1 | initial version |

Concerning your first question, you can see how to construct a custom poset by typing:

```
sage: Poset?
```

and look for the examples. There are also some pre-built posets in Sage, you can get the list by typing:

```
sage: posets.<TAB>
```

where `<TAB>`

stands for the tabulation.

Concerning your second question, if `L`

denotes the list you constructed, you can build the poset of its elements (viewed as subsets of ${1, 2, 4, 3, 6, 12}$) ordered by the inclusion as follows:

```
sage: PP = Poset(([Set(s) for s in L], attrcall("issubset")))
```

Concerning your third question, the parapeter of the `.order_ideals()`

method is a list of elements of your poset. It returns the elements of `P`

that are smaller of some element of the given list.

In your case:

```
sage: P.order_ideal([12])
[1, 2, 4, 3, 6, 12]
sage: P.order_ideal([4])
[1, 2, 4]
sage: P.order_ideal([6])
[1, 2, 3, 6]
sage: P.order_ideal([6,4])
[1, 2, 4, 3, 6]
sage: P.order_ideal([])
[]
```

2 | No.2 Revision |

Concerning your first question, you can see how to construct a custom poset by typing:

```
sage: Poset?
```

and look ~~for the examples. ~~at the `EXAMPLES:`

section. There are also some pre-built posets in Sage, you can get the list by typing:

```
sage: posets.<TAB>
```

where `<TAB>`

stands for the tabulation.

Concerning your second question, if `L`

denotes the list you constructed, you can build the poset of its elements (viewed as subsets of ${1, 2, 4, 3, 6, 12}$) ordered by the inclusion as follows:

```
sage: PP = Poset(([Set(s) for s in L], attrcall("issubset")))
```

Concerning your third question, the parapeter of the `.order_ideals()`

method is a list of elements of your poset. It returns the elements of `P`

that are smaller of some element of the given list.

In your case:

```
sage: P.order_ideal([12])
[1, 2, 4, 3, 6, 12]
sage: P.order_ideal([4])
[1, 2, 4]
sage: P.order_ideal([6])
[1, 2, 3, 6]
sage: P.order_ideal([6,4])
[1, 2, 4, 3, 6]
sage: P.order_ideal([])
[]
```

3 | No.3 Revision |

Concerning your first question, you can see how to construct a custom poset by typing:

```
sage: Poset?
```

and look at the `EXAMPLES:`

section. There are also some pre-built posets in Sage, you can get the list by typing:

```
sage: posets.<TAB>
```

where `<TAB>`

stands for the tabulation.

Concerning your second question, if `L`

denotes the list you constructed, you can build the poset of its elements (viewed as subsets of ${1, 2, 4, 3, 6, 12}$) ordered by the inclusion as follows:

```
sage: PP = Poset(([Set(s) for s in L], attrcall("issubset")))
```

Concerning your third question, the parapeter of the `.order_ideals()`

method is a list of elements of your poset. It returns the elements of `P`

that are smaller of some element of the given list.

In your case:

```
sage: P.order_ideal([12])
[1, 2, 4, 3, 6, 12]
sage: P.order_ideal([4])
[1, 2, 4]
sage: P.order_ideal([6])
[1, 2, 3, 6]
sage: P.order_ideal([6,4])
[1, 2, 4, 3, 6]
sage: P.order_ideal([])
[]
```

4 | No.4 Revision |

Concerning your first question, you can see how to construct a custom poset by typing:

```
sage: Poset?
```

and look at the `EXAMPLES:`

section. There are also some pre-built posets in Sage, you can get the list by typing:

```
sage: posets.<TAB>
```

where `<TAB>`

stands for the tabulation.

Concerning your second question, if `L`

denotes the list you constructed, you can build the poset of its elements (viewed as subsets of ~~${1, ~~`{1, `

`2, 4, 3, 6, `

) ordered by the inclusion as follows:~~12}$) ~~12}

```
sage: PP = Poset(([Set(s) for s in L], attrcall("issubset")))
```

Concerning your third question, the ~~parapeter ~~parameter of the `.order_ideals()`

method is a list of elements of your poset. It returns the elements of `P`

that are smaller of some element of the given list.

In your case:

```
sage: P.order_ideal([12])
[1, 2, 4, 3, 6, 12]
sage: P.order_ideal([4])
[1, 2, 4]
sage: P.order_ideal([6])
[1, 2, 3, 6]
sage: P.order_ideal([6,4])
[1, 2, 4, 3, 6]
sage: P.order_ideal([])
[]
```

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