > standard complex number form, i.e. a + ib: > > Clear[x, y, z]; > Clear[fCZ, fCXY]; > x /: Im[x] = 0; > x /: Re[x] = x; > y /: Im[y] = 0; > y /: Re[y] = y; > fCZ[z_] := \[ImaginaryI] z + \[ImaginaryI]; > fCXY = ComplexExpand[f[x + \[ImaginaryI] y]]; > Print["f(z) = ", f[z]]; > Print["Let z = x + \[ImaginaryI]y"]; > > (* The following line is where my question pertains*) > Print["f(x + \[ImaginaryI]y) = ", fCXY, " = ", Re[fCXY], > " + \[ImaginaryI]"Im[fCXY], "."]; > > Print["The real part of f(z) = ", fCZ[z], " is ", Re[fCXY], > " and the imaginary part is ", Im[fCXY], "."]; > > If you evaluate the above, you'll find that the line directly > below the commented line has its final outpu as -y + i(x + 1) which is > what I want. However, my means of getting it to look that way seem a > bit inelegant,, and I feel certain there is a better way. I do > realize that looking at the expression with TreeForm[], I can extract > whatever I want out of an expression, but that also seems inelegant. > What I feel must be possible is to set up some sort of a pattern or > transformation rule which will say in effect, "Place the output in > this form, i.e. a + ib, regardless of what a and b are". I ask this > question not only for the specific example given but also in a broader > sense because I will and have wanted to display expressions in a > certain format, but have always had to resort to the kinds of > contrivances already mentioned. > Before submitting my question I perused the sections on Patterns > and the section on Transformation Rules in Wolfram's 4th edition Mathematica > book. If I missed a glaring answer to my question, I apologize. > > Thanks again, > > JT >

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