floor division (//) for IntegerFactorization objects Implemented

[Hapsa21]

📝 Description

This PR implements the __floordiv__ method for IntegerFactorization objects, enabling the use of the floor division operator (//).

Previously, using // on IntegerFactorization objects (e.g., factor(100) // factor(2)) raised a TypeError. This implementation:

1. Extracts the integer values from the factorization objects.
2. Performs standard integer floor division.
3. Returns the factorization of the result (e.g., factor(50)).

It correctly handles mixed types (e.g., factor(100) // 3) and lets Python raise ZeroDivisionError naturally when dividing by zero.

Fixes #40812.

📝 Checklist

• 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.

⌛ Dependencies

None

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[Hapsa21]

@cxzhong Is this fix ok ?

[yyyyx4]

What is the motivation for this? I don't think I know any algorithms that would require this kind of thing, and in any case, blindly re-factoring the result of the division essentially defeats the purpose of the Factorization object...

[Hapsa21]

What is the motivation for this? I don't think I know any algorithms that would require this kind of thing, and in any case, blindly re-factoring the result of the division essentially defeats the purpose of the Factorization object...

The motivation is to ensure consistency with standard Python operators and improve interactive convenience, as requested in Issue #40812.

Blindly re-factoring is inefficient. I can update the implementation to check for divisibility first and subtract exponents directly where possible, only falling back to full re-factorization when necessary. Would that be fine?