1 | initial version |

The problem is adding expressions in `a`

and `B`

.

Your code tries to do that in the second coordinate of `P`

.

Here is a simpler incarnation of your problem.

```
sage: k.<B> = NumberField(x^2 - 2)
sage: k.<a> = NumberField(x^4 - 5*x^2 - 32)
sage: a^2-4*B
Traceback (most recent call last)
...
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with defining polynomial x^4 - 5*x^2 - 32' and 'Number Field in B with defining polynomial x^2 - 2'
```

2 | No.2 Revision |

The problem is adding expressions ~~in ~~involving `a`

and `B`

.

~~Your code tries to do that in the ~~The second coordinate of `P`

in your code is `27*a*(a^2-4*B-5)`

.

Here is a simpler incarnation of your problem.

```
sage: k.<B> = NumberField(x^2 - 2)
sage: k.<a> = NumberField(x^4 - 5*x^2 - 32)
sage: a^2-4*B
Traceback (most recent call last)
...
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with defining polynomial x^4 - 5*x^2 - 32' and 'Number Field in B with defining polynomial x^2 - 2'
```

3 | No.3 Revision |

The problem is adding expressions involving `a`

and `B`

.

The second coordinate of `P`

in your code is `27*a*(a^2-4*B-5)`

.

Here is a simpler incarnation of your problem.

```
sage: k.<B> = NumberField(x^2 - 2)
sage: k.<a> = NumberField(x^4 - 5*x^2 - 32)
sage: a^2-4*B
Traceback (most recent call last)
...
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with defining polynomial x^4 - 5*x^2 - 32' and 'Number Field in B with defining polynomial x^2 - 2'
```

Maybe you need to use relative number fields?

See the documentation for relative number fields at http://doc.sagemath.org/html/en/reference/number_fields/sage/rings/number_field/number_field_rel.html

4 | No.4 Revision |

The problem is adding expressions involving `a`

and `B`

.

The second coordinate of `P`

in your code is `27*a*(a^2-4*B-5)`

.

Here is a simpler incarnation of your problem.

```
sage: k.<B> = NumberField(x^2 - 2)
sage: k.<a> = NumberField(x^4 - 5*x^2 - 32)
sage: a^2-4*B
Traceback (most recent call last)
...
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with defining polynomial x^4 - 5*x^2 - 32' and 'Number Field in B with defining polynomial x^2 - 2'
```

Maybe you need to use relative number fields?

See the documentation for relative number fields at http://doc.sagemath.org/html/en/reference/number_fields/sage/rings/number_field/number_field_rel.html

If instead of the above you define a relative number fields, this works.

```
sage: k.<a> = NumberField(x^4 - 5*x^2 - 32)
sage: K.<B> = k.extension(x^2+2)
sage: a^2-4*B
-4*B + a^2
```

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.