Help implementing `Scalar` for dual number

[dimforge]

Help implementing `Scalar` for dual number

[sebcrozet]

Are you referring to the Scalar trait from nalgebra there? If so, it is automatically implemented for any type that already implements Copy + PartialEq + Debug + Any.

[ChristopherRabotin]

Yes, I am referring to that Scalar trait.

Allow me to get to the details. I'd like to be able to multiply vectors of Dual<T: Scalar+Num>, but I currently cannot seem to be able to do this (note that the following code requires the latest master from dual_num which isn't published on crates.io yet):

let x = Vector2::new(Dual::from(1.0f64), Dual::from(-2.0f64));
println!("{}", Dual::from(2.0f64) * x);

Which leads to the following error:

Compiling dual_num v0.2.0 (file:///home/chris/Workspace/rust/dual_num)
error[E0277]: cannot multiply `na::Matrix<dual_num::Dual<f64>, na::U2, na::U1, na::MatrixArray<dual_num::Dual<f64>, na::U2, na::U1>>` to `dual_num::Dual<f64>`
   --> tests/lib.rs:247:39
    |
247 |     println!("{}", Dual::from(2.0f64) * x);
    |                                       ^ no implementation for `dual_num::Dual<f64> * na::Matrix<dual_num::Dual<f64>, na::U2, na::U1, na::MatrixArray<dual_num::Dual<f64>, na::U2, na::U1>>`
    |
    = help: the trait `std::ops::Mul<na::Matrix<dual_num::Dual<f64>, na::U2, na::U1, na::MatrixArray<dual_num::Dual<f64>, na::U2, na::U1>>>` is not implemented for `dual_num::Dual<f64>`

error: aborting due to previous error

So I assumed, perhaps incorrectly, that the Scalar trait wasn't implemented because from the following code, I think that PartialEq, Debug and Copy are all implemented.

Note that the Dual struct is defined as follows:

#[derive(Clone, Copy)]
pub struct Dual<T: Scalar>(na::Vector2<T>);
/// ...
impl<T: Scalar + PartialEq> PartialEq<Self> for Dual<T> {
    fn eq(&self, rhs: &Self) -> bool {
        self.0 == rhs.0
    }
}
// ...
impl<T: Scalar + PartialEq> PartialEq<T> for Dual<T> {
    fn eq(&self, rhs: &T) -> bool {
        *self.real_ref() == *rhs
    }
}
/// ...
impl<T: Scalar> Debug for Dual<T> {
    fn fmt(&self, f: &mut Formatter) -> FmtResult {
        f.debug_tuple("Dual").field(self.real_ref()).field(self.dual_ref()).finish()
    }
}

Any hint is appreciated, thanks

[ChristopherRabotin]

For the record:
The solution was trivial (as pointed out by sebcrozet on IRC). The scalar multiplication of a vector must be as vector * x due to the limitations of the compilers (which prevents implementing traits on structs defined by other traits).

Thanks for the support!