Domain module refactoring

[GiovanniCanali]

Description

This PR fixes #574

Checklist

• Code follows the project’s Code Style Guidelines
• Tests have been added or updated
• Documentation has been updated if necessary
• Pull request is linked to an open issue

[GiovanniCanali]

This PR introduces the following improvements:

• Renames files to align with the PINA naming conventions (see Names convention #445).
• Separates the abstract interface from the base classes (see Adding base classes with only method definition #672).
• Implements the partial method for all domains and set operations, enabling full-boundary retrieval.
• Fixes uniform sampling for EllipsoidDomain and SimplexDomain, ensuring a truly uniform distribution.
• Redefines the sampling strategy for improved speed and robustness.
• Adds stricter, shared validation checks across all domains to prevent initialization issues.
• Expands the test suite for domains and set operations.
• Updates tutorial6.

These modifications do not affect the user experience, aside from the new additions.

[GiovanniCanali]

MEMO: if #717 is merged into dev before this PR, fix the conditions related to the spatial boundaries (use partial method).

[FilippoOlivo]

Hi @GiovanniCanali, thank you for the PR. It is a great improvement PINA geometries. I started the review and I have some doubts about how BaseDomain is structured. Specifically in how sampling modes are handled. I leaved some comments on the involved lines of code. I will continue the review and give you a feedback also on other classes soon

[FilippoOlivo]

Are these available for all the domains?

[GiovanniCanali]

__AVAILABLE_MODES stores all sampling modes defined in PINA. Each domain generally uses only a subset of these modes. In the __init__ of every class inheriting from BaseDomain, you’ll find a line like:

self.sample_modes = [...]

This calls the corresponding setter, which serves two purposes:

1. It defines the sampling modes available for that specific domain.
2. It validates the mode defined in the __init__, raising an error if it is not included in __AVAILABLE_MODES.

The only exception is CartesianDomain, which does not call the setter (it does not even have a __init__), because its available modes coincide exactly with the full set in __AVAILABLE_MODES.

[GiovanniCanali]

Basically, this is just a variable storing all available modes. Through the setter, each domain defines a subset of these values.

[FilippoOlivo]

In my opinion, it is better to have a distance __AVAILABLE_MODES for each subclass

[FilippoOlivo]

I think the name of the variable is not the best one. Can you rename it like "variables_dict"?

[FilippoOlivo]

Can you make a separate function for that?

[GiovanniCanali]

Deleted previous comment, that was my mistake.

I would keep this logic inside the same function: the base class __init__ performs all necessary checks, and this behavior belongs to that same scope.