1 | initial version |

`ComplexField()`

(in short `CC`

) is the field of floating-point numbers that are *emulated* by MPFR (with 53 bits of precision by default). If instead, you use the `ComplexDoubleField()`

(in short `CDF`

), that is the field of floating-point numbers that the processor can directly work with (with 53bits of precisions as well). Just replace `ComplexField()`

with `CDF`

in you code and you will see how faster it is.

2 | No.2 Revision |

`ComplexField()`

(in short `CC`

) is the field of floating-point numbers that are *emulated* by MPFR (with 53 bits of precision by default). If instead, you use the `ComplexDoubleField()`

(in short `CDF`

), that is the field of floating-point numbers that the processor can directly work with (with 53bits of precisions as well). Just replace `ComplexField()`

with `CDF`

in you code and you will see how faster it is.

That said, note that apparently you lose some roots on the way.

Note that exact computation does not give the same picture: if you use the rational field `QQ`

instead of `ComplexField()`

and look for the roots in the algebraic field `QQbar`

, you get a different picture:

```
sage: sols=s.roots(QQbar, multiplicities=False)
sage: points((i.real(),i.imag()) for i in sols)
```

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