Re: Easiest Mathematica algorhitm needed

• To: mathgroup at smc.vnet.net
• Subject: [mg92822] Re: Easiest Mathematica algorhitm needed
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 14 Oct 2008 04:57:31 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gcq09i\$c30\$1@smc.vnet.net> <200810120835.EAA08892@smc.vnet.net> <gcv7ef\$e31\$1@smc.vnet.net>

```Artur wrote:

> Who know which Matrhematica function uses to separate square free part
> of number.

Pattern matching seems the more appropriate.

> e.g.
> In[1]: Table[Sqrt[n!], {n, 1, 10}]
> Out[1]: {1, Sqrt[2], Sqrt[6], 2 Sqrt[6], 2 Sqrt[30], 12 Sqrt[5], 12
> Sqrt[35],
>  24 Sqrt[70], 72 Sqrt[70], 720 Sqrt[7]}
> What to do to take squre-free parts:
> {1, 2, 6, 6, 30, 5, 35, 70, 70, 7}

In[1]:= lst = Table[Sqrt[n!], {n, 1, 10}]

Out[1]= {1, Sqrt[2], Sqrt[6], 2 Sqrt[6], 2 Sqrt[30], 12 Sqrt[5],
12 Sqrt[35], 24 Sqrt[70], 72 Sqrt[70], 720 Sqrt[7]}

In[2]:= Cases[lst, ___*Sqrt[n_] | Sqrt[n_] -> n]

Out[2]= {2, 6, 6, 30, 5, 35, 70, 70, 7}

> or square parts
> {1, 1, 1, 2, 2, 12, 12, 24, 72, 720}

In[3]:= List @@ lst /. Sqrt[__] -> 1

Out[3]= {1, 1, 1, 2, 2, 12, 12, 24, 72, 720}

HTH,
-- Jean-Marc

```

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