1 | initial version |

Try using polynomials a polynomial ring.

Then you can define

- two polynomials in it,
- the rational fraction obtained by dividing one by the other
- the quotient and remainder

Define a polynomial ring:

```
sage: R.<x> = QQ[]
```

Or just a polynomial ring generator:

```
sage: x = polygen(QQ)
```

Define two polynomials:

```
sage: a = 3*x^3 + x^2 - 3*x + 5
sage: b = x + 1
```

Divide:

```
sage: c = a / b
sage: c
3*x^3 + x^2 - 3*x + 5)/(x + 1)
```

Quotient and remainder

```
sage: q = a // b
sage: q
3*x^2 - 2*x - 1
sage: r = a % b
sage: r
6
```

Both at once

```
sage: q, r = a.quo_rem(b)
sage: q
3*x^2 - 2*x - 1
sage: r
6
```

Check:

```
sage: q + r/b
(3*x^3 + x^2 - 3*x + 5)/(x + 1)
```

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