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MathGroup Archive 2006

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Re: Code to translate to negative base...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64620] Re: Code to translate to negative base...
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Fri, 24 Feb 2006 00:18:15 -0500 (EST)
  • References: <dte2au$rie$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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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