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:

2004-08-27

Version:

1 (Revision 1)

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 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

---

[Next: minute] [Last: calendar_year] [Top]

---

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="relation1"/>
  <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="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_time1">minute</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">60</cn>
   <csymbol cd="units_time1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

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

Popcorn

1 * units_time1.minute = 60 * units_time1.second

Rendered Presentation MathML

$$1\mathrm{minute}=60\mathrm{second}$$

Signatures:

sts

---

[Next: hour] [Previous: second] [Top]

---

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="relation1"/>
  <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="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_time1">hour</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">60</cn>
   <csymbol cd="units_time1">minute</csymbol>
  </apply>
 </apply>
</math>

Prefix

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

Popcorn

1 * units_time1.hour = 60 * units_time1.minute

Rendered Presentation MathML

$$1\mathrm{hour}=60\mathrm{minute}$$

Signatures:

sts

---

[Next: day] [Previous: minute] [Top]

---

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="relation1"/>
  <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="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_time1">day</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">24</cn>
   <csymbol cd="units_time1">hour</csymbol>
  </apply>
 </apply>
</math>

Prefix

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

Popcorn

1 * units_time1.day = 24 * units_time1.hour

Rendered Presentation MathML

$$1\mathrm{day}=24\mathrm{hour}$$

Signatures:

sts

---

[Next: week] [Previous: hour] [Top]

---

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="relation1"/>
  <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="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_time1">week</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">7</cn>
   <csymbol cd="units_time1">day</csymbol>
  </apply>
 </apply>
</math>

Prefix

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

Popcorn

1 * units_time1.week = 7 * units_time1.day

Rendered Presentation MathML

$$1\mathrm{week}=7\mathrm{day}$$

Signatures:

sts

---

[Next: calendar_month] [Previous: day] [Top]

---

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 type="integer">28</cn>
   <cn type="integer">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

---

[Next: calendar_year] [Previous: week] [Top]

---

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 type="integer">365</cn>
   <cn type="integer">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="relation1"/>
  <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="relation1">eq</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">1</cn>
   <csymbol cd="units_time1">calendar_year</csymbol>
  </apply>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">12</cn>
   <csymbol cd="units_time1">calendar_month</csymbol>
  </apply>
 </apply>
</math>

Prefix

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

Popcorn

1 * units_time1.calendar_year = 12 * units_time1.calendar_month

Rendered Presentation MathML

$$1\mathrm{calendar\_year}=12\mathrm{calendar\_month}$$

Signatures:

sts

---

[First: second] [Previous: calendar_month] [Top]