Module dimension 

Physical dimensions as an abelian group of rational exponent vectors.

A dimension is what a quantity measures — length, mass, time, or a product/quotient of them (area = L², speed = L·T⁻¹, force = M·L·T⁻²). It is NOT a unit: metres and feet share the dimension Length. We model a dimension as a vector of rational exponents over the base dimensions, so dimensional algebra is exact vector arithmetic:

• × adds exponent vectors (Length × Length = Length²),
• ÷ subtracts them (Area ÷ Length = Length),
• integer powers scale them, and the nth root divides them (so √(Length²) = Length).

Exponents are rational (not just integer) because real derived quantities need fractional powers — noise density is V·Hz^(−1/2). The group’s identity is the dimensionless vector; every dimension has an inverse (recip). Dimension is Copy + Eq + Hash, so it is a cheap catalog key, rides inside the compiler’s type lattice, and tags a runtime quantity.

Structs

Dimension

A physical dimension: a vector of rational exponents over BaseDim. The group operation is mul (axiswise exponent addition); the identity is Dimension::DIMENSIONLESS; the inverse is Dimension::recip.

Exp

A signed rational exponent in lowest terms with a strictly positive denominator — so equal exponents share one representation (Eq/Hash are structural). Admits fractional powers (L^(1/2)) while the common integer case is just den == 1.

Enums

BaseDim

The base dimensions: the SI seven, plus the extensions Logos tracks end-to-end. Plane angle and solid angle are SI-dimensionless but tracked here to catch radian/steradian mix-ups; information (the bit) is tracked so data sizes are first-class. “Dimensionless” is the all-zero vector, not an axis.