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Adapt QQBar documentation
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lgoettgens committed Apr 17, 2024
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24 changes: 6 additions & 18 deletions docs/src/algebraic.md
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Nemo allows working with exact real and complex algebraic numbers.

The default algebraic number type in Nemo is provided by Calcium. The
associated field of algebraic numbers is represented by the constant
parent object called `CalciumQQBar`.
associated field of algebraic numbers can be constructed using
`QQBar = algebraic_closure(QQ)`.

For convenience we define

```
QQBar = CalciumQQBar
```

so that algebraic numbers can be constructed using `QQBar` instead of
`CalciumQQBar`. Note that this is the name of a specific parent object,
not the name of its type.


Library | Element type | Parent type
----------------|---------------|--------------------
Calcium | `QQBarFieldElem` | `QQBarField`
Library | Element type | Parent type
----------------|------------------|--------------------
Calcium | `QQBarFieldElem` | `QQBarField`

**Important note on performance**

Expand All @@ -38,8 +27,7 @@ For fast calculation in $\overline{\mathbb{Q}}$,
`CalciumField` should typically be used instead (see the section
on *Exact real and complex numbers*).
Alternatively, to compute in a fixed subfield of $\overline{\mathbb{Q}}$,
you may fix a generator $a$ and construct an
Antic number field to represent $\mathbb{Q}(a)$.
you may fix a generator $a$ and construct a number field to represent $\mathbb{Q}(a)$.

## Algebraic number functionality

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2 changes: 1 addition & 1 deletion docs/src/exact.md
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## Conversions and numerical evaluation

Calcium numbers can created from integers (`ZZ`), rationals (`QQ`)
and algebraic numbers (`QQbar`), and through the application of
and algebraic numbers (`algebraic_closure(QQ)`), and through the application of
arithmetic operations and transcendental functions.

Calcium numbers can be converted to integers, rational and algebraic fields
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