OpenMath Content Dictionary: physical_consts1

Canonical URL:

http://www.openmath.org/cd/physical_consts1.ocd

CD Base:

http://www.openmath.org/cd

CD File:

physical_consts1.ocd

CD as XML Encoded OpenMath:

physical_consts1.omcd

Defines:

Avogadros_constant, Boltzmann_constant, Faradays_constant, Loschmidt_constant, Planck_constant, absolute_zero, gas_constant, gravitational_constant, light_year, magnetic_constant, mole, speed_of_light, zero_Celsius, zero_Fahrenheit

Date:

2005-05-28

Version:

3 (Revision 1)

Review Date:

2006-03-30

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.

This CD defines symbols which represent some elementary physical constants.

absolute_zero

Role:

constant

Description:

This symbol represents the absolute zero of temperature, synonymous with the object of that temperature having zero latent heat.

Signatures:

sts

zero_Celsius

Role:

constant

Description:

This symbol represents the zero of the Celsius temperature scale.

Signatures:

sts

zero_Fahrenheit

Role:

constant

Description:

This symbol represents the zero of the Fahrenheit temperature scale.

Signatures:

sts

light_year

Role:

constant

Description:

This symbol represents the distant for which a beam of light would take a year to traverse, in a vacuum.

Commented Mathematical property (CMP):

one light year is approximately 9221136415095314 metres

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="approx"/>
    <OMS cd="physical_consts1" name="light_year"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMI> 9221136415095314 </OMI>
      <OMS cd="units_metric1" name="metre"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="physical_consts1">light_year</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>9221136415095314</cn><csymbol cd="units_metric1">metre</csymbol></apply>
 </apply>
</math>

Prefix

approx (light_year, times ( 9221136415095314 , metre) )

Popcorn

relation1.approx(physical_consts1.light_year, 9221136415095314 * units_metric1.metre)

Rendered Presentation MathML

$$\mathrm{light\_year}\approx 9221136415095314\mathrm{metre}$$

Signatures:

sts

speed_of_light

Role:

constant

Description:

This symbol represents the speed of light in a vacuum. It is approximately 299792458 metres per second.

Commented Mathematical property (CMP):

The speed of light is approximately 299792458 metres per second

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="approx"/>
    <OMS cd="physical_consts1" name="speed_of_light"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMI> 299792458 </OMI>
      <OMS cd="units_metric1" name="metres_per_second"/>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="physical_consts1">speed_of_light</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>299792458</cn><csymbol cd="units_metric1">metres_per_second</csymbol></apply>
 </apply>
</math>

Prefix

approx (speed_of_light, times ( 299792458 , metres_per_second) )

Popcorn

relation1.approx(physical_consts1.speed_of_light, 299792458 * units_metric1.metres_per_second)

Rendered Presentation MathML

$$\mathrm{speed\_of\_light}\approx 299792458\mathrm{metres\_per\_second}$$

Signatures:

sts

Planck_constant

Role:

constant

Description:

This symbol represents the fundamental constant equal to the ratio of the energy of a quantum of energy to its frequency. It is approximately equal to 6.6260755*10^(-34) +/- 4.0*10^(-40) Joule seconds.

Commented Mathematical property (CMP):

The Planck constant is 6.6260755*10^(-34) +/- 4.0*10^(-40) Joule seconds this is equivalent to There exists P s.t. 6.626075... -4.0... < P and 6.626075... +4.0... > P and Planck constant = P*Joule*second

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMBIND>
  <OMS cd="quant1" name="exists"/>
  <OMBVAR>
    <OMV name="P"/>
  </OMBVAR>
  <OMA>
    <OMS cd="logic1" name="and"/>
    <OMA>
      <OMS cd="relation1" name="lt"/>
      <OMA>
        <OMS cd="arith1" name="minus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="6.6260755"/><OMI>10</OMI><OMI>-34</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="4.0"/><OMI>10</OMI><OMI>-40</OMI>
        </OMA>
      </OMA>
      <OMV name="P"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="gt"/>
      <OMA>
        <OMS cd="arith1" name="plus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="6.6260755"/><OMI>10</OMI><OMI>-34</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="4.0"/><OMI>10</OMI><OMI>-40</OMI>
        </OMA>
      </OMA>
      <OMV name="P"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="eq"/>
      <OMS cd="physical_consts1" name="Planck_constant"/>
      <OMA>
        <OMS cd="arith1" name="times"/>
        <OMV name="P"/>
        <OMV name="Joule"/> 
        <OMS cd="units_metric1" name="second"/>
      </OMA>
    </OMA>
  </OMA>
</OMBIND>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <bind><csymbol cd="quant1">exists</csymbol>
  <bvar><ci>P</ci></bvar>
  <apply><csymbol cd="logic1">and</csymbol>
   <apply><csymbol cd="relation1">lt</csymbol>
    <apply><csymbol cd="arith1">minus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">6.6260755</cn>
      <cn>10</cn>
      <cn>-34</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">4.0</cn>
      <cn>10</cn>
      <cn>-40</cn>
     </apply>
    </apply>
    <ci>P</ci>
   </apply>
   <apply><csymbol cd="relation1">gt</csymbol>
    <apply><csymbol cd="arith1">plus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">6.6260755</cn>
      <cn>10</cn>
      <cn>-34</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">4.0</cn>
      <cn>10</cn>
      <cn>-40</cn>
     </apply>
    </apply>
    <ci>P</ci>
   </apply>
   <apply><csymbol cd="relation1">eq</csymbol>
    <csymbol cd="physical_consts1">Planck_constant</csymbol>
    <apply><csymbol cd="arith1">times</csymbol>
     <ci>P</ci>
     <ci>Joule</ci>
     <csymbol cd="units_metric1">second</csymbol>
    </apply>
   </apply>
  </apply>
 </bind>
</math>

Prefix

exists [ P ] . (and (lt (minus (bigfloat ( 6.6260755 , 10, -34) , bigfloat ( 4.0 , 10, -40) ) , P) , gt (plus (bigfloat ( 6.6260755 , 10, -34) , bigfloat ( 4.0 , 10, -40) ) , P) , eq (Planck_constant, times ( P, Joule, second) ) ) )

Popcorn

quant1.exists[$P -> bigfloat1.bigfloat(6.6260755, 10, -34) - bigfloat1.bigfloat(4.0, 10, -40) < $P and bigfloat1.bigfloat(6.6260755, 10, -34) + bigfloat1.bigfloat(4.0, 10, -40) > $P and physical_consts1.Planck_constant = $P * $Joule * units_metric1.second]

Rendered Presentation MathML

$$\exists \hspace{0.17em}P.(6.6260755\times {10}^{-34}-4.0\times {10}^{-40})<P\wedge (6.6260755\times {10}^{-34}+4.0\times {10}^{-40})>P\wedge \mathrm{Planck\_constant}=P\mathrm{Joule}\mathrm{second}$$

Signatures:

sts

mole

Role:

constant

Description:

This symbol represents the number of atoms in one gramme of carbon(12).

Signatures:

sts

gravitational_constant

Role:

constant

Description:

This symbol represents the constant of proportionality in Newtons law of universal gravitation which states; Two bodies attract each other with equal and opposite forces; the magnitude of this force is proportional to the product of the two masses and is also proportional to the inverse square of the distance between the centers of mass of the two bodies. It is approximately equal to: 6.672*10^(-11) Newton square metres per kilogramme squared.

Commented Mathematical property (CMP):

The gravitational constant is approximately 6.672*10^(-11) Newton square metres per kilogramme squared

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="approx"/>
    <OMS cd="physical_consts1" name="gravitational_constant"/>
    <OMA>
      <OMS cd="arith1" name="times"/>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMF dec="6.672"/>
        <OMI>10</OMI><OMI>-11</OMI>
      </OMA>
      <OMS cd="units_metric1" name="Newton"/>
      <OMA>
        <OMS cd="arith1" name="divide"/>
        <OMS cd="units_metric1" name="metre_sqrd"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMA>
            <OMS cd="arith1" name="times"/>
            <OMI>1000</OMI><OMS cd="units_metric1" name="gramme"/>
          </OMA>
          <OMI>2</OMI>
        </OMA>
      </OMA>
    </OMA>
  </OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="physical_consts1">gravitational_constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">6.672</cn>
    <cn>10</cn>
    <cn>-11</cn>
   </apply>
   <csymbol cd="units_metric1">Newton</csymbol>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="units_metric1">metre_sqrd</csymbol>
    <apply><csymbol cd="arith1">power</csymbol>
     <apply><csymbol cd="arith1">times</csymbol><cn>1000</cn><csymbol cd="units_metric1">gramme</csymbol></apply>
     <cn>2</cn>
    </apply>
   </apply>
  </apply>
 </apply>
</math>

Prefix

approx (gravitational_constant, times (bigfloat ( 6.672 , 10, -11) , Newton, divide (metre_sqrd, power (times (1000, gramme) , 2) ) ) )

Popcorn

relation1.approx(physical_consts1.gravitational_constant, bigfloat1.bigfloat(6.672, 10, -11) * units_metric1.Newton * units_metric1.metre_sqrd / (1000 * units_metric1.gramme) ^ 2)

Rendered Presentation MathML

$$\mathrm{gravitational\_constant}\approx 6.672\times {10}^{-11}\mathrm{Newton}\frac{\mathrm{metre\_sqrd}}{{(1000\mathrm{gramme})}^2}$$

Signatures:

sts

Avogadros_constant

Role:

constant

Description:

This symbol represents the number of atoms in 12 grammes of pure carbon(12). It is approximately 6.0221367*10^(23) +/- 3.6*10^(17).

Commented Mathematical property (CMP):

Avogadros constant is 6.0221367*10^(23) +/- 3.6*10^(17).

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="logic1" name="and"/>
  <OMA>
    <OMS cd="relation1" name="lt"/>
    <OMA>
      <OMS cd="arith1" name="minus"/>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMF dec="6.0221367"/><OMI>10</OMI><OMI>23</OMI>
      </OMA>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMF dec="3.6"/><OMI>10</OMI><OMI>17</OMI>
      </OMA>
    </OMA>
    <OMS cd="physical_consts1" name="Avogadros_constant"/>
  </OMA>
  <OMA>
    <OMS cd="relation1" name="gt"/>
    <OMA>
      <OMS cd="arith1" name="plus"/>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMF dec="6.0221367"/><OMI>10</OMI><OMI>23</OMI>
      </OMA>
      <OMA>
        <OMS cd="bigfloat1" name="bigfloat"/>
        <OMF dec="3.6"/><OMI>10</OMI><OMI>17</OMI>
      </OMA>
    </OMA>
    <OMS cd="physical_consts1" name="Avogadros_constant"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="logic1">and</csymbol>
  <apply><csymbol cd="relation1">lt</csymbol>
   <apply><csymbol cd="arith1">minus</csymbol>
    <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
     <cn type="real">6.0221367</cn>
     <cn>10</cn>
     <cn>23</cn>
    </apply>
    <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
     <cn type="real">3.6</cn>
     <cn>10</cn>
     <cn>17</cn>
    </apply>
   </apply>
   <csymbol cd="physical_consts1">Avogadros_constant</csymbol>
  </apply>
  <apply><csymbol cd="relation1">gt</csymbol>
   <apply><csymbol cd="arith1">plus</csymbol>
    <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
     <cn type="real">6.0221367</cn>
     <cn>10</cn>
     <cn>23</cn>
    </apply>
    <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
     <cn type="real">3.6</cn>
     <cn>10</cn>
     <cn>17</cn>
    </apply>
   </apply>
   <csymbol cd="physical_consts1">Avogadros_constant</csymbol>
  </apply>
 </apply>
</math>

Prefix

and (lt (minus (bigfloat ( 6.0221367 , 10, 23) , bigfloat ( 3.6 , 10, 17) ) , Avogadros_constant) , gt (plus (bigfloat ( 6.0221367 , 10, 23) , bigfloat ( 3.6 , 10, 17) ) , Avogadros_constant) )

Popcorn

bigfloat1.bigfloat(6.0221367, 10, 23) - bigfloat1.bigfloat(3.6, 10, 17) < physical_consts1.Avogadros_constant and bigfloat1.bigfloat(6.0221367, 10, 23) + bigfloat1.bigfloat(3.6, 10, 17) > physical_consts1.Avogadros_constant

Rendered Presentation MathML

$$(6.0221367\times {10}^{23}-3.6\times {10}^{17})<\mathrm{Avogadros\_constant}\wedge (6.0221367\times {10}^{23}+3.6\times {10}^{17})>\mathrm{Avogadros\_constant}$$

Signatures:

sts

Faradays_constant

Role:

constant

Description:

This symbol represents the electric charge carried by one mole of electrons. It is approximately 96485.309 +/- 0.029 Coulombs per mole.

Commented Mathematical property (CMP):

Faradays constant is 96485.309 +/- 0.029 Coulombs per mole.

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMBIND>
  <OMS cd="quant1" name="exists"/>
  <OMBVAR>
    <OMV name="F"/>
  </OMBVAR>
  <OMA>
    <OMS cd="logic1" name="and"/>
    <OMA>
      <OMS cd="relation1" name="lt"/>
      <OMA>
        <OMS cd="arith1" name="minus"/>
        <OMF dec="96485.309"/><OMF dec="0.029"/>
      </OMA>
      <OMV name="F"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="gt"/>
      <OMA>
        <OMS cd="arith1" name="plus"/>
        <OMF dec="96485.309"/><OMF dec="0.029"/>
      </OMA>
      <OMV name="F"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="eq"/>
      <OMS cd="physical_consts1" name="Faradays_constant"/>
      <OMA>
        <OMS cd="arith1" name="times"/>
        <OMV name="F"/>
        <OMS cd="units_metric1" name="Coulomb"/>
      </OMA>
    </OMA>
  </OMA>
</OMBIND>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <bind><csymbol cd="quant1">exists</csymbol>
  <bvar><ci>F</ci></bvar>
  <apply><csymbol cd="logic1">and</csymbol>
   <apply><csymbol cd="relation1">lt</csymbol>
    <apply><csymbol cd="arith1">minus</csymbol>
     <cn type="real">96485.309</cn>
     <cn type="real">0.029</cn>
    </apply>
    <ci>F</ci>
   </apply>
   <apply><csymbol cd="relation1">gt</csymbol>
    <apply><csymbol cd="arith1">plus</csymbol>
     <cn type="real">96485.309</cn>
     <cn type="real">0.029</cn>
    </apply>
    <ci>F</ci>
   </apply>
   <apply><csymbol cd="relation1">eq</csymbol>
    <csymbol cd="physical_consts1">Faradays_constant</csymbol>
    <apply><csymbol cd="arith1">times</csymbol><ci>F</ci><csymbol cd="units_metric1">Coulomb</csymbol></apply>
   </apply>
  </apply>
 </bind>
</math>

Prefix

exists [ F ] . (and (lt (minus ( 96485.309 , 0.029 ) , F) , gt (plus ( 96485.309 , 0.029 ) , F) , eq (Faradays_constant, times ( F, Coulomb) ) ) )

Popcorn

quant1.exists[$F -> 96485.309 - 0.029 < $F and 96485.309 + 0.029 > $F and physical_consts1.Faradays_constant = $F * units_metric1.Coulomb]

Rendered Presentation MathML

$$\exists \hspace{0.17em}F.(96485.309-0.029)<F\wedge (96485.309+0.029)>F\wedge \mathrm{Faradays\_constant}=F\mathrm{Coulomb}$$

Signatures:

sts

gas_constant

Role:

constant

Description:

This symbol represents the constant which is equal to the ratio of the pressure times the volume and the temperature of an ideal gas. It is approximately 8.31451 +/- 7.0*10^(-05) Joules per mole per Kelvin.

Commented Mathematical property (CMP):

The gas constant is 8.31451 +/- 7.0*10^(-05) Joules per mole per Kelvin.

Signatures:

sts

Loschmidt_constant

Role:

constant

Description:

This symbol represents the number of particles per unit volume of an ideal gas at standard temperature and pressure. It is approximately 2.686763 * 10^(25) +/- 2.3 * 10^(20) per metre cubed.

Commented Mathematical property (CMP):

The Loschmidt constant is 2.686763 * 10^(25) +/- 2.3 * 10^(20) per metre cubed.

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMBIND>
  <OMS cd="quant1" name="exists"/>
  <OMBVAR>
    <OMV name="L"/>
  </OMBVAR>
  <OMA>
    <OMS cd="logic1" name="and"/>
    <OMA>
      <OMS cd="relation1" name="lt"/>
      <OMA>
        <OMS cd="arith1" name="minus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="2.686763"/><OMI>10</OMI><OMI>25</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="2.3"/><OMI>10</OMI><OMI>20</OMI>
        </OMA>
      </OMA>
      <OMV name="L"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="gt"/>
      <OMA>
        <OMS cd="arith1" name="plus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="2.686763"/><OMI>10</OMI><OMI>25</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="2.3"/><OMI>10</OMI><OMI>20</OMI>
        </OMA>
      </OMA>
      <OMV name="L"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="eq"/>
      <OMS cd="physical_consts1" name="Loschmidt_constant"/>
      <OMA>
        <OMS cd="arith1" name="divide"/>
        <OMV name="L"/>
        <OMA>
          <OMS cd="arith1" name="power"/>
          <OMS cd="units_metric1" name="metre"/>
          <OMI>3</OMI>
        </OMA>
      </OMA>
    </OMA>
  </OMA>
</OMBIND>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <bind><csymbol cd="quant1">exists</csymbol>
  <bvar><ci>L</ci></bvar>
  <apply><csymbol cd="logic1">and</csymbol>
   <apply><csymbol cd="relation1">lt</csymbol>
    <apply><csymbol cd="arith1">minus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">2.686763</cn>
      <cn>10</cn>
      <cn>25</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">2.3</cn>
      <cn>10</cn>
      <cn>20</cn>
     </apply>
    </apply>
    <ci>L</ci>
   </apply>
   <apply><csymbol cd="relation1">gt</csymbol>
    <apply><csymbol cd="arith1">plus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">2.686763</cn>
      <cn>10</cn>
      <cn>25</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">2.3</cn>
      <cn>10</cn>
      <cn>20</cn>
     </apply>
    </apply>
    <ci>L</ci>
   </apply>
   <apply><csymbol cd="relation1">eq</csymbol>
    <csymbol cd="physical_consts1">Loschmidt_constant</csymbol>
    <apply><csymbol cd="arith1">divide</csymbol>
     <ci>L</ci>
     <apply><csymbol cd="arith1">power</csymbol><csymbol cd="units_metric1">metre</csymbol><cn>3</cn></apply>
    </apply>
   </apply>
  </apply>
 </bind>
</math>

Prefix

exists [ L ] . (and (lt (minus (bigfloat ( 2.686763 , 10, 25) , bigfloat ( 2.3 , 10, 20) ) , L) , gt (plus (bigfloat ( 2.686763 , 10, 25) , bigfloat ( 2.3 , 10, 20) ) , L) , eq (Loschmidt_constant, divide ( L, power (metre, 3) ) ) ) )

Popcorn

quant1.exists[$L -> bigfloat1.bigfloat(2.686763, 10, 25) - bigfloat1.bigfloat(2.3, 10, 20) < $L and bigfloat1.bigfloat(2.686763, 10, 25) + bigfloat1.bigfloat(2.3, 10, 20) > $L and physical_consts1.Loschmidt_constant = $L / units_metric1.metre ^ 3]

Rendered Presentation MathML

$$\exists \hspace{0.17em}L.(2.686763\times {10}^{25}-2.3\times {10}^{20})<L\wedge (2.686763\times {10}^{25}+2.3\times {10}^{20})>L\wedge \mathrm{Loschmidt\_constant}=\frac{L}{{\mathrm{metre}}^3}$$

Signatures:

sts

magnetic_constant

Role:

constant

Description:

This symbol represents the ratio of the magnetic flux density in a substance to the external field strength for vacuum. It is equal to 4 pi x 10^(-7) H/m.

Commented Mathematical property (CMP):

The magnetic constant is equal to 4 pi x 10^(-7) H/m.

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="physical_consts1" name="magnetic_constant"/>
  <OMA>
    <OMS cd="arith1" name="times"/>
    <OMS cd="nums1" name="pi"/>
    <OMA>
      <OMS cd="bigfloat1" name="bigfloat"/>
      <OMI>4</OMI><OMI>10</OMI><OMI>-7</OMI>
    </OMA>
    <OMA>
      <OMS cd="arith1" name="divide"/>
      <OMV name="H"/>
      <OMS cd="units_metric1" name="metre"/>
    </OMA>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="physical_consts1">magnetic_constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <csymbol cd="nums1">pi</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol><cn>4</cn><cn>10</cn><cn>-7</cn></apply>
   <apply><csymbol cd="arith1">divide</csymbol><ci>H</ci><csymbol cd="units_metric1">metre</csymbol></apply>
  </apply>
 </apply>
</math>

Prefix

eq (magnetic_constant, times (pi, bigfloat (4, 10, -7) , divide ( H, metre) ) )

Popcorn

physical_consts1.magnetic_constant = nums1.pi * bigfloat1.bigfloat(4, 10, -7) * $H / units_metric1.metre

Rendered Presentation MathML

$$\mathrm{magnetic\_constant}=\pi 4\times {10}^{-7}\frac{H}{\mathrm{metre}}$$

Signatures:

sts

Boltzmann_constant

Role:

constant

Description:

A constant which describes the relationship between temperature and kinetic energy for molecules in an ideal gas. It is approximately 1.380658*10^(-23) +/- 1.2*10^(-28) Joules per Kelvin.

Commented Mathematical property (CMP):

The Boltzmann constant is equal to 1.380658*10^(-23) +/- 1.2*10^(-28) Joules per Kelvin.

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMBIND>
  <OMS cd="quant1" name="exists"/>
  <OMBVAR>
    <OMV name="B"/>
  </OMBVAR>
  <OMA>
    <OMS cd="logic1" name="and"/>
    <OMA>
      <OMS cd="relation1" name="lt"/>
      <OMA>
        <OMS cd="arith1" name="minus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="1.380658"/><OMI>10</OMI><OMI>-23</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="1.2"/><OMI>10</OMI><OMI>-28</OMI>
        </OMA>
      </OMA>
      <OMV name="B"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="gt"/>
      <OMA>
        <OMS cd="arith1" name="plus"/>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="1.380658"/><OMI>10</OMI><OMI>-23</OMI>
        </OMA>
        <OMA>
          <OMS cd="bigfloat1" name="bigfloat"/>
          <OMF dec="1.2"/><OMI>10</OMI><OMI>-28</OMI>
        </OMA>
      </OMA>
      <OMV name="B"/>
    </OMA>
    <OMA>
      <OMS cd="relation1" name="eq"/>
      <OMS cd="physical_consts1" name="Boltzmann_constant"/>
      <OMA>
        <OMS cd="arith1" name="times"/>
        <OMV name="B"/>
        <OMA>
          <OMS cd="arith1" name="divide"/>
          <OMV name="Joules"/>
          <OMS cd="units_metric1" name="degree_Kelvin"/>
        </OMA>
      </OMA>
    </OMA>
  </OMA>
</OMBIND>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <bind><csymbol cd="quant1">exists</csymbol>
  <bvar><ci>B</ci></bvar>
  <apply><csymbol cd="logic1">and</csymbol>
   <apply><csymbol cd="relation1">lt</csymbol>
    <apply><csymbol cd="arith1">minus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">1.380658</cn>
      <cn>10</cn>
      <cn>-23</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">1.2</cn>
      <cn>10</cn>
      <cn>-28</cn>
     </apply>
    </apply>
    <ci>B</ci>
   </apply>
   <apply><csymbol cd="relation1">gt</csymbol>
    <apply><csymbol cd="arith1">plus</csymbol>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">1.380658</cn>
      <cn>10</cn>
      <cn>-23</cn>
     </apply>
     <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
      <cn type="real">1.2</cn>
      <cn>10</cn>
      <cn>-28</cn>
     </apply>
    </apply>
    <ci>B</ci>
   </apply>
   <apply><csymbol cd="relation1">eq</csymbol>
    <csymbol cd="physical_consts1">Boltzmann_constant</csymbol>
    <apply><csymbol cd="arith1">times</csymbol>
     <ci>B</ci>
     <apply><csymbol cd="arith1">divide</csymbol><ci>Joules</ci><csymbol cd="units_metric1">degree_Kelvin</csymbol></apply>
    </apply>
   </apply>
  </apply>
 </bind>
</math>

Prefix

exists [ B ] . (and (lt (minus (bigfloat ( 1.380658 , 10, -23) , bigfloat ( 1.2 , 10, -28) ) , B) , gt (plus (bigfloat ( 1.380658 , 10, -23) , bigfloat ( 1.2 , 10, -28) ) , B) , eq (Boltzmann_constant, times ( B, divide ( Joules, degree_Kelvin) ) ) ) )

Popcorn

quant1.exists[$B -> bigfloat1.bigfloat(1.380658, 10, -23) - bigfloat1.bigfloat(1.2, 10, -28) < $B and bigfloat1.bigfloat(1.380658, 10, -23) + bigfloat1.bigfloat(1.2, 10, -28) > $B and physical_consts1.Boltzmann_constant = $B * $Joules / units_metric1.degree_Kelvin]

Rendered Presentation MathML

$$\exists \hspace{0.17em}B.(1.380658\times {10}^{-23}-1.2\times {10}^{-28})<B\wedge (1.380658\times {10}^{-23}+1.2\times {10}^{-28})>B\wedge \mathrm{Boltzmann\_constant}=B\frac{\mathrm{Joules}}{\mathrm{degree\_Kelvin}}$$

Signatures:

sts