Re: Re: More /.{I->-1} craziness

*To*: mathgroup at smc.vnet.net*Subject*: [mg106573] Re: [mg106525] Re: More /.{I->-1} craziness*From*: "David Park" <djmpark at comcast.net>*Date*: Sat, 16 Jan 2010 06:14:58 -0500 (EST)*References*: <hhf5s3$h4o$1@smc.vnet.net> <hhhmhl$o48$1@smc.vnet.net> <18423897.1263546085556.JavaMail.root@n11>

There is a perfectly simple explanation why it doesn't work for I. It's like saying that because I can calculate a determinant for 2 x 2 and 3 x 3 matrices by adding the products on the diagonals I should be able to do the same thing with any order matrix and students will be confused if they have to do otherwise. No, they can just learn how to do it. It's part of their education. And maybe they shouldn't be taught the limited method in the first place. Mathematica represents complex NUMBERS as atomic expressions, Complex[n1,n2] where n1 and n2 are NUMBERS. It seems to me to be a pretty reasonable design decision. It makes sense to think of complex numbers as entities in their own right. Then they used I as a input shortcut, and displayed complex numbers with \[ImaginaryI] to conform to standard notation. Maybe WRI should not have allowed I for input or ImaginaryI on display. If everyone had to type Complex[a,b], and saw it on output, they might not have to learn the difference between input, display and internal representation. If WRI did that, I'm sure there would be many more complaints and you would be near the head of the line. The other choice would be to do away with the Complex representation altogether. Then complex NUMBERS would be represented as Plus expressions and would no longer be number entities in their own right. I don't know what all the implications of that would be in the Mathematica handling of complex expressions, but I don't think it would be good. Mathematica would have to continually parse expressions to recognize complex numbers. For example, how would Mathematica know to simplify (3+4I)/(1-5I)? It should be able to simplify it just as easily as 4/2. When students get to the point where they are treating complex numbers and functions they can just learn the difference between input and internal representation. If they can't understand that, I don't see how they can understand much about complex algebra. And they should long ago have learned that it is worth while having convenient input forms and output displays. So don't teach them I -> -I. Teach them Complex[a_,b_] -> Complex[a,-b], or Conjugate and ComplexExpand. Teach them about complex NUMBERS. It's not that difficult. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: AES [mailto:siegman at stanford.edu] But a single character on the lhs? It works correctly AFAIK for every other single-character in the alphabet. Why shouldn't one expect it to work for I?