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ucon.basis.builtin

Standard basis instances shipped with ucon.

Built-in dimensional bases shipped with ucon.

Bases

  • SI: The International System of Units (8 components)
  • CGS: Centimetre-gram-second system (3 components)
  • CGS_ESU: CGS electrostatic units (4 components, charge is fundamental)
  • NATURAL: Natural units (1 component, energy)

SI = Basis('SI', [BasisComponent('time', 'T'), BasisComponent('length', 'L'), BasisComponent('mass', 'M'), BasisComponent('current', 'I'), BasisComponent('temperature', 'Θ'), BasisComponent('luminous_intensity', 'J'), BasisComponent('amount_of_substance', 'N'), BasisComponent('information', 'B')]) module-attribute

The International System of Units.

8 base dimensions in canonical order: time, length, mass, current, temperature, luminous_intensity, amount_of_substance, and information (T, L, M, I, Θ, J, N, B).

CGS = Basis('CGS', [BasisComponent('length', 'L'), BasisComponent('mass', 'M'), BasisComponent('time', 'T')]) module-attribute

Centimetre-gram-second system.

3 base dimensions: length, mass, time. Mechanical quantities only.

CGS_ESU = Basis('CGS-ESU', [BasisComponent('length', 'L'), BasisComponent('mass', 'M'), BasisComponent('time', 'T'), BasisComponent('charge', 'Q')]) module-attribute

CGS electrostatic units.

4 base dimensions: length, mass, time, charge. In CGS-ESU, charge is a fundamental dimension (unlike SI where current is fundamental and charge is derived as current * time).

NATURAL = Basis('natural', [BasisComponent('energy', 'E')]) module-attribute

Natural units basis with single energy dimension.

In natural units (particle physics conventions), physical constants c, ℏ, and k_B are set to 1. This collapses length, time, mass, and temperature into expressions of energy:

  • c = 1 → Length and time have same dimension
  • ℏ = 1 → Energy × time is dimensionless
  • k_B = 1 → Temperature is energy

As a result: - Mass [M] → E (via E = mc²) - Length [L] → E⁻¹ (via ℏc/E) - Time [T] → E⁻¹ (via ℏ/E) - Temperature [Θ] → E (via k_B T) - Velocity is dimensionless (c = 1)

Electromagnetic quantities (current, etc.) are not representable in pure natural units and will raise LossyProjection.