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Using a new functions in libbraiding in zariski_vankampen #39301

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The file zariski_vankampen used some libbraiding functions in order to compute the relations of the group obtained applying Zariski-van Kampen method. The use of the super_summit_set allowed to end computations which did not finish with a straightforward approach. But, when one works with large braid groups, the mehtod super_summit_set can be very long, and running along its output is even longer. The new libbraiding version includes the method super_summit_set_element which simplifies and fasten the computations. The main changes are in method conjugate_positive_form

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  • The title is concise and informative.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation and checked the documentation preview.

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LGTM.

vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 10, 2025
…kampen

<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->

The file `zariski_vankampen` used some `libbraiding` functions in order
to compute the relations of the  group obtained applying Zariski-van
Kampen method. The use of the `super_summit_set` allowed to end
computations which did not finish with a straightforward approach. But,
when one works with large braid groups, the mehtod `super_summit_set`
can be very long, and running along its output is even longer. The new
`libbraiding` version includes the method `super_summit_set_element`
which simplifies and fasten the computations. The main changes are in
method `conjugate_positive_form`

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [X] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->

URL: sagemath#39301
Reported by: Enrique Manuel Artal Bartolo
Reviewer(s): Travis Scrimshaw
vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 12, 2025
…kampen

    
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->

The file `zariski_vankampen` used some `libbraiding` functions in order
to compute the relations of the  group obtained applying Zariski-van
Kampen method. The use of the `super_summit_set` allowed to end
computations which did not finish with a straightforward approach. But,
when one works with large braid groups, the mehtod `super_summit_set`
can be very long, and running along its output is even longer. The new
`libbraiding` version includes the method `super_summit_set_element`
which simplifies and fasten the computations. The main changes are in
method `conjugate_positive_form`


### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [X] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
    
URL: sagemath#39301
Reported by: Enrique Manuel Artal Bartolo
Reviewer(s): Travis Scrimshaw
vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 16, 2025
…kampen

    
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->

The file `zariski_vankampen` used some `libbraiding` functions in order
to compute the relations of the  group obtained applying Zariski-van
Kampen method. The use of the `super_summit_set` allowed to end
computations which did not finish with a straightforward approach. But,
when one works with large braid groups, the mehtod `super_summit_set`
can be very long, and running along its output is even longer. The new
`libbraiding` version includes the method `super_summit_set_element`
which simplifies and fasten the computations. The main changes are in
method `conjugate_positive_form`


### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [X] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
    
URL: sagemath#39301
Reported by: Enrique Manuel Artal Bartolo
Reviewer(s): Travis Scrimshaw
vbraun pushed a commit to vbraun/sage that referenced this pull request Jan 17, 2025
…kampen

    
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->

The file `zariski_vankampen` used some `libbraiding` functions in order
to compute the relations of the  group obtained applying Zariski-van
Kampen method. The use of the `super_summit_set` allowed to end
computations which did not finish with a straightforward approach. But,
when one works with large braid groups, the mehtod `super_summit_set`
can be very long, and running along its output is even longer. The new
`libbraiding` version includes the method `super_summit_set_element`
which simplifies and fasten the computations. The main changes are in
method `conjugate_positive_form`


### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [X] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
    
URL: sagemath#39301
Reported by: Enrique Manuel Artal Bartolo
Reviewer(s): Travis Scrimshaw
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