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

Review Date:

2006-08-27

Status:

experimental

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

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

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>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>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

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>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

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

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

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

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

Newton

Description:

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

Signatures:

sts

Joule

Description:

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

Signatures:

sts

Watt

Description:

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

Signatures:

sts

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>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

degree_Celsius

Description:

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

Signatures:

sts

Pascal

Description:

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

Signatures:

sts

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

Coulomb

Description:

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

Signatures:

sts

amp

Description:

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

Signatures:

sts

volt

Description:

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

Signatures:

sts