1 | initial version |

Here are two ways to solve your first problem.

use the Python version of the complex imaginary unit,

`1j`

.sage: R.<x,y> = CC['x,y'] sage: f = x + 1j

*y sage: f x + 1.00000000000000*I*y sage: f.parent() Multivariate Polynomial Ring in x, y over Complex Field with 53 bits of precisionredefine

`I`

to be the imaginary unit in`CC`

.sage: I = CC.gen() sage: I = CC.gen() sage: f = x + I * y sage: f x + 1.00000000000000

*I*y sage: f.parent() Multivariate Polynomial Ring in x, y over Complex Field with 53 bits of precision

Regarding your second problem, the following fails because `R`

is not a principal ideal domain.

```
sage: span([f], R)
```

2 | No.2 Revision |

Here are two ways to solve your first problem.

use the Python version of the complex imaginary unit,

`1j`

.`sage: R.<x,y> = CC['x,y'] sage: f = x +`

~~1j~~*y**1j*y sage: f x +*I*y 1.00000000000000*I*y sage: f.parent() Multivariate Polynomial Ring in x, y over Complex Field with 53 bits of~~1.00000000000000~~~~precision~~precisionredefine

`I`

to be the imaginary unit in`CC`

.`sage: I = CC.gen() sage: I = CC.gen() sage: f = x + I * y sage: f x +`

~~1.00000000000000~~1.00000000000000*I*y sage: f.parent() Multivariate Polynomial Ring in x, y over Complex Field with 53 bits of*I*y~~precision~~precision

Regarding your second problem, the following fails because `R`

is not a principal ideal domain.

```
sage: span([f], R)
```

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