Enhance Repository Categorization and Clarify CAS Definitions

[Foadsf]

Issue Description

As the repository grows and includes a broader array of FLOSS Computer Algebra Systems (CAS), valuable feedback suggests the need for better categorization and more precise definitions regarding the nature of the tools listed. This issue addresses these points by categorizing the tools into more specific groups and clarifying which tools are inherently CAS and which are libraries or languages that can perform CAS functions with additional libraries.

Proposed Categories

1. Domain-Specific CAS Languages:

   • Example: Maxima, REDUCE
   • These are standalone environments explicitly designed for symbolic mathematics.

2. Languages with CAS Libraries:

   • General-Purpose Languages
     • Example: Python with SymPy
     • These are not CAS by nature but can perform CAS tasks through specific libraries.
   • Domain-Specific Languages for Numerical and Algebraic Calculations:
     • Example: Scilab, Octave, Julia
     • These languages are specifically designed for numerical computations such as linear algebra and can perform CAS tasks through specific libraries.

3. CAS Libraries:

   • Interpreted Libraries:
     • Example: SymPy (Python)
     • These libraries are used within an interpreted language and do not require compilation, making them accessible for rapid prototyping and use.
   • Compiled Libraries:
     • Example: GiNaC (C++)
     • These require compilation and are typically used to integrate CAS capabilities into applications written in compiled languages.

4. User Interfaces, Editors, and IDEs for CAS:

   • Example: WxMaxima, Jupyter, Spyder, MathAction
   • These tools provide environments and interfaces that enhance the usability of CAS tools, either as standalone applications or as part of larger systems.

Tools Needing Clarification

Several tools have been mentioned which might require further discussion to determine if they should be included as FLOSS and/or CAS:

• Scilab
• Octave
• SageMath
• GAP
• PARI/GP
• Singular
• CoCoA

Task List

• Categorize all listed tools under the proposed categories.
• Verify the FLOSS status and CAS capabilities of Scilab, Octave, SageMath, GAP, PARI/GP, Singular, and CoCoA.
• Update the README with these categorizations and clarifications.
• Solicit community feedback on the proposed changes.

Call for Contributions

I am excited to see contributors help with this task by researching the tools, suggesting categorizations, and updating documentation. This will help make our repository a more structured and informative resource for everyone interested in FLOSS CAS tools.

Thank you for your support and contributions!