Re: Creating a Random Function to Select an Irrational Number

• To: mathgroup at smc.vnet.net
• Subject: [mg102259] Re: Creating a Random Function to Select an Irrational Number
• From: divisor <congruentialuminaire at yahoo.com>
• Date: Mon, 3 Aug 2009 05:46:01 -0400 (EDT)
• References: <h4uf6j\$j2q\$1@smc.vnet.net>

```Hello BenT:

If I understand correctly, 2 of those definitions can be implemented
thusly:

randomIrr[n_Integer]:=Pi^n

randomIrr1[n_Integer] := Module[
{a=RandomInteger[n], b=RandomInteger[n], c, d}
,  c = First /@ FactorInteger[a];
d = First /@ FactorInteger[b];
If[c != d, Log[a, b],(* what to do?? *)0]
]

and invoking these seems to work:

N[randomIrr[500],25]

N[randomIrr1[500],25]

Note that N[] produces inexact numbers.

Also, note that I have only implemented the MathWorld definitions and
have not proved their irrationality.

Regards..

Roger Williams
Franklin Laboratory
On Jul 31, 2:57 am, BenT <brt... at pdmusic.org> wrote:
> Although Mathematica has built-in functiona to obtain random integers and=
real
> numbers, I need to select a random irrational number. At this
> webpage,
>
> http://mathworld.wolfram.com/IrrationalNumber.html
>
> several definitions are given for known conditions to create
> irrational numbers, such as
>
> Numbers of the form n^(1/m) are irrational unless n is the mth power
> of an integer.
>
> Can anyone define a function to allow a similar capability as Random[]
> in selecting a "member" from the above defined "set" of values, or any
> other of the definitions listed on the same webpage?

```

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