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Re: Radical conjugates

• To: mathgroup at smc.vnet.net
• Subject: [mg129696] Re: Radical conjugates
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 4 Feb 2013 22:24:23 -0500 (EST)
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• References: <20130204062157.5F2466891@smc.vnet.net>

Clear[radicalConjugate1, radicalConjugate2]

radicalConjugate1[x_] := Module[{c},
  c = Cases[x, Power[_]];
  If[Length[c] > 0, x /. c[[1]] -> -c[[1]], x]]

radicalConjugate2[n_] :=
  n /. (y_.*Sqrt[z_] + x_. -> x - y*Sqrt[z]);

testData = {a + b Sqrt[c], a Sqrt[b] + c Sqrt[d],
   c Sqrt[d] + a Sqrt[b], a Sqrt[b]};

radicalConjugate1 /@ testData

{-a + b Sqrt[c], -a Sqrt[b] + c Sqrt[d], -a Sqrt[b] + c Sqrt[d], -a Sqrt[b]}

radicalConjugate2 /@ testData

{a - b Sqrt[c], -a Sqrt[b] + c Sqrt[d], -a Sqrt[b] + c Sqrt[d], -a Sqrt[b]}

Note the difference in the handling of the first test case.


Bob Hanlon


On Mon, Feb 4, 2013 at 1:21 AM, Francisco Javier Garc=EDa Capit=E1n
<garciacapitan at gmail.com> wrote:
>
> Hello, I wanted a function that takes a numerical expression of the form
>
> a + b Sqrt[c]
>
> or
>
> a Sqrt[b] + c Sqrt[d]
>
> and returns its conjugate, namely a - b Sqrt[c]  and (a Sqrt[b] - c
> Sqrt[d]) respectively.
>
> I wrote
>
> RadicalConjugate[x_] := Module[{c},
>   c = Cases[x, Power[_]];
>   If[Length[c] > 0, x /. c[[1]] -> -c[[1]], x]
>   ]
>
> and it seems that it works. Anyway, do you have a different approach?
>
> Thank you.
>
> --
> ---
> Francisco Javier Garc=EDa Capit=E1n
> http://garciacapitan.99on.com
>
>

• References:
  • Radical conjugates
    • From: Francisco Javier García Capitán <garciacapitan@gmail.com>