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Re: Re:QuestionUsenet


On 20 Jun 2007, at 10:19, Andrzej Kozlowski wrote:

> *This message was transferred with a trial version of CommuniGate 
> (tm) Pro*
>
> On 19 Jun 2007, at 19:59, JanPax wrote:
>
>>
>>   Hi,
>>   what is the easiest way to generate (in Mathematica) ALL terms  
>> given some
>>   function symbols and their arities
>>   and variables x,y, like e.g. f unary, g binary, up to depth N?
>>   x,y, f(x),f(y),g(x,f(x)),g(x,f(y))....
>>   Or even better, to generate *next* term at one step, so that all  
>> terms up
>>   to depth N  will be reached once.
>>
>>   Thank you, JP
>>
>>
>
> Assuming that you mean what I think you mean, here is one way (up  
> to level 2 - it's clear how to continue beyond that).

I should have written "up to depth three" .

Andrzej Kozlowski




>
> SetAttributes[F, {Flat, OneIdentity, Orderless}]
>
> FF0[l_List] := ReplaceList[l, {___, x_ /; Length[{x}] == 1, ___} :>  
> G[x]]
> FF1[l_List] := ReplaceList[(F[##1] & ) @@ l, F[x_, y_] :> F[x, G[y]]]
> FF2[l_List] := ReplaceList[(F[##1] & ) @@ l, F[x_, y_] :> F[G[x], G 
> [y]]]
>
> p = Tuples[{a, b}, 2];
>
> Reverse[Union[Flatten[({FF0[#1], FF1[##1], FF2[##1]} & ) /@ p]]] /.  
> {F -> g, G -> f}
>
> {f[b], f[a], g[f[b], f[b]], g[f[a], f[b]], g[f[a], f[a]], g[b, f 
> [b]], g[b, f[a]],
>   g[a, f[b]], g[a, f[a]]}
>
> q=Tuples[{a,b,c},2];
>
> Reverse[Union[Flatten[({FF0[#1], FF1[##1], FF2[##1]} & ) /@ q]]] /.
>   {F -> g, G -> f}
>
> {f[c], f[b], f[a], g[f[c], f[c]], g[f[b], f[c]], g[f[b], f[b]], g[f 
> [a], f[c]],
>   g[f[a], f[b]], g[f[a], f[a]], g[c, f[c]], g[c, f[b]], g[c, f[a]],  
> g[b, f[c]],
>   g[b, f[b]], g[b, f[a]], g[a, f[c]], g[a, f[b]], g[a, f[a]]}
>
> etc.
>
>
> Andrzej Kozlowski







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