# AxiomX

**AxiomX** is a lightweight Python scientific math library focused on numerical computation, series-based evaluation, and foundational mathematical functions.
It is designed to be simple, fast and extensible—ideal for learning, experimentation, and building advanced math systems.
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## 🚀 Features

### 📚 Constants (included in `AxiomX.constants`)
* `pi`
* `e`
* lemniscate constant (`lemniscate`)
* gauss constant (`gauss`)
* `infinity`
* square roots of 2, 3 and 5 (`sqrt_2`, `sqrt_3`, `sqrt_5`)
* golden ratio (`golden_ratio`)
* silver ratio (`silver_ratio`)
* `metallic_ratio(n)` - Returns the metallic ratio of the order n.
* euler-mascheroni constant (`euler_mascheroni`)


### 🔢 Mathematical Functions (included in `AxiomX.functions`)

* `absolute(x)`
* `sqrt(n)` - using Halley's Method
* `cbrt(n)` - using Newton-Raphson Method
* `gamma(x)`
* `factorial(n)` - using gamma function
* `zeta(n)` - returns the Riemann Zeta function evaluated at n
* `beta(n)` - returns the Dirichlet Beta function evaluated at n
* `bc(n, k)` - returns the binomial coefficient evaluated at n and k
* `pascal(row)` - returns a list containing all the numbers at the *row*th row in the Pascal Triangle.

### 📈 Exponential Functions (included in `AxiomX.exp`)

* `exp(n)` - returns e^n, where e is Euler's number.
* `ln(x)` - returns the natural logarithm of *x*.
* `log10(x)` - returns the common logarithm of *x*.
* `log2(x)` - returns the binary logarithm of *x*.
* `log(arg, base)` - returns the logarithm of *arg* to the base *base*.

### 📐 Trigonometric Functions (included in `AxiomX.trig`)

- `sin(x)` — Calculated from Taylor series expansion
- `cos(x)` — derived from sine
- `tan(x)`, `cot(x)`, `sec(x)`, `cosec(x)`
- `radians(deg)` — degrees → radians  
- `degrees(rad)` — radians → degrees  

### 🔄 Inverse Trigonometric Functions (also included in `AxiomX.trig`)

- `arcsin(x)` — Newton's method
- `arccos(x)`
- `arctan(x)`
- `arccot(x)`
- `arcsec(x)`
- `arccosec(x)`

### 🔥 Hyperbolic Functions and Inverse Functions (included in `AxiomX.hyperbolic`)

* `sinh(x)` - calculated using formula
* `cosh(x)`, `tanh(x)`, `sech(x)`, `cosech(x)`, `coth(x)`
* `arcsinh(x)`, `arccosh(x)`, `arctanh(x)`, `arccoth(x)`, `arcsech(x)`, `arccosech(x)`
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## 🧠 Usage

```
from AxiomX import trig, constants, calculus

print(trig.sin(constants.pi)) # prints 0
print(calculus.converges(lambda x: 1 / x)) # prints False
```
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## 🛣️ Roadmap

Upcoming improvements:
* Limit evaluation engine
* Convergence detection for series
* Combinatorics utilities, Pascal's Triangle
* Performance optimizations.
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## 🤝 Contributing

Contributions are welcome!\You can help by:
* Reporting bugs in our [Discord](https://discord.com/channels/1484861326324138016/1484861327209140366)
* Adding suggestions
* Improving performance.
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## 📦 Installation

You can install AxiomX by going into the terminal and typing *pip install AxiomX*.
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## 📄 License

This software is licensed under MIT and no one is supposed to copy code from AxiomX.
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## 🌐 Links

Website: [https://axiomxpy.wordpress.com](https://axiomxpy.wordpress.com)\
Discord Invite: [https://discord.gg/CrEf8mDB](https://discord.gg/CrEf8mDB)
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## ⭐ Support
If you like AxiomX, consider:
* Sharing it with other friends
* Using it in your projects
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