Re: [math-fun] [EXTERNAL] Re: Computing pi (or anything else) to N digits
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:
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:
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:
"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
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:
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:
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:
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:
"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
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