dimensions1.ocd

<CD xmlns="http://www.openmath.org/OpenMathCD">
<CDComment>

     This document is distributed in the hope that it will be useful, 
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          work to the original source.
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          both this document and the derived work are Content Dictionaries
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          chosen so that it cannot be confused with any works adopted by
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          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.
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     If you have questions about this license please contact the OpenMath
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</CDComment>

<CDName>dimensions1</CDName>
<CDBase>http://www.openmath.org/cd</CDBase>
<CDURL>http://www.openmath.org/cd/dimensions1.ocd</CDURL>
<CDReviewDate>2017-12-31</CDReviewDate>
<CDStatus>experimental</CDStatus>
<CDDate>2017-09-27</CDDate>
<CDVersion>4</CDVersion>
<CDRevision>3</CDRevision>
<CDComment>
  Author: OpenMath Consortium (James Davenport)
  SourceURL: https://github.com/OpenMath/CDs
</CDComment>

<Description> 
This CD defines symbols which represent basic physical dimensions.
</Description>

<CDDefinition>
<Name>length</Name>
<Role>constant</Role>
<Description>
This symbol represents the length physical dimension.
</Description>

</CDDefinition>

<CDDefinition>
<Name>area</Name>
<Role>constant</Role>
<Description>
This symbol represents the area physical dimension.
</Description>

<CMP> area = length*length </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="area"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>
</CDDefinition>

<CDDefinition>
<Name>volume</Name>
<Role>constant</Role>
<Description>
This symbol represents the volume physical dimension.
</Description>

<CMP> volume = length*length*length </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="volume"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="length"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>
</CDDefinition>

<CDDefinition>
<Name>speed</Name>
<Role>constant</Role>
<Description>
This symbol represents the speed physical dimension. It is the size of the
derivative of distance with respect to time.
</Description>

<CMP>speed = length/time</CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="speed"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="length"/>
      <OMS cd="dimensions1" name="time"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>
</CDDefinition>

<CDDefinition>
  <Name>displacement</Name>
<Role>constant</Role>
  <Description>
This symbol represents the spatial difference between two points.
The direction of the displacement is taken into account as well as the
distance between the points.
  </Description>
</CDDefinition>

<CDDefinition>
<Name>velocity</Name>
<Role>constant</Role>
<Description>
This symbol represents the velocity physical dimension. It is the
derivative of distance with respect to time.
</Description>

<CMP> velocity = displacement/time</CMP>
<FMP>
    <OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
      <OMA>
        <OMS cd="relation1" name="eq"/>
        <OMS cd="dimensions1" name="velocity"/>
        <OMA>
          <OMS cd="arith1" name="divide"/>
          <OMS cd="dimensions1" name="displacement"/>
          <OMS cd="dimensions1" name="time"/>
        </OMA>
      </OMA>
    </OMOBJ>
</FMP>
<CMP> speed is the Euclidean norm of velocity </CMP>
<FMP>
<OMOBJ xmlns="http://www.openmath.org/OpenMath">
  <OMA>
    <OMS name="eq" cd="relation1"/>
    <OMS name="speed" cd="dimensions1"/>
    <OMA>
      <OMS name="Euclidean_norm" cd="norm1"/>
      <OMS name="velocity" cd="dimensions1"/>
    </OMA>
  </OMA>
</OMOBJ>
</FMP>

</CDDefinition>

<CDDefinition>
<Name>acceleration</Name>
<Role>constant</Role>
<Description>
This symbol represents the acceleration physical dimension. It is the
second derivative of distance with respect to time.
</Description>

<CMP>acceleration = displacement/(time^2)</CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="acceleration"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="displacement"/>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="time"/>
        <OMI> 2 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>time</Name>
<Role>constant</Role>
<Description>
This symbol represents the time physical dimension.
Note that the main units for time are defined in the units_time1 CD.
</Description>
</CDDefinition>

<CDDefinition>
<Name>mass</Name>
<Role>constant</Role>
<Description>
This symbol represents the mass physical dimension.
</Description>
</CDDefinition>

<CDDefinition>
<Name>force</Name>
<Role>constant</Role>
<Description>
This symbol represents the force physical dimension. 
</Description>

<CMP> force = mass*length/time^2 </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="force"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMA>
        <OMS cd="arith1" name="divide"/>
        <OMS cd="dimensions1" name="length"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMS cd="dimensions1" name="time"/>
          <OMI> 2 </OMI>
        </OMA>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>temperature</Name>
<Role>constant</Role>
<Description>
This symbol represents the temperature physical dimension.
</Description>

</CDDefinition>

<CDDefinition>
<Name>pressure</Name>
<Role>constant</Role>
<Description>
This symbol represents the pressure physical dimension.
</Description>

<CMP> pressure = force/area </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="pressure"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="force"/>
      <OMS cd="dimensions1" name="area"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>charge</Name>
<Role>constant</Role>
<Description>
This symbol represents the charge physical dimension.
</Description>

<CMP> charge = current/voltage </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="charge"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="current"/>
      <OMS cd="dimensions1" name="voltage"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>current</Name>
<Role>constant</Role>
<Description>
This symbol represents the current physical dimension.
</Description>

<CMP> current = voltage*charge </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="current"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="voltage"/>
      <OMS cd="dimensions1" name="charge"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>voltage</Name>
<Role>constant</Role>
<Description>
This symbol represents the voltage physical dimension.
</Description>

<CMP> voltage = current/charge </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="voltage"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="current"/>
      <OMS cd="dimensions1" name="charge"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>resistance</Name>
<Role>constant</Role>
<Description>
This symbol represents the resistance physical dimension, it is the
resistance that an electrical circuit has to flow of charge.
</Description>

<CMP> resistance = voltage/current </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="resistance"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="voltage"/>
      <OMS cd="dimensions1" name="current"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>density</Name>
<Role>constant</Role>
<Description>
This symbol represents the density physical dimension, it is the mass
per unit volume.
</Description>

<CMP> density = mass/volume </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="density"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMS cd="dimensions1" name="volume"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>energy</Name>
<Role>constant</Role>
<Description>
This symbol represents the energy physical dimension.
</Description>

<CMP> energy = mass*length^2/time^2 </CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="energy"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="force"/>
      <OMS cd="dimensions1" name="length"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

<CMP> energy = force*length </CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="energy"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMA>
        <OMS cd="arith1" name="times"/>
        <OMS cd="dimensions1" name="mass"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMS cd="dimensions1" name="length"/>
          <OMI> 2 </OMI>
        </OMA>
      </OMA>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="time"/>
        <OMI> 2 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>concentration</Name>
<Role>constant</Role>
<Description>
This symbol represents the concentration physical dimension, it is the
amount of a substance in a volume.
</Description>

<CMP> concentration = mass/length^3 </CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="concentration"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMA>
        <OMS cd="arith1" name="power"/>
        <OMS cd="dimensions1" name="length"/>
        <OMI> 3 </OMI>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>momentum</Name>
<Role>constant</Role>
<Description>
This symbol represents the momentum physical dimension, it is mass
times velocity.
</Description>

<CMP> momentum = mass*velocity </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="momentum"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMS cd="dimensions1" name="mass"/>
      <OMS cd="dimensions1" name="velocity"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

<CDDefinition>
<Name>power</Name>
<Description>
This symbol represents the power physical dimension, it is energy
per time.
</Description>

<CMP> power = energy/time </CMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
  <OMA>
    <OMS cd="relation1" name="eq"/>
    <OMS cd="dimensions1" name="power"/>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMS cd="dimensions1" name="energy"/>
      <OMS cd="dimensions1" name="time"/>
    </OMA>
  </OMA>
</OMOBJ></FMP>

</CDDefinition>

</CD>