sagemathgh-37209: Added rational Tamari lattices
    
Added the possibility to provide a rational slope parameter m in the
GeneralizedTamariLattice method.
The lattice property is no longer conjectural so the check parameter is
not necessary anymore.
Also updated the references.

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URL: sagemath#37209
Reported by: Cchenevi
Reviewer(s): Frédéric Chapoton

sagemathgh-37221: Added the alt nu-tamari lattices
    
The alt nu-Tamari lattices are a generalization of the nu-Tamari
lattices. These lattices depend on a North-East path `\nu` and an
integer sequence `\delta`, which is an increment vector with respect to
`\nu`. A special choice of `\delta` gives the classical nu-Tamari
lattice, and another choice of `\delta` gives the inclusion order on
`\nu`-paths---North-East paths weakly above the path `\nu`.

These partial orders are implemented in the nu_tamari_lattice module.
The special case of the nu-Tamari lattice can be recovered by not
precising any vector delta, and benchmark tests suggest that this new
method is in fact slightly more efficient than the previous one, even in
this case.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [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 accordingly.

### ⌛ Dependencies

sagemath#37209
    
URL: sagemath#37221
Reported by: Cchenevi
Reviewer(s): Cchenevi, Frédéric Chapoton

sagemathgh-37221: Added the alt nu-tamari lattices
    
The alt nu-Tamari lattices are a generalization of the nu-Tamari
lattices. These lattices depend on a North-East path `\nu` and an
integer sequence `\delta`, which is an increment vector with respect to
`\nu`. A special choice of `\delta` gives the classical nu-Tamari
lattice, and another choice of `\delta` gives the inclusion order on
`\nu`-paths---North-East paths weakly above the path `\nu`.

These partial orders are implemented in the nu_tamari_lattice module.
The special case of the nu-Tamari lattice can be recovered by not
precising any vector delta, and benchmark tests suggest that this new
method is in fact slightly more efficient than the previous one, even in
this case.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [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 accordingly.

### ⌛ Dependencies

sagemath#37209
    
URL: sagemath#37221
Reported by: Cchenevi
Reviewer(s): Cchenevi, Frédéric Chapoton

sagemathgh-37221: Added the alt nu-tamari lattices
    
The alt nu-Tamari lattices are a generalization of the nu-Tamari
lattices. These lattices depend on a North-East path `\nu` and an
integer sequence `\delta`, which is an increment vector with respect to
`\nu`. A special choice of `\delta` gives the classical nu-Tamari
lattice, and another choice of `\delta` gives the inclusion order on
`\nu`-paths---North-East paths weakly above the path `\nu`.

These partial orders are implemented in the nu_tamari_lattice module.
The special case of the nu-Tamari lattice can be recovered by not
precising any vector delta, and benchmark tests suggest that this new
method is in fact slightly more efficient than the previous one, even in
this case.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [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 accordingly.

### ⌛ Dependencies

sagemath#37209
    
URL: sagemath#37221
Reported by: Cchenevi
Reviewer(s): Cchenevi, Frédéric Chapoton