all algebraic numbers in a sequence

The beginning of the sequence of all algebraic numbersMathworldPlanetmath ordered as explained in the parent ( entry is as follows:

0;-1, 1;-2,-12,-i,i,12, 2;-3,-1-52,-2,-12,1-52,-1-i32,-1+i32,-13,

-i2,-i2,i2,i2,13,1-i32,1+i32,-1+52,12,2,1+52, 3;

The first number corresponds to the algebraic equationx=0,  the two following numbers to the equations  x±1=0,  the six following to the equations  x±2=0,  2x±1=0,  x2+1=0,  the twenty following to the equations  x±3=0,  3x±1=0,  x2±x±1=0,  x2±2=0,  2x2±1=0.

In practice, one cannot continue the sequence very far since the higher degree equations – quintic and so on – are non-solvable by radicalsPlanetmathPlanetmathPlanetmathPlanetmath (; instead we can list the equations satisfied by the numbers as far we want and tell how many roots ( they have.  In principle, the number sequence does exist!

Title all algebraic numbers in a sequence
Canonical name AllAlgebraicNumbersInASequence
Date of creation 2013-03-22 15:13:58
Last modified on 2013-03-22 15:13:58
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 11
Author pahio (2872)
Entry type Result
Classification msc 11R04
Classification msc 03E10
Synonym counting the algebraic numbers
Related topic FieldOfAlgebraicNumbers