Class DIMENSIONLESS-QUANTITY

• Defined in theory: Physical-quantities
• Source code: physical-quantities.lisp

Slots on this class:

Documentation:

Although it sounds contradictory, a dimensionless-quantity is a quantity whose dimension is the identity-dimension. All numeric tensors, including real numbers, are nondimensional quantities.

Instance-Of: Class

Subclass-Of: Constant-quantity

Superclass-Of: Real-number

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Slots on instances of this class:

Quantity.Dimension: Identity-dimension

Equivalence Axioms:

(<=> (Dimensionless-Quantity ?X)
     (And (Constant-Quantity ?X)
          (= (Quantity.Dimension ?X) Identity-Dimension)))

Axioms:

(Constant-Quantity ?X)

Other Related Axioms:

(<= (Quantity.Dimension $X Identity-Dimension)
    (Dimensionless-Quantity $X))

(<=> (Dimensionless-Quantity ?X)
     (And (Constant-Quantity ?X)
          (= (Quantity.Dimension ?X) Identity-Dimension)))

(Nth-Domain Magnitude 3 Dimensionless-Quantity)

(Forall (?Q ?Unit ?Mag)
        (=> (And (Constant-Quantity ?Q)
                 (Unit-Of-Measure ?Unit)
                 (Dimensionless-Quantity ?Mag)
                 (Defined (* ?Mag ?Q)))
            (= (Magnitude (* ?Mag ?Q) ?Unit)
               (* ?Mag (Magnitude ?Q ?Unit)))))

(=> (= (Magnitude ?Q ?Unit) ?Mag) (Dimensionless-Quantity ?Mag))

(Nth-Domain Magnitude-In-System-Of-Units 3 Dimensionless-Quantity)

Notes:

• Formerly-Named: nondimensional-constant-quantity