I would expect "constructible" to be short for "ruler-and-compass constructible", so to only allow square roots. --Michael On Tue, Oct 16, 2012 at 9:30 PM, Henry Baker <hbaker1@pipeline.com> wrote:
Perhaps we can call an algebraic number that can be represented with rational ops and roots a "constructible" number.
Then what I want is a non-constructible algebraic number.
Is there a shorter and/or traditional name for non-constructible algebraic number?
At 05:56 PM 10/16/2012, Michael Kleber wrote:
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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