1 | initial version |

Indeed, in Sage the name of the undeterminates matters. You can define the mapping as follows:

```
sage: h = bRing.hom([aa])
sage: h
Ring morphism:
From: Number Field in a with defining polynomial b^2 + 1
To: Number Field in a with defining polynomial a^2 + 1
Defn: a |--> a
sage: h(bb) == aa
True
```

2 | No.2 Revision |

Indeed, in Sage the name of the undeterminates ~~matters. ~~matters, this is not a bug. Think about the multivariate case to be convinced of the reason why.

You can define the mapping as follows:

```
sage: h = bRing.hom([aa])
sage: h
Ring morphism:
From: Number Field in a with defining polynomial b^2 + 1
To: Number Field in a with defining polynomial a^2 + 1
Defn: a |--> a
sage: h(bb) == aa
True
```

3 | No.3 Revision |

Indeed, in Sage the name of the ~~undeterminates ~~indeterminates matters, this is not a bug. Think about the multivariate case to be convinced of the reason why.

You can define the mapping as follows:

```
sage: h = bRing.hom([aa])
sage: h
Ring morphism:
From: Number Field in a with defining polynomial b^2 + 1
To: Number Field in a with defining polynomial a^2 + 1
Defn: a |--> a
sage: h(bb) == aa
True
```

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