# det-rs
Calculate the determinant of a square matrix using a Rust macro
This macro should not be used directly. Instead, it should be called inside a function that is used elsewhere.
## Usage
Calculate the area of a parallelogram:
```rust
pub fn find_orthonormal_4(a: &Vector2<f32>, b: &Vector2<f32>) -> f32 {
det_copy!(a.x, a.y,
b.x, b.y)
}
```
Calculate a 4D orthogonal vector using nalgebra:
```rust
pub fn find_orthonormal_4(a: &Vector4<f32>, b: &Vector4<f32>, c: &Vector4<f32>) -> Vector4<f32> {
det_copy!(Vector4::x(), Vector4::y(), Vector4::z(), Vector4::w(),
a.x, a.y, a.z, a.w,
b.x, b.y, b.z, b.w,
c.x, c.y, c.z, c.w )
}
```
Usually `det!` should be used in these cases, but strangely, it causes a type recursion error,
so we use `det_copy!` instead. Note, that the constructors (eg. `Vector4::x()`) are executed multiple times.
To avoid this, bind the vectors to a variable first and pass in the variable instead.
## Requirements
There are various macros for various types of values.
- `det_copy!`
1. `T: Copy`
2. `T: Mul<T, Output=T>`
3. `T: Sub<T, Output=T>`
4. `T: Add<T, Output=T>`
- `det_clone!`
1. `T: Clone`
2. `T: Mul<T, Output=T>`
3. `T: Sub<T, Output=T>`
4. `T: Add<T, Output=T>`
- `det!`
1. `T: Mul<T, Output=T>`
2. `for<'a> &'a T: Mul<T, Output=T>`
3. `for<'a, 'b> &'a T: Mul<&'b T, Output=T>`
4. `T: Sub<T, Output=T>`
5. `T: Add<T, Output=T>`