1 | initial version |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic \pi`, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case,`

8.0`is first transformed into a symbolic`

8.0|`and then divided by the symbolic`

pi`, which results in an element of the symbolic ring.

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of $pi$, which is `RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

2 | No.2 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic ~~\pi~~

case, `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that ~~case,~~`8.0`

symbolic ` is first transformed into a `

~~symbolic~~`8.0|`

pi`, symbolic ` and then divided by the `

~~symbolic~~`\pi`

, which results in an element of the symbolic ring.

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of $pi$, which is `RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

3 | No.3 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic

and then divided by the symbolic ~~8.0|~~8.0

, which results in an element of the symbolic ring.~~\pi~~pi

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of ~~$pi$, ~~$`pi$, `

`which `

RR.pi()`:~~is ~~is`RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

4 | No.4 Revision |

`sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of ~~$~~`pi$, `

`$pi$, which `

RR.pi()`:is ~~is~~`RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

5 | No.5 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you ~~noticed, ~~noticed in your first example, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of $pi$, which is `RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

6 | No.6 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed in your first example, the `sqrt`

method for integers returns elements of the symbolic ring.

When you write `80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

`RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

7 | No.7 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed in your first example, the `sqrt`

method for (non square) integers returns elements of the symbolic ring.

`80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

`RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

8 | No.8 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed in your first example, the `sqrt`

method for (non square) integers returns elements of the symbolic ~~ring.~~ring `SR`

.

`80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

`RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

Note that `pi`

is nothing else than `SR.pi()`

, you can redefine `pi = RR.pi()`

if you want to type things more easily.

9 | No.9 Revision |

When you write `sqrt(8.0)`

, Sage calls the `sqrt`

method of the floating-point number 8.0 (an element of `RR`

). Hence you get a floating-point number. As you noticed in your first example, the `sqrt`

method for (non square) integers returns elements of the symbolic ring `SR`

.

`80.0 / pi`

, Sage uses *coercion* (look at the manual for more details about this important concept in Sage) : it first searches for the common parent between floating-point `8.0`

and symbolic `pi`

, which is the symbolic ring, it transforms the two elements in this parent, and does the division there. So, in that case, `8.0`

is first transformed into a symbolic `8.0`

and then divided by the symbolic `pi`

, which results in an element of the symbolic ring.

If you want the division between two floating-point numbers, and get a floating-point number, you can use the floating-point number version of ~~$pi$, ~~$\pi$, which is `RR.pi()`

:

```
sage: 8.0 / RR.pi()
2.54647908947033
```

Note that `pi`

is nothing else than `SR.pi()`

, you can redefine `pi = RR.pi()`

if you want to type things more easily.