# OpenMath Content Dictionary: SI_functions1

Canonical URL:
http://www.openmath.org/cd/SI_functions1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
SI_functions1.ocd
CD as XML Encoded OpenMath:
SI_functions1.omcd
Defines:
dim, kind, num, unit
Date:
2009-01-10
Version:
1 (Revision 1)
Review Date:
2017-12-31
Status:
experimental


This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work.  Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society.  In particular, if there is a Content
Dictionary Group whose name is, for example, math' containing
Content Dictionaries named math1', math2' etc., then you should
not name a derived Content Dictionary mathN' where N is an integer.
However you are free to name it private_mathN' or some such.  This
is because the names mathN' may be used by the OpenMath Society
for future extensions.
compilation of derived works, but keep paragraphs a) and b)
intact.  The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
society at http://www.openmath.org.

Author: Joseph B. Collins (2009), Naval Research Laboratory, Washington, DC.
Copyright Notice:  This is a work of the U.S. Government and is not
may apply.


  Author: J B Collins


This CD defines symbols for functions applied to SI quantities and units.

## dim

Role:
application
Description:

The symbol to represent the function that returns the physical dimension of its argument in terms of products of powers of SI base quantities. The dim operation may be meaningfully applied to SI quantities, SI units, and numbers without physical dimension.

Commented Mathematical property (CMP):
The dim operator acts as the identity operation when applied to an SI base quantity.
Commented Mathematical property (CMP):
The dim operator returns the corresponding SI base quantity when applied to an SI base unit.
Commented Mathematical property (CMP):
For named SI derived quantities and named units, the value returned by the dim operator shall be defined for each case.
Commented Mathematical property (CMP):
The dim operator applied to a product is equal to the associative product of the dim operator applied to the individual factors.
Commented Mathematical property (CMP):
The dim operator applied to a product is equal to the commutative product of the dim operator applied to the factors.
Commented Mathematical property (CMP):
The dim operator applied to a multiplicative inverse of a quantity is equal to the multiplicative inverse of the dim operator applied to the same quantity.
Commented Mathematical property (CMP):
The dim operator returns a value of one when applied to a dimensionless quantity or number.
Signatures:
sts

 [Next: unit] [Last: kind] [Top]

## unit

Role:
application
Description:

The symbol to represent the function that returns the units of its argument in terms of a product of powers of SI base units.

Commented Mathematical property (CMP):
The unit operator may be applied to any physical quantity.
Commented Mathematical property (CMP):
The unit operator applied to an SI base quantity returns the corresponding SI base unit.
Commented Mathematical property (CMP):
The unit operator applied to an SI base unit or SI coherent unit acts as the identity operator, returning that unit.
Commented Mathematical property (CMP):
The unit operator applied to any derived quantity is equal to the unit operator applied to the result of applying the dim operator to the same quantity, i.e., unit(Q) = unit(dim(Q)).
Commented Mathematical property (CMP):
The unit operator applied to a product is equal to the commutative product of the unit operator applied to the factors.
Commented Mathematical property (CMP):
The unit operator applied to a product is equal to the associative product of the unit operator applied to the factors.
Commented Mathematical property (CMP):
The unit operator applied to a multiplicative inverse of a quantity is equal to the multiplicative inverse of the unit operator applied to the same quantity.
Commented Mathematical property (CMP):
The unit operator returns a value of one when applied to a dimensionless quantity or number.
Signatures:
sts

 [Next: num] [Previous: dim] [Top]

## num

Role:
application
Description:

The symbol to represent the function to return the numerical value of a quantity in terms of a product of powers of SI base units.

Commented Mathematical property (CMP):
The num operator may be applied to any physical quantity.
Commented Mathematical property (CMP):
The num operator applied to an SI base quantity or unit returns the value one.
Commented Mathematical property (CMP):
The quantity num(Q)*unit(Q), may replace any quantity, Q, in a set of physical relations, if all such quantities in the set of relations are so replaced. The quantity num(Q)*unit(Q) is not always the same as Q, however dim(Q) = dim(num(Q)*unit(Q)).
Signatures:
sts

 [Next: kind] [Previous: unit] [Top]

## kind

Role:
application
Description:

The symbol to represent the function to return the kind of a quantity. The value of this function is referred to, but not defined in the SI. Its value, kind(Q) for a given quantity, Q, is left to the user to assign.

Signatures:
sts

 [First: dim] [Previous: num] [Top]