OpenMath Content Dictionary: units_metric1

Canonical URL:

http://www.openmath.org/cd/units_metric1.ocd

CD File:

units_metric1.ocd

CD as XML Encoded OpenMath:

units_metric1.omcd

Defines:

Coulomb, Joule, Newton, Newton_per_sqr_metre, Pascal, Watt, amp, degree_Celsius, degree_Kelvin, gramme, litre, litre_pre1964, metre, metre_sqrd, metres_per_second, metres_per_second_sqrd, second, volt

Date:

2004-08-27

Version:

3 (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.
       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: OpenMath Consortium (James Davenport)
  SourceURL: https://github.com/OpenMath/CDs
            

This CD defines symbols to represent the basic physical units in the SI (syst\'eme international) system of units. It should probably be renamed units_si.

---

metre

Description:

This symbol represents the measure of one metre. This is the standard SI unit measure for physical distance.

Commented Mathematical property (CMP):

This is a base unit for the SI system

Signatures:

sts

---

[Next: metre_sqrd] [Last: volt] [Top]

---

metre_sqrd

Description:

This symbol represents the measure of one metre squared. This is the standard SI measure for physical area.

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="metre_sqrd" cd="units_metric1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMS name="metre" cd="units_metric1"/>
    <OMS name="metre" cd="units_metric1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_metric1">metre_sqrd</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="units_metric1">metre</csymbol>
   <csymbol cd="units_metric1">metre</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (metre_sqrd, times (metre, metre) )

Popcorn

units_metric1.metre_sqrd = units_metric1.metre * units_metric1.metre

Rendered Presentation MathML

$$\mathrm{metre\_sqrd}=\mathrm{metre}\times \mathrm{metre}$$

Signatures:

sts

---

[Next: litre] [Previous: metre] [Top]

---

litre

Description:

This symbol represents the measure of one litre. This is a standard metric measure for physical volume.

Commented Mathematical property (CMP):

A litre is, since 1964, a cubic decimetre, or a thousandth of a cubic metre, as the FMP below states.

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="units_metric1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMF dec="0.001"/>
    <OMA>
      <OMS name="power" cd="arith1"/>
      <OMS name="metre" cd="units_metric1"/>
      <OMI> 3 </OMI>
    </OMA>
  </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="units_metric1">litre</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">0.001</cn>
   <apply><csymbol cd="arith1">power</csymbol>
    <csymbol cd="units_metric1">metre</csymbol>
    <cn type="integer">3</cn>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , litre) , times ( 0.001 , power (metre, 3 ) ) )

Popcorn

1 * units_metric1.litre = 0.001 * units_metric1.metre ^ 3

Rendered Presentation MathML

$$1\mathrm{litre}=0.001{\mathrm{metre}}^3$$

Signatures:

sts

---

[Next: litre_pre1964] [Previous: metre_sqrd] [Top]

---

litre_pre1964

Description:

This symbol represents the previous (1901-1964) measure of one litre. This used to be a standard metric measure for physical volume.

Commented Mathematical property (CMP):

A litre is, since 1901 and until 1964, the volume occupied by a kilogramme of water at maximum density and standard pressure. The difference is about 0.0028%.

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_pre1964" cd="units_metric1"/>
    </OMA>
    <OMA>
      <OMS name="times" cd="arith1"/>
      <OMF dec="1.000028"/>
      <OMS name="litre" cd="units_metric1"/>
    </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="units_metric1">litre_pre1964</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="real">1.000028</cn>
   <csymbol cd="units_metric1">litre</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , litre_pre1964) , times ( 1.000028 , litre) )

Popcorn

1 * units_metric1.litre_pre1964 = 1.000028 * units_metric1.litre

Rendered Presentation MathML

$$1\mathrm{litre\_pre1964}=1.000028\mathrm{litre}$$

Signatures:

sts

---

[Next: metres_per_second] [Previous: litre] [Top]

---

metres_per_second

Description:

This symbol represents the measure of one metre per second. This is the standard SI measure for speed.

Commented Mathematical property (CMP):

1 metres_per_second = 1 metre in 1 second

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="metres_per_second" cd="units_metric1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/> 
    <OMS name="metre" cd="units_metric1"/> 
    <OMS name="second" cd="units_time1"/> 
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_metric1">metres_per_second</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_metric1">metre</csymbol>
   <csymbol cd="units_time1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (metres_per_second, divide (metre, second) )

Popcorn

units_metric1.metres_per_second = units_metric1.metre / units_time1.second

Rendered Presentation MathML

$$\mathrm{metres\_per\_second}=\frac{\mathrm{metre}}{\mathrm{second}}$$

Signatures:

sts

---

[Next: metres_per_second_sqrd] [Previous: litre_pre1964] [Top]

---

metres_per_second_sqrd

Description:

This symbol represents the measure of one metre per second squared. This is the standard SI measure for acceleration.

Commented Mathematical property (CMP):

1 metres_per_second_sqrd = 1 metres_per_second (change) in 1 second

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="metres_per_second_sqrd" cd="units_metric1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/> 
    <OMS name="metres_per_second" cd="units_metric1"/> 
    <OMS name="second" cd="units_time1"/> 
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_metric1">metres_per_second_sqrd</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_metric1">metres_per_second</csymbol>
   <csymbol cd="units_time1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (metres_per_second_sqrd, divide (metres_per_second, second) )

Popcorn

units_metric1.metres_per_second_sqrd = units_metric1.metres_per_second / units_time1.second

Rendered Presentation MathML

$$\mathrm{metres\_per\_second\_sqrd}=\frac{\mathrm{metres\_per\_second}}{\mathrm{second}}$$

Signatures:

sts

---

[Next: second] [Previous: metres_per_second] [Top]

---

second

Description:

This symbol represents the measure of one second. This is the standard SI measure for time.

Commented Mathematical property (CMP):

The Si unit is the same as the UTC unit, to which we refer

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relation1"/>
  <OMS name="second" cd="units_metric1"/>
  <OMS name="second" cd="units_time1"/>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_metric1">second</csymbol>
  <csymbol cd="units_time1">second</csymbol>
 </apply>
</math>

Prefix

eq (second, second)

Popcorn

units_metric1.second = units_time1.second

Rendered Presentation MathML

$$\mathrm{second}=\mathrm{second}$$

Signatures:

sts

---

[Next: gramme] [Previous: metres_per_second_sqrd] [Top]

---

gramme

Description:

This symbol represents the measure of one gramme. This is not quite the standard SI measure for mass, which is the kilogramme, but OpenMath chooses to regard the gramme as standard, otherwise one would have to call it the milli-kilogramme.

Commented Mathematical property (CMP):

This is a basic unit of the SI system

Signatures:

sts

---

[Next: Newton] [Previous: second] [Top]

---

Newton

Description:

This symbol represents the measure of one Newton. This is the standard SI measure for force.

Signatures:

sts

---

[Next: Joule] [Previous: gramme] [Top]

---

Joule

Description:

This symbol represents the measure of one Joule. This is the standard SI measure for energy.

Signatures:

sts

---

[Next: Watt] [Previous: Newton] [Top]

---

Watt

Description:

This symbol represents the measure of one Watt. This is the standard SI measure for power.

Signatures:

sts

---

[Next: degree_Kelvin] [Previous: Joule] [Top]

---

degree_Kelvin

Description:

This symbol represents the measure of one degree Kelvin. This is a standard SI measure for temperature relative to absolute zero.

Commented Mathematical property (CMP):

1 degree Kelvin = 1 - 273.15 degrees Celsius

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_Kelvin" cd="units_metric1"/>
    </OMA>
    <OMA>
      <OMS name="minus" cd="arith1"/>
      <OMS name="degree_Celsius" cd="units_metric1"/>
      <OMF dec="273.15"/>
    </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="units_metric1">degree_Kelvin</csymbol>
  </apply>
  <apply><csymbol cd="arith1">minus</csymbol>
   <csymbol cd="units_metric1">degree_Celsius</csymbol>
   <cn type="real">273.15</cn>
  </apply>
 </apply>
</math>

Prefix

eq (times ( 1 , degree_Kelvin) , minus (degree_Celsius, 273.15 ) )

Popcorn

1 * units_metric1.degree_Kelvin = units_metric1.degree_Celsius - 273.15

Rendered Presentation MathML

$$1\mathrm{degree\_Kelvin}=\mathrm{degree\_Celsius}-273.15$$

Signatures:

sts

---

[Next: degree_Celsius] [Previous: Watt] [Top]

---

degree_Celsius

Description:

This symbol represents the measure of one degree Celsius. This is a standard metric measure for temperature.

Signatures:

sts

---

[Next: Pascal] [Previous: degree_Kelvin] [Top]

---

Pascal

Description:

This symbol represents the measure of one Newton per square metre. This is the standard SI measure for pressure.

Signatures:

sts

---

[Next: Newton_per_sqr_metre] [Previous: degree_Celsius] [Top]

---

Newton_per_sqr_metre

Description:

This symbol represents the measure of one Newton per square metre. This is another (deprecated in OpenMath) name for the standard SI measure for pressure, the Pascal.

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMS name="Newton_per_sqr_metre" cd="units_metric1"/>
    <OMS name="Pascal" cd="units_metric1"/>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="units_metric1">Newton_per_sqr_metre</csymbol>
  <csymbol cd="units_metric1">Pascal</csymbol>
 </apply>
</math>

Prefix

eq (Newton_per_sqr_metre, Pascal)

Popcorn

units_metric1.Newton_per_sqr_metre = units_metric1.Pascal

Rendered Presentation MathML

$$\mathrm{Newton\_per\_sqr\_metre}=\mathrm{Pascal}$$

Signatures:

sts

---

[Next: Coulomb] [Previous: Pascal] [Top]

---

Coulomb

Description:

This symbol represents the measure of one Coulomb. This is the standard SI measure for charge.

Signatures:

sts

---

[Next: amp] [Previous: Newton_per_sqr_metre] [Top]

---

amp

Description:

This symbol represents the measure of one amp. This is the standard SI measure for current.

Signatures:

sts

---

[Next: volt] [Previous: Coulomb] [Top]

---

volt

Description:

This symbol represents the measure of one volt. This is the standard SI measure for voltage.

Signatures:

sts

---

[First: metre] [Previous: amp] [Top]