Thanks very much! "radical number" it is, then! At 01:46 PM 10/18/2012, W. Edwin Clark wrote:

I agree that the Maple definition is poorly worded. It does return true for recursively built stuff. For example Maple 16 gives:

...

a:= sqrt(1+sqrt(3)): type(a,radnum); true

...

b:=(a^(1/5)+a^(9/10))^(7/11) + a + 1/2: type(b,radnum); true

On Wed, Oct 17, 2012 at 4:54 PM, Henry Baker <hbaker1@pipeline.com> wrote:

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Hmmm... I speculate that this definition from Maple is poorly worded; I suspect that recursively built stuff like sqrt(1+sqrt2) is allowed within the Maple definition.

Is anyone here from Maple, or does anyone here have a Maple system to try this out on?

At 01:39 PM 10/17/2012, Schroeppel, Richard wrote:

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This appears to exclude recursively built stuff like sqrt(1+sqrt2). --Rich

-----Original Message----- From: Henry Baker [mailto:hbaker1@pipeline.com] Sent: Wednesday, October 17, 2012 10:37 AM To: math-fun Cc: rcs@xmission.com; Schroeppel, Richard Subject: Re: [math-fun] [EXTERNAL] Re: Computing pi (or anything else) to N digits

Maple seems to like "radical number":

http://www.maplesoft.com/support/help/Maple/view.aspx?path=type/radnum

"A radical number is defined as either a rational number or I, or a combination of roots of rational numbers specified in terms of radicals. A sum, product, or quotient of these is also a radical number."

At 07:54 AM 10/17/2012, Schroeppel, Richard wrote:

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Radical numbers?

-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Michael Kleber Sent: Tuesday, October 16, 2012 6:57 PM To: math-fun Subject: [EXTERNAL] Re: [math-fun] Computing pi (or anything else) to N digits

On Mon, Oct 15, 2012 at 10:45 PM, Henry Baker <hbaker1@pipeline.com> wrote:

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"Transcendental" means not the root of any finite polynomial with integer coefficients.

http://en.wikipedia.org/wiki/Transcendental_number

Is there a name for a number which isn't algebraic for a _solvable_ Galois polynomial -- i.e., a number which can't be constructed by rational & root operations?

I think the most common description would be "[not] solvable/expressible by radicals". I don't know of a dedicated term for either state.

--Michael