Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Extracting a Function's Domain and Image

• To: mathgroup at smc.vnet.net
• Subject: [mg67970] Extracting a Function's Domain and Image
• From: Bruce Colletti <vze269bv at verizon.net>
• Date: Wed, 19 Jul 2006 05:21:10 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Re Mathematica 5.2.2.

Why does the last line of code return {x} and not {a,b,_}, while if the f[_]=0 is struck, the answer is {a,b}?  

I want to extract the domain and image of a user-defined function, and tech support recommended using DownValues (pretty handy).  If you have an easier approach, please share it.  Thanks.

Bruce

Remove@f;
f[_]=0;
f["a"]=1;
f["b"]=2;
Clear@x;
h=DownValues@f
Cases[h,f[x_]->x,Infinity]

Out[52]=
{HoldPattern[f[a]]:>1,HoldPattern[f[
   b]]:>2,HoldPattern[f[_]]:>0}

Out[53]=
{x} 

• Follow-Ups:
  • Re: Extracting a Function's Domain and Image
    • From: "Carl K. Woll" <carlw@wolfram.com>
  • Re: Extracting a Function's Domain and Image
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>