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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106036] Re: More /.{I->-1} craziness
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Thu, 31 Dec 2009 03:13:51 -0500 (EST)
  • References: <hhf5s3$h4o$1@smc.vnet.net>

AES wrote:
> The more I play with these I->-I substitution rules, the more seemingly 
> wildly inconsistent results emerge.  For example:  
> 
>    In[1]:= -I/.I->-I
> 
>    Out[1]= -I
> 
..snip..
> 
These examples you give are perfectly consistent with a certain world 
view which is that I is not a symbol, but a functional form, 
Complex[0,1], and -I is a different form, Complex[0,-1].

The fact that this is not what you expect as a mathematician is simply 
your fault.:)

You might find these examples. some old, some new,  confusing as well. 
(in Mathematica 6.0)

Here are some puzzles for you.  Guess what they return. (Answers below)
3 /. 3->4
3  /.3->4
3 /0.3->4     (which helps explain previous line)

3 / . 3 ->4

3 /. 3.0->4

3/.3.0->4
3.0/. 3.0->4

a. 3/. a->b
a.3 /. a->b

a .3 . 4  /. 3 -> c
a. 3 . 4  /. 3 -> c

.......answers.........

3 /. 3->4    returns 4
3  /.3->4    returns 10.->4
3 /0.3->4    returns 10.->4   (which helps explain previous line)

3 / . 3 ->4   syntax error

3 /. 3.0->4  returns 3

3/.3.0->4    returns 0.->4
3.0/. 3.0->4 returns 4

a. 3/. a->b  returns b.3
a.3 /. a->b  returns 0.3*b

a .3 . 4  /. 3 -> c returns a 0.3.4
a. 3 . 4  /. 3 -> c returns a.c.4




and yes, I know the explanation for all of these.


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