OpenMath Content Dictionary: interval_types

Canonical URL:

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

CD File:

interval_types.ocd

CD as XML Encoded OpenMath:

interval_types.omcd

Defines:

algebraicIntervalType, integerIntervalType, intervalType, rationalIntervalType, realIntervalType

Date:

2002-08-25

Version:

0 (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: Bill Naylor

A CD of basic interval type constructors. This CD holds constructors of individual instances of the different types of intervals.

---

intervalType

Description:

This symbol represents the type of intervals.

Commented Mathematical property (CMP):

interval type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="intervalType"/>
      <OMS cd="aggregate_cats" name="setType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">intervalType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (intervalType, setType)

Popcorn

meta_cats.has(interval_types.intervalType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{intervalType},\mathrm{setType})$$

Signatures:

sts

---

[Next: integerIntervalType] [Last: realIntervalType] [Top]

---

integerIntervalType

Description:

This symbol represents the type of integer intervals.

Commented Mathematical property (CMP):

integer interval type has rational interval type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="integerIntervalType"/>
      <OMS cd="interval_types" name="rationalIntervalType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">integerIntervalType</csymbol>
  <csymbol cd="interval_types">rationalIntervalType</csymbol>
 </apply>
</math>

Prefix

has (integerIntervalType, rationalIntervalType)

Popcorn

meta_cats.has(interval_types.integerIntervalType, interval_types.rationalIntervalType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{integerIntervalType},\mathrm{rationalIntervalType})$$

Commented Mathematical property (CMP):

integer interval type has discrete set type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="integerIntervalType"/>
      <OMS cd="aggregate_cats" name="discreteSetType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">integerIntervalType</csymbol>
  <csymbol cd="aggregate_cats">discreteSetType</csymbol>
 </apply>
</math>

Prefix

has (integerIntervalType, discreteSetType)

Popcorn

meta_cats.has(interval_types.integerIntervalType, aggregate_cats.discreteSetType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{integerIntervalType},\mathrm{discreteSetType})$$

Signatures:

sts

---

[Next: rationalIntervalType] [Previous: intervalType] [Top]

---

rationalIntervalType

Description:

This symbol represents the type of rational intervals.

Commented Mathematical property (CMP):

rational interval type has algebraic interval type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="rationalIntervalType"/>
      <OMS cd="interval_types" name="algebraicIntervalType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">rationalIntervalType</csymbol>
  <csymbol cd="interval_types">algebraicIntervalType</csymbol>
 </apply>
</math>

Prefix

has (rationalIntervalType, algebraicIntervalType)

Popcorn

meta_cats.has(interval_types.rationalIntervalType, interval_types.algebraicIntervalType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{rationalIntervalType},\mathrm{algebraicIntervalType})$$

Commented Mathematical property (CMP):

rational interval type has continuous set type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="rationalIntervalType"/>
      <OMS cd="aggregate_cats" name="continuousSetType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">rationalIntervalType</csymbol>
  <csymbol cd="aggregate_cats">continuousSetType</csymbol>
 </apply>
</math>

Prefix

has (rationalIntervalType, continuousSetType)

Popcorn

meta_cats.has(interval_types.rationalIntervalType, aggregate_cats.continuousSetType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{rationalIntervalType},\mathrm{continuousSetType})$$

Signatures:

sts

---

[Next: algebraicIntervalType] [Previous: integerIntervalType] [Top]

---

algebraicIntervalType

Description:

This symbol represents the type of algebraic intervals.

Commented Mathematical property (CMP):

algebraic interval type has real interval type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="algebraicIntervalType"/>
      <OMS cd="interval_types" name="realIntervalType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">algebraicIntervalType</csymbol>
  <csymbol cd="interval_types">realIntervalType</csymbol>
 </apply>
</math>

Prefix

has (algebraicIntervalType, realIntervalType)

Popcorn

meta_cats.has(interval_types.algebraicIntervalType, interval_types.realIntervalType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{algebraicIntervalType},\mathrm{realIntervalType})$$

Commented Mathematical property (CMP):

algebraic interval type has continuous set type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="algebraicIntervalType"/>
      <OMS cd="aggregate_cats" name="continuousSetType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">algebraicIntervalType</csymbol>
  <csymbol cd="aggregate_cats">continuousSetType</csymbol>
 </apply>
</math>

Prefix

has (algebraicIntervalType, continuousSetType)

Popcorn

meta_cats.has(interval_types.algebraicIntervalType, aggregate_cats.continuousSetType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{algebraicIntervalType},\mathrm{continuousSetType})$$

Signatures:

sts

---

[Next: realIntervalType] [Previous: rationalIntervalType] [Top]

---

realIntervalType

Description:

This symbol represents the type of real intervals.

Commented Mathematical property (CMP):

real interval type has interval type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="realIntervalType"/>
      <OMS cd="interval_types" name="intervalType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">realIntervalType</csymbol>
  <csymbol cd="interval_types">intervalType</csymbol>
 </apply>
</math>

Prefix

has (realIntervalType, intervalType)

Popcorn

meta_cats.has(interval_types.realIntervalType, interval_types.intervalType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{realIntervalType},\mathrm{intervalType})$$

Commented Mathematical property (CMP):

real interval type has continuous set type

Formal Mathematical property (FMP):

OpenMath XML (source)

<OMOBJ xmlns="http://www.openmath.org/OpenMath">
    <OMA>
      <OMS cd="meta_cats" name="has"/>
      <OMS cd="interval_types" name="realIntervalType"/>
      <OMS cd="aggregate_cats" name="continuousSetType"/>
    </OMA>
  </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="interval_types">realIntervalType</csymbol>
  <csymbol cd="aggregate_cats">continuousSetType</csymbol>
 </apply>
</math>

Prefix

has (realIntervalType, continuousSetType)

Popcorn

meta_cats.has(interval_types.realIntervalType, aggregate_cats.continuousSetType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{realIntervalType},\mathrm{continuousSetType})$$

Signatures:

sts

---

[First: intervalType] [Previous: algebraicIntervalType] [Top]

maybe we should also include some 'complex interval' symbols,
could have cartesian varieties, i.e. 'square', as well as polar
varieties, i.e. 'round'