Requirements
============

Here we outline the key requirements and specifications that guided the design and development of the **PyDASA** as follows:

Manage Dimensional Domain
^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Manage Fundamental Dimensions** beyond traditional physical units (L, M, T) to include computational (T, S, N) and software architecture domains (T, D, E, C, A).
2. **Switch between frameworks** for different problem domains.

Manage Symbolic and Numerical Variables
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Define dimensional parameters** with complete specifications:
    - **Specify** symbolic representation (name, LaTeX symbol).
    - **Define** dimensional formula (e.g., "L*T^-1" for velocity).
    - **Establish** numerical ranges (min, max, mean, step)
    - **Assign** classification (input, output, control).
    - **Configure** statistical distributions and dependencies.
2. **Support progressive enhancement** of variable definitions from symbolic to numerical to probabilistic within a unified class structure.
3. **Compose variables** from modular perspectives addressing conceptual, symbolic, numerical, and probabilistic aspects.

Integrate System of Units of Measurement
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Handle measurements** across unit systems (imperial, metric, custom).
2. **Convert between units** while maintaining dimensional consistency.
3. **Relate measurements** to dimensional parameters.

Discover Dimensionless Coefficients
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Generate dimensionless numbers** using the Buckingham Pi theorem:
    - **Build relevance list** by identifying mutually independent parameters influencing the phenomenon.
    - **Construct dimensional matrix** by arranging FDUs (rows) and variables (columns) into core and residual matrices.
    - **Transform to identity matrix** by applying linear transformations to the core matrix.
    - **Generate Pi coefficients** by combining residual and unity matrices to produce dimensionless groups.
2. **Classify coefficients** by repeating vs. non-repeating parameters.
3. **Manage metadata:** names, symbols, formulas, and parameter relationships.

Analyze and Simulate Coefficient Behavior
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Verify similitude principles** for model scaling and validation.
2. **Calculate coefficient ranges** and parameter influence.
3. **Run Monte Carlo simulations** to quantify uncertainty propagation.
4. **Perform sensitivity analysis** to identify dominant parameters.
5. **Generate behavioral data** for dimensionless relationships.

Export, Integrate, and Visualize Data
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

1. **Export data formats** compatible with pandas, matplotlib, seaborn.
2. **Structure results** for integration with visualization libraries.
3. **Provide standardized outputs** for dimensionless charts and parameter influence plots.