(maxima.info)Introduction to ezunits

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57.1 Introduction to ezunits
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'ezunits' is a package for working with dimensional quantities,
including some functions for dimensional analysis.  'ezunits' can carry
out arithmetic operations on dimensional quantities and unit
conversions.  The built-in units include Systeme Internationale (SI) and
US customary units, and other units can be declared.  See also
'physical_constants', a collection of physical constants.

   'load("ezunits")' loads this package.  'demo("ezunits")' displays
several examples.  The convenience function 'known_units' returns a list
of the built-in and user-declared units, while
'display_known_unit_conversions' displays the set of known conversions
in an easy-to-read format.

   An expression a ` b represents a dimensional quantity, with 'a'
indicating a nondimensional quantity and 'b' indicating the dimensional
units.  A symbol can be used as a unit without declaring it as such;
unit symbols need not have any special properties.  The quantity and
unit of an expression a ` b can be extracted by the 'qty' and 'units'
functions, respectively.

   A symbol may be declared to be a dimensional quantity, with specified
quantity or specified units or both.

   An expression a ` b `` c converts from unit 'b' to unit 'c'.
'ezunits' has built-in conversions for SI base units, SI derived units,
and some non-SI units.  Unit conversions not already known to 'ezunits'
can be declared.  The unit conversions known to 'ezunits' are specified
by the global variable 'known_unit_conversions', which comprises
built-in and user-defined conversions.  Conversions for products,
quotients, and powers of units are derived from the set of known unit
conversions.

   As Maxima generally prefers exact numbers (integers or rationals) to
inexact (float or bigfloat), so 'ezunits' preserves exact numbers when
they appear in dimensional quantities.  All built-in unit conversions
are expressed in terms of exact numbers; inexact numbers in declared
conversions are coerced to exact.

   There is no preferred system for display of units; input units are
not converted to other units unless conversion is explicitly indicated.
'ezunits' recognizes the prefixes m-, k-, M, and G- (for milli-, kilo-,
mega-, and giga-) as applied to SI base units and SI derived units, but
such prefixes are applied only when indicated by an explicit conversion.

   Arithmetic operations on dimensional quantities are carried out by
conventional rules for such operations.

   * (x ` a) * (y ` b) is equal to (x * y) ` (a * b).
   * (x ` a) + (y ` a) is equal to (x + y) ` a.
   * (x ` a)^y is equal to x^y ` a^y when 'y' is nondimensional.

   'ezunits' does not require that units in a sum have the same
dimensions; such terms are not added together, and no error is reported.

   'ezunits' includes functions for elementary dimensional analysis,
namely the fundamental dimensions and fundamental units of a dimensional
quantity, and computation of dimensionless quantities and natural units.
The functions for dimensional analysis were adapted from similar
functions in another package, written by Barton Willis.

   For the purpose of dimensional analysis, a list of fundamental
dimensions and an associated list of fundamental units are maintained;
by default the fundamental dimensions are length, mass, time, charge,
temperature, and quantity, and the fundamental units are the associated
SI units, but other fundamental dimensions and units can be declared.