Is there a commonly accepted notation for algebraic numbers?

Question

In this question I needed a way to denote an algebraic number using a polynomial equation it satisfies and its isolating polynomial. Because I am not aware of any commonly accepted notation for this, I resorted to an explanation in English.

But I recall that I saw somewhere a notation like this: $$\rho=\left[12\,x^8-12\,x^4-8\,x^2-1\right]_{1<x<2}$$

Is it commonly accepted and understandable? If not, can you suggest another good notation for that?

MathWorld sometimes uses a similar notation (see below the formula $(19)$ at the bottom of this page), but with a root index rather than an isolating interval in the subscript. I do not think it is very common though. — Vladimir Reshetnikov, Dec 01 '13 at 23:06
I think that notation is fine, in fact it looks pretty good to me. — goblin GONE, Sep 17 '15 at 01:07

score 4 · Answer 1 · answered Dec 01 '13 at 22:56

4

I have not seen the notation you have used. The easiest way is to write it out explicitly, i.e., $\rho$ is such that $\rho \in (1,2)$ and is a root of $f(x) = 12x^8 - 12 x^4 - 8x^2 - 1$.

answered Dec 01 '13 at 22:56

score 0 · Answer 2 · answered Sep 17 '15 at 01:07

0

You can use the definite description quantifier. As in:

$$\mathop{\iota}_{x:(1,2)}(0=12x^8−12x^4−8x^2−1)$$

But, I prefer your notation.

answered Sep 17 '15 at 01:07

goblin GONE

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Is there a commonly accepted notation for algebraic numbers?

2 Answers2