1 | initial version |

Perhaps mathematica is not able to answer since you do not say over which ring you want your element to be integral ($\mathbb{Z} ??$). In your case, you can get conviced by typing:

```
sage: P = a.absolute_minpoly() ; P
x^6 - 2*x^3 + 2
sage: P(a)
0
sage: P in ZZ[x]
True
sage: P.is_monic()
True
```

2 | No.2 Revision |

~~Perhaps mathematica is not able to answer since you do not say over which ring you want your element to be integral ($\mathbb{Z} ??$). ~~In your case, you can get conviced by typing:

```
sage: P = a.absolute_minpoly() ; P
x^6 - 2*x^3 + 2
sage: P(a)
0
sage: P in ZZ[x]
True
sage: P.is_monic()
True
```

3 | No.3 Revision |

In your case, you can get conviced by typing:

```
sage: P = a.absolute_minpoly() ; P
x^6 - 2*x^3 + 2
sage: P(a)
0
sage: P in ZZ[x]
True
sage: P.is_monic()
True
```

https://en.wikipedia.org/wiki/Algebraic_integer

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.