OpenMath Content Dictionary: plangeo6

Canonical URL:

plangeo6.ocd

CD File:

plangeo6.ocd

CD as XML Encoded OpenMath:

plangeo6.omcd

Defines:

are_on_conic, conic

Date:

2004-06-01

Version:

0 (Revision 3)

Review Date:

2006-06-01

Status:

experimental

Uses CD:

plangeo1

This CD defines symbols for planar Euclidean geometry related to conics. amc: 18 March 2004 added are_on_conic

conic

Description:

The symbol represents a conic. The conic may be subject to constraints.

Example:

The conic G, incident to A,B,C,D and E is given by

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA>
    <OMS cd="plangeo6" name="conic"/>
    <OMV name="G"/>
    <OMA>
      <OMS cd="plangeo1" name="incident"/>
      <OMV name="G"/>
      <OMV name="A"/>
    </OMA>
    <OMA>
      <OMS cd="plangeo1" name="incident"/>
      <OMV name="G"/>
      <OMV name="B"/>
    </OMA>
    <OMA>
      <OMS cd="plangeo1" name="incident"/>
      <OMV name="G"/>
      <OMV name="C"/>
    </OMA>
    <OMA>
      <OMS cd="plangeo1" name="incident"/>
      <OMV name="G"/>
      <OMV name="D"/>
    </OMA>
    <OMA>
      <OMS cd="plangeo1" name="incident"/>
      <OMV name="G"/>
      <OMV name="E"/>
    </OMA>
  </OMA>
</OMOBJ>

conic ( G, incident ( G, A) , incident ( G, B) , incident ( G, C) , incident ( G, D) , incident ( G, E) )

$$\mathrm{conic}(G,\mathrm{incident}(G,A),\mathrm{incident}(G,B),\mathrm{incident}(G,C),\mathrm{incident}(G,D),\mathrm{incident}(G,E))$$

Signatures:

sts

are_on_conic

Description:

The symbol is a boolean n-ary function. Its arguments should be points. When applied to a sequence of points, its evaluated to true if and only if there is a conic on which all arguments lie.

Commented Mathematical property (CMP):

If G is the conic determined by A,B,C,D, and E, whereas F is a point incident with G, then A,B,C,D, E, and F are on a conic.

Formal Mathematical property (FMP):

xml prefix mathml

<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0">
  <OMA><OMS cd="logic1" name="implies"/>
       <OMA><OMS cd="set1" name="in"/>
            <OMV name="F"/>
            <OMA><OMS cd="plangeo6" name="conic"/>
                 <OMV name="G"/>
                 <OMA><OMS cd="plangeo1" name="incident"/>
                      <OMV name="G"/>     <OMV name="A"/>
                 </OMA>
                 <OMA><OMS cd="plangeo1" name="incident"/>
                      <OMV name="G"/>     <OMV name="B"/>
                 </OMA>
                 <OMA><OMS cd="plangeo1" name="incident"/>
                      <OMV name="G"/>      <OMV name="C"/>
                 </OMA>
                 <OMA><OMS cd="plangeo1" name="incident"/>
                      <OMV name="G"/>    <OMV name="D"/>
                 </OMA>
                 <OMA><OMS cd="plangeo1" name="incident"/>
                      <OMV name="G"/>      <OMV name="E"/>
                 </OMA>
            </OMA>
       </OMA>
       <OMA><OMS cd="plangeo6" name="are_on_conic"/>
            <OMV name="A"/><OMV name="B"/><OMV name="C"/>
            <OMV name="D"/><OMV name="E"/><OMV name="F"/>
       </OMA>
  </OMA>
</OMOBJ>

implies (in ( F, conic ( G, incident ( G, A) , incident ( G, B) , incident ( G, C) , incident ( G, D) , incident ( G, E) ) ) , are_on_conic ( A, B, C, D, E, F) )

$$F\in \mathrm{conic}(G,\mathrm{incident}(G,A),\mathrm{incident}(G,B),\mathrm{incident}(G,C),\mathrm{incident}(G,D),\mathrm{incident}(G,E))\Rightarrow \mathrm{are\_on\_conic}(A,B,C,D,E,F)$$

Signatures:

sts