Crate tuppu_scalar 

Exact scalar arithmetic with uncertainty tracking.

This crate provides the Scalar type which combines:

• SymbolicExpr: Exact symbolic representation in Q(√2,√3,√5)[π,e]
• Ball: Interval arithmetic for uncertainty tracking

Architecture

Scalar = SymbolicExpr + Option<Ball>
         ↓               ↓
     Exact symbolic    Lazy numerical
     computation       bounds

Key Types

• Rational: Arbitrary-precision rationals with GCD overflow protection
• BasisElement: Algebraic basis {1, √2, √3, √5, √6, √10, √15, √30} × {1, π, e, πe, …}
• SymbolicExpr: Sparse linear combination of basis elements
• Ball: Interval [center - radius, center + radius]
• Scalar: The unified type combining symbolic + ball

Example

use tuppu_scalar::{Scalar, SymbolicExpr};

// Create exact values
let half = Scalar::from_ratio(1, 2);
let sqrt2 = Scalar::sqrt2();
let pi = Scalar::pi();

// Arithmetic preserves exactness
let cos_45 = sqrt2.mul(&half);  // √2/2 exactly

// Get numerical approximation when needed
assert!((cos_45.to_f64() - 0.7071067811865476).abs() < 1e-10);

Re-exports

pub use rational::Rational;

pub use ball::Ball;

pub use basis::BasisElement;

pub use symbolic::SymbolicExpr;

pub use scalar::Scalar;

pub use traits::ScalarValue;

pub use traits::MultivectorValue;

pub use error::MathError;

Modules

ball

Ball arithmetic for uncertainty tracking.

basis

Basis elements for the algebraic field Q(√2,√3,√5)[π,e].

error

Error types for scalar arithmetic.

identity

Identity database for exact simplification.

rational

Arbitrary-precision rational numbers with overflow protection.

scalar

The unified Scalar type combining symbolic and ball arithmetic.

symbolic

Sparse symbolic expressions over Q(√2,√3,√5)[π,e].

traits

Trait definitions for scalar and multivector values.

unit

Physical unit system for dimensional analysis.