RE: problems with the definition of a function
- To: mathgroup at smc.vnet.net
- Subject: [mg36653] RE: [mg36651] problems with the definition of a function
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Wed, 18 Sep 2002 02:09:28 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
>-----Original Message----- >From: bagarell at unipa.it [mailto:bagarell at unipa.it] To: mathgroup at smc.vnet.net >Sent: Monday, September 16, 2002 6:34 AM >Subject: [mg36653] [mg36651] problems with the definition of a function >I have quite an easy and annoying problem with mathematica: >I need to define a function f(x,y) which takes some values for >x=0,2pi,4pi (indepently of y) and has a different expression for all >the other values of y. This is easily done for one-dimensional >functions but I am in serious troubles for my two-dimensional problem: >any suggestion? >Thanks a lot, >Fabio It's difficult to guess what you wanted to attain and what your problems were. Perhaps this example might help you: In[11]:= f[x_, _] /; Mod[x, 2Pi] == 0 := x/(2Pi) In[12]:= f[x_, y_] := x + y In[13]:= epsilon = $MachineEpsilon Out[13]= 2.220446049250313*^-16 In[14]:= f[6Pi(1 + epsilon Sin[#]), #] & /@ Range[0, 4Pi, Pi 10^-1] Out[14]= {3, 3., 19.4779, 19.792, 20.1062, 20.4204, 20.7345, 21.0487, 21.3628, 3., 3, \ 22.3053, 22.6195, 22.9336, 23.2478, 23.5619, 23.8761, 24.1903, 24.5044, \ 24.8186, 3, 3., 25.7611, 26.0752, 26.3894, 26.7035, 27.0177, 27.3319, 27.646, \ 3., 3, 28.5885, 28.9027, 29.2168, 29.531, 29.8451, 30.1593, 30.4734, 30.7876, \ 31.1018, 3} Look close at the values returned (compare with epsilon Sin[Range[0, 4Pi, Pi 10^-1]]), also to recognize the dangers of such a definition. -- Hartmut