Computing with Impure Numbers: Automatic Consistency Checking and Units Conversion Using Computer Algebra

This note shows how computer-algebra systems may be used to include symbolic physical units in computer calculations, with automatic detection of dimensionally-inhomogeneous formulas and automatic conversion of inconsistent units in a dimensionally-homogeneous formula. Inhomogeneity errors are a prevalent type that is undetected in traditional programming languages, and the user is relieved of the tedious, error-prone units-conversion process.