# Ticket #6627(closed defect: fixed)

Opened 4 years ago

## [with patch, positive review] fix lyndon and standard factorization of words

Reported by: Owned by: saliola saliola major sage-4.1.2 combinatorics slabbe Vincent Delecroix Franco Saliola Sage 4.1.2.alpha0

### Description

The last 1 in the word disappeared:

```sage: Word([1,2,1,3,1,2,1]).lyndon_factorization()
(1213.12)
```

Lyndon factorization of the empty word should work.

```sage: Words('01')('').lyndon_factorization()
Traceback (most recent call last):
...
StopIteration
```

The standard factorization of 321 is 32.1.

```sage: sage: Word([3,2,1]).standard_factorization()
(321.)
```

The standard factorization of the empty word should return the empty word, and not two copies of the empty word.

```sage: Words('123')('').standard_factorization()
(.)
```

## Change History

### Changed 4 years ago by saliola

based on sage-4.1.1.alpha0

### comment:1 Changed 4 years ago by saliola

• Summary changed from lyndon and standard factorization of words is broken to [with patch, needs review] fix lyndon and standard factorization of words

This new implementation is correct and also faster.

```sage: sage: Word([1,2,1,3,1,2,1]).lyndon_factorization()
(1213, 12, 1)
sage: sage: Words('01')('').lyndon_factorization()
()
sage: sage: sage: Word([3,2,1]).standard_factorization()
(32, 1)
sage: sage: Words('123')('').standard_factorization()
()
```

I also changed the repr of the (word) Factorization class to use ',' instead of '.' because otherwise the period is confusing if you factor a long word:

```sage: WordOptions(truncate_length=10)
sage: tm = words.ThueMorseWord()
sage: tm[:100].lyndon_factorization()
(011, 01, 0011, 00101101, 0010110011..., 0010110011..., 0010110011..., 0010110011, 0)
```

### comment:2 Changed 4 years ago by vdelecroix

• Reviewers set to vdelecroix

### comment:3 Changed 4 years ago by vdelecroix

• Summary changed from [with patch, needs review] fix lyndon and standard factorization of words to [with patch, positive review] fix lyndon and standard factorization of words

### comment:4 Changed 4 years ago by mvngu

• Status changed from new to closed
• Reviewers changed from vdelecroix to Vincent Delecroix
• Resolution set to fixed
• Merged in set to Sage 4.1.2.alpha0
• Authors set to Franco Saliola

### comment:5 Changed 4 years ago by mvngu

• Milestone changed from sage-combinat to sage-4.1.2
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