Re: a definition : tomic polynomial

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.

quasi

What's the ring here? Are -1, 0, and 1 considered to be in the
complex number system, or are they the multiplicative identity (and
its additive inverse) in any ring - along with the additive identity?

Irrecducibility varies depending on the ring structure.

Now, if your coefficients are considered as complex numbers, then the
Fundamental Theorem of Algebra affirms your conjecture.

I haven't seen the post prior to this, so I might be missing something
simple.

Thanks,

Brian

.

Relevant Pages

  • Re: a definition : tomic polynomial
    ... the reason i post this is because i like algebra and perhaps someone can learn me something nice about these "tomic polynomials". ... What's the ring here? ... with integer coefficients. ... Fundamental Theorem of Algebra affirms your conjecture. ...
    (sci.math)
  • Re: a definition : tomic polynomial
    ... the reason i post this is because i like algebra and perhaps someone can learn me something nice about these "tomic polynomials". ... zero is not a root of the polynomial ...
    (sci.math)
  • Re: a definition : tomic polynomial
    ... the reason i post this is because i like algebra and perhaps someone can learn me something nice about these "tomic polynomials". ... zero is not a root of the polynomial ...
    (sci.math)
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