OpenMath Content Dictionary: units_time1

Canonical URL:

http://www.openmath.org/cd/units_time1.ocd

CD File:

units_time1.ocd

CD as XML Encoded OpenMath:

units_time1.omcd

Defines:

calendar_month, calendar_year, day, hour, minute, second, week

Date:

2003-08-21

Version:

1

Review Date:

2004-04-01

Status:

experimental

Uses CD:

interval1, arith1, relations1, set1

This CD defines symbols to represent the basic physical units of time in the SI (syst\'eme international) system of units. and therefore most other modern systems such as "Imperial" and "U.S.".

second

Description:

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

Commented Mathematical property (CMP):

This is a base unit for the SI system

Signatures:

sts

minute

Description:

This symbol represents the measure of one minute of time.

Commented Mathematical property (CMP):

1 minute = 60 seconds

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relations1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="minute" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 60 </OMI>
    <OMS name="second" cd="units_time1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relations1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>1</cn><csymbol cd="units_time1">minute</csymbol></apply>
  <apply><csymbol cd="arith1">times</csymbol><cn>60</cn><csymbol cd="units_time1">second</csymbol></apply>
 </apply>
</math>

Prefix

eq (times ( 1 , minute) , times ( 60 , second) )

Popcorn

relations1.eq(1 * units_time1.minute, 60 * units_time1.second)

Rendered Presentation MathML

$$\mathrm{eq}(1\mathrm{minute},60\mathrm{second})$$

Signatures:

sts

hour

Description:

This symbol represents the measure of one hour of time.

Commented Mathematical property (CMP):

1 hour = 60 minutes

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relations1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="hour" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 60 </OMI>
    <OMS name="minute" cd="units_time1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relations1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>1</cn><csymbol cd="units_time1">hour</csymbol></apply>
  <apply><csymbol cd="arith1">times</csymbol><cn>60</cn><csymbol cd="units_time1">minute</csymbol></apply>
 </apply>
</math>

Prefix

eq (times ( 1 , hour) , times ( 60 , minute) )

Popcorn

relations1.eq(1 * units_time1.hour, 60 * units_time1.minute)

Rendered Presentation MathML

$$\mathrm{eq}(1\mathrm{hour},60\mathrm{minute})$$

Signatures:

sts

day

Description:

This symbol represents the measure of one day of time. The definitions below ignore the possibilities of "leap seconds".

Commented Mathematical property (CMP):

1 day = 24 hours

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relations1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="day" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 24 </OMI>
    <OMS name="hour" cd="units_time1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relations1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>1</cn><csymbol cd="units_time1">day</csymbol></apply>
  <apply><csymbol cd="arith1">times</csymbol><cn>24</cn><csymbol cd="units_time1">hour</csymbol></apply>
 </apply>
</math>

Prefix

eq (times ( 1 , day) , times ( 24 , hour) )

Popcorn

relations1.eq(1 * units_time1.day, 24 * units_time1.hour)

Rendered Presentation MathML

$$\mathrm{eq}(1\mathrm{day},24\mathrm{hour})$$

Signatures:

sts

week

Description:

This symbol represents the measure of one week of time.

Commented Mathematical property (CMP):

1 week = 7 days

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relations1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="week" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 7 </OMI>
    <OMS name="day" cd="units_time1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relations1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>1</cn><csymbol cd="units_time1">week</csymbol></apply>
  <apply><csymbol cd="arith1">times</csymbol><cn>7</cn><csymbol cd="units_time1">day</csymbol></apply>
 </apply>
</math>

Prefix

eq (times ( 1 , week) , times ( 7 , day) )

Popcorn

relations1.eq(1 * units_time1.week, 7 * units_time1.day)

Rendered Presentation MathML

$$\mathrm{eq}(1\mathrm{week},7\mathrm{day})$$

Signatures:

sts

calendar_month

Description:

This symbol represents the measure of one month of (calendar) time.

Commented Mathematical property (CMP):

1 month = 28..31 days

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="in" cd="set1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/>
    <OMS name="calendar_month" cd="units_time1"/>
    <OMS name="day" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS cd="interval1" name="integer_interval"/>
    <OMI> 28 </OMI>
    <OMI> 31 </OMI>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="set1">in</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_time1">calendar_month</csymbol>
   <csymbol cd="units_time1">day</csymbol>
  </apply>
  <apply><csymbol cd="interval1">integer_interval</csymbol><cn>28</cn><cn>31</cn></apply>
 </apply>
</math>

Prefix

in (divide (calendar_month, day) , integer_interval ( 28 , 31 ) )

Popcorn

set1.in(units_time1.calendar_month / units_time1.day, interval1.integer_interval(28, 31))

Rendered Presentation MathML

$$\frac{\mathrm{calendar\_month}}{\mathrm{day}}\in [28,31]$$

Signatures:

sts

calendar_year

Description:

This symbol represents the measure of one year of (calendar) time.

Commented Mathematical property (CMP):

1 year = 365..366 days

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="in" cd="set1"/>
  <OMA>
    <OMS name="divide" cd="arith1"/>
    <OMS name="calendar_year" cd="units_time1"/>
    <OMS name="day" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS cd="interval1" name="integer_interval"/>
    <OMI> 365 </OMI>
    <OMI> 366 </OMI>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="set1">in</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="units_time1">calendar_year</csymbol>
   <csymbol cd="units_time1">day</csymbol>
  </apply>
  <apply><csymbol cd="interval1">integer_interval</csymbol><cn>365</cn><cn>366</cn></apply>
 </apply>
</math>

Prefix

in (divide (calendar_year, day) , integer_interval ( 365 , 366 ) )

Popcorn

set1.in(units_time1.calendar_year / units_time1.day, interval1.integer_interval(365, 366))

Rendered Presentation MathML

$$\frac{\mathrm{calendar\_year}}{\mathrm{day}}\in [365,366]$$

Commented Mathematical property (CMP):

1 year = 12 months

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
<OMA>
  <OMS name="eq" cd="relations1"/>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 1 </OMI>
    <OMS name="calendar_year" cd="units_time1"/>
  </OMA>
  <OMA>
    <OMS name="times" cd="arith1"/>
    <OMI> 12 </OMI>
    <OMS name="calendar_month" cd="units_time1"/>
  </OMA>
</OMA>
</OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relations1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol><cn>1</cn><csymbol cd="units_time1">calendar_year</csymbol></apply>
  <apply><csymbol cd="arith1">times</csymbol><cn>12</cn><csymbol cd="units_time1">calendar_month</csymbol></apply>
 </apply>
</math>

Prefix

eq (times ( 1 , calendar_year) , times ( 12 , calendar_month) )

Popcorn

relations1.eq(1 * units_time1.calendar_year, 12 * units_time1.calendar_month)

Rendered Presentation MathML

$$\mathrm{eq}(1\mathrm{calendar\_year},12\mathrm{calendar\_month})$$

Signatures:

sts