OpenMath Content Dictionary: dimensions1

Canonical URL:

http://www.openmath.org/cd/dimensions1.ocd

CD Base:

http://www.openmath.org/cd

CD File:

dimensions1.ocd

CD as XML Encoded OpenMath:

dimensions1.omcd

Defines:

acceleration, area, charge, concentration, current, density, displacement, energy, force, length, mass, momentum, power, pressure, resistance, speed, temperature, time, velocity, voltage, volume

Date:

2017-09-27

Version:

4 (Revision 3)

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 which represent basic physical dimensions.

---

length

Role:

constant

Description:

This symbol represents the length physical dimension.

Signatures:

sts

---

[Next: area] [Last: power] [Top]

---

area

Role:

constant

Description:

This symbol represents the area physical dimension.

Commented Mathematical property (CMP):

area = length*length

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">area</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (area, times (length, length) )

Popcorn

dimensions1.area = dimensions1.length * dimensions1.length

Rendered Presentation MathML

$$\mathrm{area}=\mathrm{length}\times \mathrm{length}$$

Signatures:

sts

---

[Next: volume] [Previous: length] [Top]

---

volume

Role:

constant

Description:

This symbol represents the volume physical dimension.

Commented Mathematical property (CMP):

volume = length*length*length

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">volume</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (volume, times (length, length, length) )

Popcorn

dimensions1.volume = dimensions1.length * dimensions1.length * dimensions1.length

Rendered Presentation MathML

$$\mathrm{volume}=\mathrm{length}\times \mathrm{length}\times \mathrm{length}$$

Signatures:

sts

---

[Next: speed] [Previous: area] [Top]

---

speed

Role:

constant

Description:

This symbol represents the speed physical dimension. It is the size of the derivative of distance with respect to time.

Commented Mathematical property (CMP):

speed = length/time

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">speed</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
   <csymbol cd="dimensions1">time</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (speed, divide (length, time) )

Popcorn

dimensions1.speed = dimensions1.length / dimensions1.time

Rendered Presentation MathML

$$\mathrm{speed}=\frac{\mathrm{length}}{\mathrm{time}}$$

Signatures:

sts

---

[Next: displacement] [Previous: volume] [Top]

---

displacement

Role:

constant

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.

Signatures:

sts

---

[Next: velocity] [Previous: speed] [Top]

---

velocity

Role:

constant

Description:

This symbol represents the velocity physical dimension. It is the derivative of distance with respect to time.

Commented Mathematical property (CMP):

velocity = displacement/time

Formal Mathematical property (FMP):

OpenMath XML (source)

    <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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">velocity</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">displacement</csymbol>
   <csymbol cd="dimensions1">time</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (velocity, divide (displacement, time) )

Popcorn

dimensions1.velocity = dimensions1.displacement / dimensions1.time

Rendered Presentation MathML

$$\mathrm{velocity}=\frac{\mathrm{displacement}}{\mathrm{time}}$$

Commented Mathematical property (CMP):

speed is the Euclidean norm of velocity

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">speed</csymbol>
  <apply><csymbol cd="norm1">Euclidean_norm</csymbol><csymbol cd="dimensions1">velocity</csymbol></apply>
 </apply>
</math>

Prefix

eq (speed, Euclidean_norm (velocity) )

Popcorn

dimensions1.speed = norm1.Euclidean_norm(dimensions1.velocity)

Rendered Presentation MathML

$$\mathrm{speed}=\mathrm{Euclidean\_norm}\left(\mathrm{velocity}\right)$$

Signatures:

sts

---

[Next: acceleration] [Previous: displacement] [Top]

---

acceleration

Role:

constant

Description:

This symbol represents the acceleration physical dimension. It is the second derivative of distance with respect to time.

Commented Mathematical property (CMP):

acceleration = displacement/(time^2)

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">acceleration</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">displacement</csymbol>
   <apply><csymbol cd="arith1">power</csymbol>
    <csymbol cd="dimensions1">time</csymbol>
    <cn type="integer">2</cn>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (acceleration, divide (displacement, power (time, 2 ) ) )

Popcorn

dimensions1.acceleration = dimensions1.displacement / dimensions1.time ^ 2

Rendered Presentation MathML

$$\mathrm{acceleration}=\frac{\mathrm{displacement}}{{\mathrm{time}}^2}$$

Signatures:

sts

---

[Next: time] [Previous: velocity] [Top]

---

time

Role:

constant

Description:

This symbol represents the time physical dimension. Note that the main units for time are defined in the units_time1 CD.

Signatures:

sts

---

[Next: mass] [Previous: acceleration] [Top]

---

mass

Role:

constant

Description:

This symbol represents the mass physical dimension.

Signatures:

sts

---

[Next: force] [Previous: time] [Top]

---

force

Role:

constant

Description:

This symbol represents the force physical dimension.

Commented Mathematical property (CMP):

force = mass*length/time^2

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">force</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">mass</csymbol>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="dimensions1">length</csymbol>
    <apply><csymbol cd="arith1">power</csymbol>
     <csymbol cd="dimensions1">time</csymbol>
     <cn type="integer">2</cn>
    </apply>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (force, times (mass, divide (length, power (time, 2 ) ) ) )

Popcorn

dimensions1.force = dimensions1.mass * dimensions1.length / dimensions1.time ^ 2

Rendered Presentation MathML

$$\mathrm{force}=\mathrm{mass}\frac{\mathrm{length}}{{\mathrm{time}}^2}$$

Signatures:

sts

---

[Next: temperature] [Previous: mass] [Top]

---

temperature

Role:

constant

Description:

This symbol represents the temperature physical dimension.

Signatures:

sts

---

[Next: pressure] [Previous: force] [Top]

---

pressure

Role:

constant

Description:

This symbol represents the pressure physical dimension.

Commented Mathematical property (CMP):

pressure = force/area

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">pressure</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">force</csymbol>
   <csymbol cd="dimensions1">area</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (pressure, divide (force, area) )

Popcorn

dimensions1.pressure = dimensions1.force / dimensions1.area

Rendered Presentation MathML

$$\mathrm{pressure}=\frac{\mathrm{force}}{\mathrm{area}}$$

Signatures:

sts

---

[Next: charge] [Previous: temperature] [Top]

---

charge

Role:

constant

Description:

This symbol represents the charge physical dimension.

Commented Mathematical property (CMP):

charge = current/voltage

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">charge</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">current</csymbol>
   <csymbol cd="dimensions1">voltage</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (charge, divide (current, voltage) )

Popcorn

dimensions1.charge = dimensions1.current / dimensions1.voltage

Rendered Presentation MathML

$$\mathrm{charge}=\frac{\mathrm{current}}{\mathrm{voltage}}$$

Signatures:

sts

---

[Next: current] [Previous: pressure] [Top]

---

current

Role:

constant

Description:

This symbol represents the current physical dimension.

Commented Mathematical property (CMP):

current = voltage*charge

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">current</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">voltage</csymbol>
   <csymbol cd="dimensions1">charge</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (current, times (voltage, charge) )

Popcorn

dimensions1.current = dimensions1.voltage * dimensions1.charge

Rendered Presentation MathML

$$\mathrm{current}=\mathrm{voltage}\times \mathrm{charge}$$

Signatures:

sts

---

[Next: voltage] [Previous: charge] [Top]

---

voltage

Role:

constant

Description:

This symbol represents the voltage physical dimension.

Commented Mathematical property (CMP):

voltage = current/charge

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">voltage</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">current</csymbol>
   <csymbol cd="dimensions1">charge</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (voltage, divide (current, charge) )

Popcorn

dimensions1.voltage = dimensions1.current / dimensions1.charge

Rendered Presentation MathML

$$\mathrm{voltage}=\frac{\mathrm{current}}{\mathrm{charge}}$$

Signatures:

sts

---

[Next: resistance] [Previous: current] [Top]

---

resistance

Role:

constant

Description:

This symbol represents the resistance physical dimension, it is the resistance that an electrical circuit has to flow of charge.

Commented Mathematical property (CMP):

resistance = voltage/current

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">resistance</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">voltage</csymbol>
   <csymbol cd="dimensions1">current</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (resistance, divide (voltage, current) )

Popcorn

dimensions1.resistance = dimensions1.voltage / dimensions1.current

Rendered Presentation MathML

$$\mathrm{resistance}=\frac{\mathrm{voltage}}{\mathrm{current}}$$

Signatures:

sts

---

[Next: density] [Previous: voltage] [Top]

---

density

Role:

constant

Description:

This symbol represents the density physical dimension, it is the mass per unit volume.

Commented Mathematical property (CMP):

density = mass/volume

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">density</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">mass</csymbol>
   <csymbol cd="dimensions1">volume</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (density, divide (mass, volume) )

Popcorn

dimensions1.density = dimensions1.mass / dimensions1.volume

Rendered Presentation MathML

$$\mathrm{density}=\frac{\mathrm{mass}}{\mathrm{volume}}$$

Signatures:

sts

---

[Next: energy] [Previous: resistance] [Top]

---

energy

Role:

constant

Description:

This symbol represents the energy physical dimension.

Commented Mathematical property (CMP):

energy = mass*length^2/time^2

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">energy</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">force</csymbol>
   <csymbol cd="dimensions1">length</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (energy, times (force, length) )

Popcorn

dimensions1.energy = dimensions1.force * dimensions1.length

Rendered Presentation MathML

$$\mathrm{energy}=\mathrm{force}\times \mathrm{length}$$

Commented Mathematical property (CMP):

energy = force*length

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">energy</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <apply><csymbol cd="arith1">times</csymbol>
    <csymbol cd="dimensions1">mass</csymbol>
    <apply><csymbol cd="arith1">power</csymbol>
     <csymbol cd="dimensions1">length</csymbol>
     <cn type="integer">2</cn>
    </apply>
   </apply>
   <apply><csymbol cd="arith1">power</csymbol>
    <csymbol cd="dimensions1">time</csymbol>
    <cn type="integer">2</cn>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (energy, divide (times (mass, power (length, 2 ) ) , power (time, 2 ) ) )

Popcorn

dimensions1.energy = (dimensions1.mass * dimensions1.length ^ 2) / dimensions1.time ^ 2

Rendered Presentation MathML

$$\mathrm{energy}=\frac{\mathrm{mass}{\mathrm{length}}^2}{{\mathrm{time}}^2}$$

Signatures:

sts

---

[Next: concentration] [Previous: density] [Top]

---

concentration

Role:

constant

Description:

This symbol represents the concentration physical dimension, it is the amount of a substance in a volume.

Commented Mathematical property (CMP):

concentration = mass/length^3

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">concentration</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">mass</csymbol>
   <apply><csymbol cd="arith1">power</csymbol>
    <csymbol cd="dimensions1">length</csymbol>
    <cn type="integer">3</cn>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (concentration, divide (mass, power (length, 3 ) ) )

Popcorn

dimensions1.concentration = dimensions1.mass / dimensions1.length ^ 3

Rendered Presentation MathML

$$\mathrm{concentration}=\frac{\mathrm{mass}}{{\mathrm{length}}^3}$$

Signatures:

sts

---

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---

momentum

Role:

constant

Description:

This symbol represents the momentum physical dimension, it is mass times velocity.

Commented Mathematical property (CMP):

momentum = mass*velocity

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">momentum</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="dimensions1">mass</csymbol>
   <csymbol cd="dimensions1">velocity</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (momentum, times (mass, velocity) )

Popcorn

dimensions1.momentum = dimensions1.mass * dimensions1.velocity

Rendered Presentation MathML

$$\mathrm{momentum}=\mathrm{mass}\times \mathrm{velocity}$$

Signatures:

sts

---

[Next: power] [Previous: concentration] [Top]

---

power

Description:

This symbol represents the power physical dimension, it is energy per time.

Commented Mathematical property (CMP):

power = energy/time

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="dimensions1">power</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="dimensions1">energy</csymbol>
   <csymbol cd="dimensions1">time</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (power, divide (energy, time) )

Popcorn

dimensions1.power = dimensions1.energy / dimensions1.time

Rendered Presentation MathML

$$\mathrm{power}=\frac{\mathrm{energy}}{\mathrm{time}}$$

Signatures:

sts

---

[First: length] [Previous: momentum] [Top]