Re: a definition : tomic polynomial
- From: quasi <quasi@xxxxxxxx>
- Date: Fri, 24 Aug 2007 23:44:51 -0400
On Fri, 24 Aug 2007 22:31:24 -0400, quasi <quasi@xxxxxxxx> wrote:
On Thu, 23 Aug 2007 17:14:46 EDT, tommy1729 <tommy1729@xxxxxxxxx>
wrote:
just wanted to explain my definition "tomic polynomial"
it might already have a name ; i am unaware of that ...
the reason i post this is because i like algebra and perhaps someone can learn me something nice about these "tomic polynomials". Or someone can give me the real name of them , so that i can look for info on them on the internet e.g.
( ternary polynomial maybe ? )
its also plausable that this concept might arise in the future in one of my threaths , so ill clarify in advance.
i hope it is clearly stated by me...
***
tomic polynomial:
all coefficients are E [-1,0,1]
none of its zero's is a root of unity / [-1,1]
zero is not a root of the polynomial
***
Conjecture:
Every reducible tomic polynomial has at least one nonconstant
irreducible tomic factor.
Well, Maple kills my conjecture ...
The tomic polynomial
x^12 + x^11 + x^9 - x^8 + x^6 - x^4 - x^3 - x + 1
factors into two irreducible polynomials
(x^6 - x^5 + x^4 - x^2 + 2x - 1) (x^6 + 2x^5 + x^4 - x^2 - x - 1)
neither of which is tomic.
quasi
.
- References:
- a definition : tomic polynomial
- From: tommy1729
- Re: a definition : tomic polynomial
- From: quasi
- a definition : tomic polynomial
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