Re: RE Map

• To: mathgroup at smc.vnet.net
• Subject: [mg29740] Re: RE Map
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 6 Jul 2001 03:24:35 -0400 (EDT)
• References: <9i06i3\$h19\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ranko,

>   b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001}
>
> If we try to apply a function g to levels 2 and 3 we get
>
>  ClearAll[g]
>  Map[g,b,{2,3}]
>
{{g[1],g[5],g[10]},{g[25],g[0],g[{g[1],g[2],g[3],g[4]}]},{g[55],g[5],g[2001]
}}
>
>  but this is clearly not what we wanted because of the term
>  g[{g[1],g[2],g[3],g[4]}]}
>
>  The only way to obtain the correct result in this case is to make g
> listable

Not in this case:

b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001}}
{{1,5,10},{25,0,{1,2,3,4}},{55,5,2001}}

Map[g,b,{-1}]

{{g[1],g[5],g[10]},{g[25],g[0],{g[1],g[2],g[3],g[4]}},{g[55],g[5],g[2001]}}

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Ranko Bojanic" <bojanic at math.ohio-state.edu> wrote in message
news:9i06i3\$h19\$1 at smc.vnet.net...
>
>
>
> Benedetto Bongiorno wanted to convert the list
>      a={{1, 5, 10},{25, 0, 2000},{55, 5, 2001}
> into the list
>       {{01, 05,10},{25, 00, 2000},{55, 05, 2001}
> His program
>
> Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),#]&,a]
>
> did not work but, as several readers pointed out, this could be
> easily corrected by adding the correct level specification:
>
> Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),#]&,a,{2}]
> {{01,05,10},{25,00,2000},{55,05,2001}}
>
> One potential problem I see here is that the result is a list of
> strings and integers
>
>
{{String,String,Integer},{Integer,String,Integer},{Integer,String,Integer}}
>
> This can be also easily corrected by writing:
>
> Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),ToString[#]]&,a,{2}]
>
> The main reason I am writing this letter is that Map with level
> specifications does not seem to work in a slightly more complicated cases,
> for instance when
>
>   b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001}
>
> If we try to apply a function g to levels 2 and 3 we get
>
>  ClearAll[g]
>  Map[g,b,{2,3}]
>
{{g[1],g[5],g[10]},{g[25],g[0],g[{g[1],g[2],g[3],g[4]}]},{g[55],g[5],g[2001]
}}
>
>  but this is clearly not what we wanted because of the term
>  g[{g[1],g[2],g[3],g[4]}]}
>
>  The only way to obtain the correct result in this case is to make g
listable:
>
>  SetAttributes[g,Listable]
>  g[b]
>
{{g[1],g[5],g[10]},{g[25],g[0],{g[1],g[2],g[3],g[4]}},{g[55],g[5],g[2001]}}
>
> This suggests the following approach to Bongiorno's problem. Define
>
> f[x_] :=If[x<10,(StringJoin[ToString[0],ToString[x]]),ToString[x]];
>
> and make it Listable
>
> SetAttributes[f,Listable]
>
> We obtain then
>
>  f[a]
> {{01 ,05, 10},{25, 00, 2000},{55, 05, 2001}}
> f[b]
> {{01,05,10},{25,00,{01,02,03,04}},{55,05,2001}}
>
> Ranko
>
>
>

```

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