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Scalar

deep_causality_num

Trait Scalar 

Source 
pub trait Scalar:
    Real
    + Div<Output = Self>
    + FromPrimitive { }
Expand description

Scalar sits in the real tower between Real and RealField: it adds division to Real but, unlike a field, does not require a total inverse. That is deliberate, so that Dual qualifies — its ε component is a zero divisor, so it has division yet is not a field. The deep_causality_calculus crate writes its differentiation and integration operators against Scalar, so a single model evaluates at f64 (the value) and at Dual (the derivative).

  • Real supplies ring arithmetic and the elementary functions (the analytic axis), without requiring field division.
  • Div lets Dual itself be a Real, so the tangent functor nests (Dual<Dual<…>> gives higher derivatives).
  • FromPrimitive is the precision-safe constant lift: a model raises its literal constants into the working scalar at any precision (f32 / f64 / Float106, and Dual over each via the blanket impl in this crate). From<f64> is deliberately not used, because f32 does not implement it.

This is distinct from multivector’s ScalarEval (which abstracts a value’s real modulus over Real/Complex for norm work); Scalar is the differentiation variable.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors§

Source§

impl<T: Real + Div<Output = T> + FromPrimitive> Scalar for T

Blanket-implemented, so every qualifying Real number is a Scalar automatically.