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

Review Date:

2005-04-01

Status:

experimental

Uses CD:

aggregate_cats, meta_cats

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):

xml prefix mathml

<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>

has (intervalType, setType)

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

Signatures:

sts

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):

xml prefix mathml

<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>

has (integerIntervalType, rationalIntervalType)

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

Commented Mathematical property (CMP):

integer interval type has discrete set type

Formal Mathematical property (FMP):

xml prefix mathml

<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>

has (integerIntervalType, discreteSetType)

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

Signatures:

sts

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):

xml prefix mathml

<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>

has (rationalIntervalType, algebraicIntervalType)

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

Commented Mathematical property (CMP):

rational interval type has continuous set type

Formal Mathematical property (FMP):

xml prefix mathml

<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>

has (rationalIntervalType, continuousSetType)

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

Signatures:

sts

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):

xml prefix mathml

<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>

has (algebraicIntervalType, realIntervalType)

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

Commented Mathematical property (CMP):

algebraic interval type has continuous set type

Formal Mathematical property (FMP):

xml prefix mathml

<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>

has (algebraicIntervalType, continuousSetType)

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

Signatures:

sts

realIntervalType

Description:

This symbol represents the type of real intervals.

Commented Mathematical property (CMP):

real interval type has interval type

Formal Mathematical property (FMP):

xml prefix mathml

<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>

has (realIntervalType, intervalType)

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

Commented Mathematical property (CMP):

real interval type has continuous set type

Formal Mathematical property (FMP):

xml prefix mathml

<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>

has (realIntervalType, continuousSetType)

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

Signatures:

sts

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