Re: Re: Code to translate to negative base...

• To: mathgroup at smc.vnet.net
• Subject: [mg64675] Re: [mg64620] Re: Code to translate to negative base...
• From: Richard Palmer <mapsinc at bellatlantic.net>
• Date: Sun, 26 Feb 2006 05:07:57 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Thanks a lot Valeri,  I owe you a drink or a coffee if you ever get to
Boston.

Richard Palmer

On 2/24/06 12:18 AM, "Valeri Astanoff" <astanoff at yahoo.fr> wrote:

> Surely not so clever or fast as Paul Abbott's solution,
> this my way to handle negative bases with "FindInstance" :
> (not thoroughly tested) :
>
> In[1]:=
> myToDigits[k_Integer, base_Integer /; base <= -2]:=
>   Module[{dd, d, n, fi},
>     dd = Table[d[i],{i,0,n = Length[IntegerDigits[k,-base]]+1}];
>     fi = FindInstance[k == Sum[d[i]base^i,{i,0,n}]&&
>           And @@ ((0 <= # <= -base-1)& /@ dd), dd, Integers];
>     (dd /. fi // First // Reverse) //. {0,u__} -> {u}
>     ];
>
> myFromDigits[digits:{_Integer..}, base_Integer /; base <= -2]:=
>   digits.Table[base^i,{i,Length[digits]-1,0,-1}];
>
> myToDigits[x_?NumericQ, base_Integer /; base <= -2,
>     numberOfOutputDigits_Integer /; numberOfOutputDigits >= 1]:=
>   Module[{y, nid},
>     y = Floor[x*(-base)^(2*numberOfOutputDigits)];
>     nid = myToDigits[y,base];
>     {nid //. {a___,0} -> {a}, Length[nid]-2*numberOfOutputDigits}
>     ];
>
> myFromDigits[{digits:{_Integer..},
>       numberOfLeftDigits_Integer /; numberOfLeftDigits >= 1},
>     base_Integer /; base <= -2]:=
>   digits.Table[base^i, {i, numberOfLeftDigits-1,
>   -(Length[digits] - numberOfLeftDigits),-1}];
>
>
> Examples :
>
> In[5]:=myToDigits[123,-10]
>
> Out[5]={2,8,3}
>
>
> In[6]:= myFromDigits[%,-10]
>
> Out[6]=123
>
>
> In[7]:=myToDigits[123.45678,-10,8]
>
> Out[7]={{2,8,4,6,6,4,8,2},3}
>
>
> In[8]:=myFromDigits[%,-10]
>
> Out[8]=6172839/50000
>
>
> In[9]:=N[%,10]
>
> Out[9]=123.4567800
>
>
> v.a.
>

```

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