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

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     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 
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          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
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       c) The derived work is distributed under terms that allow the
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     If you have questions about this license please contact the OpenMath
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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.

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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

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

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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

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

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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

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

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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

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