OpenMath Content Dictionary: interval1

Canonical URL:

http://www.openmath.org/cd/interval1.ocd

CD File:

interval1.ocd

CD as XML Encoded OpenMath:

interval1.omcd

Defines:

integer_interval, interval, interval_cc, interval_co, interval_oc, interval_oo

Date:

2001-03-12

Version:

2

Review Date:

2003-04-01

Status:

official

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This CD holds symbols which describe both discrete and continuous 1-dimensional intervals (with open/closed end points).

integer_interval

A symbol to denote a discrete 1 dimensional interval from the first argument to the second (inclusive), where the discretisation occurs at unit intervals. The arguments are the start and the end points of the interval in that order.

Example:

The integer interval 1, 2, ..., 10.

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="integer_interval"/>
    <OMI> 1 </OMI>
    <OMI> 10 </OMI>
  </OMA>
</OMOBJ>

integer_interval ( 1 , 10 )

Signatures:

sts

interval

A symbol to denote a continuous 1-dimensional interval without any information about the character of the end points (used in definite integration). The arguments are the start and the end points of the interval in that order.

Example:

The interval 1.0, ..., 10.0.

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="interval"/>
    <OMF dec="1.0"/>
    <OMF dec="10.0"/>
  </OMA>
</OMOBJ>

interval ( 1.0 , 10.0 )

Signatures:

sts

interval_oo

A symbol to denote a continuous 1-dimensional interval with both end points excluded from the interval. The arguments are the start and the end points of the interval in that order.

Example:

The continuous open interval (1,10).

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="interval_oo"/>
    <OMI> 1 </OMI>
    <OMI> 10 </OMI>
  </OMA>
</OMOBJ>

interval_oo ( 1 , 10 )

Signatures:

sts

interval_cc

A symbol to denote a continuous 1-dimensional interval with both end points included in the interval. The arguments are the start and the end points of the interval in that order.

Example:

The continuous closed interval [1,10].

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="interval_cc"/>
    <OMI> 1 </OMI>
    <OMI> 10 </OMI>
  </OMA>
</OMOBJ>

interval_cc ( 1 , 10 )

Signatures:

sts

interval_oc

A symbol to denote a continuous 1-dimensional interval with the first point excluded from the interval, but the last included. The arguments are the start and the end points of the interval in that order.

Example:

The continuous interval open at the lower bound and closed at the higher bound (1,10].

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="interval_oc"/>
    <OMI> 1 </OMI>
    <OMI> 10 </OMI>
  </OMA>
</OMOBJ>

interval_oc ( 1 , 10 )

Signatures:

sts

interval_co

A symbol to denote a continuous 1-dimensional interval with the first point included in the interval, but the last excluded. The arguments are the start and the end points of the interval in that order.

Example:

The continuous interval closed at the lower bound and open at the higher bound [1,10).

<OMOBJ>
  <OMA>
    <OMS cd="interval1" name="interval_co"/>
    <OMI> 1 </OMI>
    <OMI> 10 </OMI>
  </OMA>
</OMOBJ>

interval_co ( 1 , 10 )

Signatures:

sts