Re: A possible bug in Lists
- To: mathgroup at smc.vnet.net
- Subject: [mg34417] Re: [mg34392] A possible bug in Lists
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sun, 19 May 2002 04:14:29 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I must say, I am a little surprised that you think there could be a bug
at such a basic level, which must have presumably survived over a decade
of Mathematica's existence without anyone noticing ??
Th answer to why you can do this is: because it is very useful.
Remember, Mathematica is above all a programming language.
The mechanism responsible for this is called "listability". Suppose you
have a function, say f, and give it the attribute Listable:
In[1]:=
SetAttributes[f,Listable]
f will now thread over list of the same length, as follows:
In[2]:=
f[{a,b,c},{d,e,f}]
Out[2]=
{f[a,d],f[b,e],f[c,f]}
But additionally it will work if one of the arguments is not a list but
just a single element:
In[3]:=
f[{a,b,c},d]
Out[3]=
{f[a,d],f[b,d],f[c,d]}
The function Plus, like many mathematica functions has the attribute
Listable:
In[4]:=
Attributes[Plus]
Out[4]=
{Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected}
That basically should answer your question. One might add that
listability is defined in terms of the Mathematica function thread:
In[5]:=
ClearAll[f]
In[6]:=
Thread[f[{a,b,c},{d,e,f}]]
Out[6]=
{f[a,d],f[b,e],f[c,f]}
In[7]:=
Thread[f[{a,b,c},d]]
Out[7]=
{f[a,d],f[b,d],f[c,d]}
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/
On Saturday, May 18, 2002, at 04:50 PM, Doron wrote:
> Hello there ,
>
> I am having a problem in Mathematica 4.1 :
>
> Evaluating : 1-{1,1} or {1,1}-1 returns {0,0}
>
> Is that ok ?
>
> how is it that I can subtract a vector from a scalar ?
>
> Thank you for your help , Doron .
>
>
>