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:
 20090110

Version:
 1
(Revision 1)

Review Date:
 20171231

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.
c) The derived work is distributed under terms that allow the
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.
If you have questions about this license please contact the OpenMath
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
subject to copyright protection in the United States. Foreign copyrights
may apply.
Author: J B Collins
This CD defines symbols for functions applied to SI quantities and
units.

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

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

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

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