Re: Factorizing...

• To: mathgroup at smc.vnet.net
• Subject: [mg74150] Re: Factorizing...
• From: "Valeri Astanoff" <astanoff at gmail.com>
• Date: Mon, 12 Mar 2007 22:11:22 -0500 (EST)
• References: <esr0lj\$6hp\$1@smc.vnet.net>

```On 9 mar, 08:00, "Bruno Campanini" <B... at gmail.com> wrote:
> How can I get it from Mathematica:
>
> Factor[2+SQR(5)] = ((1+SQR(5))/2)^3
>
> ???
>
> Bruno

Good day,

Here is a DIY way to do it :

In[1]:=myFactor[p_+(q_:1)Sqrt[r_],maxi_:5]:=
Module[{y,a,b,c,n},
Table[If[Simplify[p+q* Sqrt[r] == (y=(a+b *Sqrt[r])*
(c+Sqrt[r])/n)],y],
{a,-maxi,maxi},{b,-maxi,maxi},{c,-maxi,maxi},{n,1,maxi}]//
Flatten//Cases[#,x_/;!MatchQ[x,(p+q*Sqrt[r]|Null)]]& //
Cancel//Union
];

In[2]:=myFactor[2 + Sqrt[5]]

Out[2]={(1/4)*(1+Sqrt[5])*(3+Sqrt[5]),(5+2*Sqrt[5])/Sqrt[5]}

In[3]:=(1/4)*(1+Sqrt[5])*myFactor[3+Sqrt[5]]

Out[3]={(1/8)*(1+Sqrt[5])^3,
(1/4)*(-1+Sqrt[5])*(1+Sqrt[5])*(2+Sqrt[5]),
(-(1/20))*(-5+Sqrt[5])*(1+Sqrt[5])*(5+2*Sqrt[5]),
((1+Sqrt[5])*(5+3*Sqrt[5]))/(4*Sqrt[5])}

In[4]:=%//Simplify

Out[4]={2+Sqrt[5],2+Sqrt[5],2+Sqrt[5],2+Sqrt[5]}

V.Astanoff

```

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