OpenMath Content Dictionary: SIUsed_OffSystemUnits1

Canonical URL:

http://www.openmath.org/cd/SIUsed_OffSystemUnits1.ocd

CD File:

SIUsed_OffSystemUnits1.ocd

CD as XML Encoded OpenMath:

SIUsed_OffSystemUnits1.omcd

Defines:

bel, day, degree-of-arc, hour, litre, minute, minute-of-arc, neper, second-of-arc, tonne

Date:

2009-01-10

Version:

1 (Revision 2)

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.
       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 to represent units that are off-system with respect to the SI system of units, but are retained for use with the SI. (DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-1 - "Quantities and units", 2008).

---

minute

Description:

This symbol represents the measure of one minute of time. It has the short symbol form, "min".

Commented Mathematical property (CMP):

1 minute = 60 seconds

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="minute" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 60 </OMI>
    <OMS name="second" cd="SI_BaseUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">minute</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">60</cn>
   <csymbol cd="SI_BaseUnits1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , minute) , times ( 60 , second) )

Popcorn

1 * SIUsed_OffSystemUnits1.minute = 60 * SI_BaseUnits1.second

Rendered Presentation MathML

$$1\mathrm{minute}=60\mathrm{second}$$

Signatures:

sts

---

[Next: hour] [Last: bel] [Top]

---

hour

Description:

This symbol represents the measure of one hour of time. It has the short symbol form, "h".

Commented Mathematical property (CMP):

1 hour = 60 minute

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="hour" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 60 </OMI>
    <OMS name="minute" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">hour</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">60</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">minute</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , hour) , times ( 60 , minute) )

Popcorn

1 * SIUsed_OffSystemUnits1.hour = 60 * SIUsed_OffSystemUnits1.minute

Rendered Presentation MathML

$$1\mathrm{hour}=60\mathrm{minute}$$

Signatures:

sts

---

[Next: day] [Previous: minute] [Top]

---

day

Description:

This symbol represents the measure of one day of time. It has the short symbol form, "d".

Commented Mathematical property (CMP):

1 day = 24 hour

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="day" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 24 </OMI>
    <OMS name="hour" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">day</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">24</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">hour</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , day) , times ( 24 , hour) )

Popcorn

1 * SIUsed_OffSystemUnits1.day = 24 * SIUsed_OffSystemUnits1.hour

Rendered Presentation MathML

$$1\mathrm{day}=24\mathrm{hour}$$

Signatures:

sts

---

[Next: degree-of-arc] [Previous: hour] [Top]

---

degree-of-arc

Description:

This symbol represents the angular measure of one degree of arc. It has the short symbol form of the degree symbol, a superscript circle, Unicode: U+00B0 or HTML: °.

Commented Mathematical property (CMP):

1 degree-of-arc = pi/180 radian

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="degree-of-arc" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="divide" cd="arith1"/>
      <OMS name="pi" cd="nums1"/>
      <OMI> 180 </OMI>
    </OMA>
    <OMS name="radian" cd="SI_NamedDerivedUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">degree-of-arc</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="nums1">pi</csymbol>
    <cn type="integer">180</cn>
   </apply>
   <csymbol cd="SI_NamedDerivedUnits1">radian</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , degree-of-arc) , times (divide (pi, 180 ) , radian) )

Popcorn

1 * SIUsed_OffSystemUnits1.degree-of-arc = nums1.pi / 180 * SI_NamedDerivedUnits1.radian

Rendered Presentation MathML

$$1\mathrm{degree-of-arc}=\frac{\pi }{180}\mathrm{radian}$$

Signatures:

sts

---

[Next: minute-of-arc] [Previous: day] [Top]

---

minute-of-arc

Description:

This symbol represents the angular measure of one minute of arc. It has the short symbol form, "'".

Commented Mathematical property (CMP):

1 minute-of-arc = 1/60 degree-of-arc

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="minute-of-arc" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="divide" cd="arith1"/>
    <OMS name="degree-of-arc" cd="SIUsed_OffSystemUnits1"/>
    <OMI> 60 </OMI>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">minute-of-arc</csymbol>
  </apply>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="SIUsed_OffSystemUnits1">degree-of-arc</csymbol>
   <cn type="integer">60</cn>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , minute-of-arc) , divide (degree-of-arc, 60 ) )

Popcorn

1 * SIUsed_OffSystemUnits1.minute-of-arc = SIUsed_OffSystemUnits1.degree-of-arc / 60

Rendered Presentation MathML

$$1\mathrm{minute-of-arc}=\frac{\mathrm{degree-of-arc}}{60}$$

Signatures:

sts

---

[Next: second-of-arc] [Previous: degree-of-arc] [Top]

---

second-of-arc

Description:

This symbol represents the angular measure of one second-of-arc. It has the short symbol form, '"'.

Commented Mathematical property (CMP):

1 second-of-arc = 1/60 minute-of-arc

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="second-of-arc" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="divide" cd="arith1"/>
    <OMS name="minute-of-arc" cd="SIUsed_OffSystemUnits1"/>
    <OMI> 60 </OMI>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">second-of-arc</csymbol>
  </apply>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="SIUsed_OffSystemUnits1">minute-of-arc</csymbol>
   <cn type="integer">60</cn>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , second-of-arc) , divide (minute-of-arc, 60 ) )

Popcorn

1 * SIUsed_OffSystemUnits1.second-of-arc = SIUsed_OffSystemUnits1.minute-of-arc / 60

Rendered Presentation MathML

$$1\mathrm{second-of-arc}=\frac{\mathrm{minute-of-arc}}{60}$$

Signatures:

sts

---

[Next: litre] [Previous: minute-of-arc] [Top]

---

litre

Description:

This symbol represents the volume measure of one litre. It has the short symbol form, "l" or "L".

Commented Mathematical property (CMP):

1 litre = 1 decimetre^3

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI>1</OMI>
    <OMS name="litre" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="power" cd="arith1"/>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMS name="deci" cd="units_siprefix1"/>
      <OMS name="metre" cd="SI_BaseUnits1"/>
    </OMA>
    <OMI>3</OMI>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">litre</csymbol>
  </apply>
  <apply><csymbol cd="arith1">power</csymbol>
   <apply><csymbol cd="arith1">times</csymbol>
    <csymbol cd="units_siprefix1">deci</csymbol>
    <csymbol cd="SI_BaseUnits1">metre</csymbol>
   </apply>
   <cn type="integer">3</cn>
  </apply>
 </apply>
</math>

Prefix

eq (times (1, litre) , power (times (deci, metre) , 3) )

Popcorn

1 * SIUsed_OffSystemUnits1.litre = (units_siprefix1.deci * SI_BaseUnits1.metre) ^ 3

Rendered Presentation MathML

$$1\mathrm{litre}={(\mathrm{deci}\times \mathrm{metre})}^3$$

Signatures:

sts

---

[Next: tonne] [Previous: second-of-arc] [Top]

---

tonne

Description:

This symbol represents the mass measure of one tonne. It has the short symbol form, "t".

Commented Mathematical property (CMP):

1 tonne = 1000 kilogram

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="tonne" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1000 </OMI>
    <OMS name="kilogram" cd="SI_BaseUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">tonne</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1000</cn>
   <csymbol cd="SI_BaseUnits1">kilogram</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , tonne) , times ( 1000 , kilogram) )

Popcorn

1 * SIUsed_OffSystemUnits1.tonne = 1000 * SI_BaseUnits1.kilogram

Rendered Presentation MathML

$$1\mathrm{tonne}=1000\mathrm{kilogram}$$

Signatures:

sts

---

[Next: neper] [Previous: litre] [Top]

---

neper

Description:

This symbol represents the dimensionless measure of one neper, the natural unit for representing logarithms of ratios of field amplitudes, such as voltage or pressure. It has the short symbol form, "Np".

Commented Mathematical property (CMP):

1 neper = ln(e) = 1

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="neper" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="log" cd="transc1"/>
    <OMS name="e" cd="nums1"/>
    <OMS name="e" cd="nums1"/>
  </OMA>
  <OMI> 1 </OMI>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">neper</csymbol>
  </apply>
  <apply><csymbol cd="transc1">log</csymbol>
   <csymbol cd="nums1">e</csymbol>
   <csymbol cd="nums1">e</csymbol>
  </apply>
  <cn type="integer">1</cn>
 </apply>
</math>

Prefix

eq (times ( 1 , neper) , log (e, e) , 1 )

Popcorn

1 * SIUsed_OffSystemUnits1.neper = log(nums1.e, nums1.e) = 1

Rendered Presentation MathML

$$1\mathrm{neper}={\log }_e\left(e\right)=1$$

Signatures:

sts

---

[Next: bel] [Previous: tonne] [Top]

---

bel

Description:

This symbol represents the dimensionless measure of one bel. It has the short symbol form, "B".

Commented Mathematical property (CMP):

1 bel = (ln(10))/2 neper

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="bel" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMA>
      <OMS name="divide" cd="arith1"/>
      <OMA>
	<OMS name="log" cd="transc1"/>
	<OMS name="e" cd="nums1"/>
	<OMI> 10 </OMI>
      </OMA>
      <OMI> 2 </OMI>
    </OMA>
    <OMS name="neper" cd="SIUsed_OffSystemUnits1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="SIUsed_OffSystemUnits1">bel</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="arith1">divide</csymbol>
    <apply><csymbol cd="transc1">log</csymbol>
     <csymbol cd="nums1">e</csymbol>
     <cn type="integer">10</cn>
    </apply>
    <cn type="integer">2</cn>
   </apply>
   <csymbol cd="SIUsed_OffSystemUnits1">neper</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , bel) , times (divide (log (e, 10 ) , 2 ) , neper) )

Popcorn

1 * SIUsed_OffSystemUnits1.bel = log(nums1.e, 10) / 2 * SIUsed_OffSystemUnits1.neper

Rendered Presentation MathML

$$1\mathrm{bel}=\frac{{\log }_e\left(10\right)}{2}\mathrm{neper}$$

Signatures:

sts

---

[First: minute] [Previous: neper] [Top]