# How It Works

Everything Aero is built around a generic symbolic equation manager.

Instead of hard-coding calculation steps, the solver dynamically assembles and solves
a system of equations based on a large number of equation templates (formulas) and which variables are present/provided.

---

## High-Level Flow

1. User inputs equations, assumptions, and target variables
2. Symbols are extracted and indexed variables are created
3. Equation templates are activated if solvable
4. A symbolic system is assembled
5. The system is solved using sympy
6. Assumptions are relaxed if necessary

The result may include **functions**, not just scalars.

---

## Generic Architecture

The calculator is split into three independent parts:

- Equation engine (generic, reusable)
- Equation templates (domain-specific physics)
- Web UI (built with [ngapp](https://cerbsim.github.io/ngapp))

This makes it easy to:
- Add new equations
- Create calculators for other domains
- Extend physics without changing the solver

Deployment and documentation is automatic using github actions.

---

## Equation Templates

All physics equations are defined as templates.

Example:

```python
aero_eq_manager.add_equation_template(
    equations_to_add=["Re{{i}}=L{{i}} * rho{{i}} * v{{i}} / eta{{i}}"],
    relevant_vars=[
        ("Re",  "Reynolds number [-]"),
        ("L",   "Characteristic length [m]"),
        ("rho", "Air density [kg/m³]"),
        ("v",   "Velocity [m/s]"),
        ("eta", "Dynamic viscosity [Pa·s]")
    ],
    vars_to_check=[(["Re", "L"], 1)],
    name="Reynolds Number"
)
```

```equations_to_add```

- List of strings in lhs = rhs format
- Symbols use {{i}} and {{j}} as index placeholders
- Multi-index equations are expanded automatically

```relevant_vars```

- List of (symbol, description) tuples
- Used for documentation and UI clarity
- Descriptions should be precise to avoid input errors

```vars_to_check```
- List of ([list of symbols to check], n (=number of symbols required)) tuples
- Prevents unsolvable equations from being added
- An equation is activated only if at least n symbols already exist
- Keeps the system solvable and the solver fast

---

## Assumption Handling

If the system is over-constrained:
- Equations involving assumption symbols are selectively removed (iteratively)
- Variables listed in Looking for are preserved where possible
- This process continues until a solution is found or all options are exhausted

---
## Output

Solutions are:
- Symbolic
- Displayed in LaTeX
- Highlighted according to Looking for
- This allows further analysis such as differentiation or evaluation at specific values.