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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346<CD> <CDName> relation2 </CDName> <CDURL> http://www.openmath.org/cd/relation2.ocd </CDURL> <CDReviewDate> 2003-04-16 </CDReviewDate> <CDDate> 2001-04-16 </CDDate> <CDVersion> 1 </CDVersion> <CDRevision> 0 </CDRevision> <CDStatus> experimental </CDStatus> <CDUses> <CDName>set1</CDName> <CDName>list1</CDName> </CDUses> <Description> This CD holds the binary relations. </Description> <CDDefinition> <Name> binary_relation </Name> <Description> The argument to binary_relation is a set of pairs. </Description> <FMP> </FMP> <Example> An example which represents the statement (1,2) \in r. <OMOBJ> <OMA> <OMS cd="set1" name="in"/> <OMA> <OMS cd="list1" name="list"/> <OMI> 1 </OMI> <OMI> 2 </OMI> </OMA> <OMV name="r" /> </OMA> </OMOBJ> </Example> </CDDefinition> <CDDefinition> <Name> hasse_diagram </Name> <Description> The arguments to hasse_diagram are pairs of the form (elt, list) where <list> is the list of elements which cover <elt>. Define a relation < by a < b if b covers a. Then a) < has the properties that i) (a <b) and (b<c) implies not(a<c) ii) not (a < a) b) the reflexive transitive closure of < is a partial order. </Description> <Example> An example of a hasse diagram. <OMOBJ> <OMA> <OMS cd="relation2" name="hasse_diagram"/> <OMA> <!-- 0 < a,b,c --> <OMS cd="list1" name="list"/> <OMSTR> 0 </OMSTR> <OMA> <OMS cd="list1" name="list"/> <OMSTR> a </OMSTR> <OMSTR> b </OMSTR> <OMSTR> c </OMSTR> </OMA> </OMA> <OMA> <!-- a < 1 --> <OMS cd="list1" name="list"/> <OMSTR> a </OMSTR> <OMA> <OMS cd="list1" name="list"/> <OMSTR> 1 </OMSTR> </OMA> </OMA> <OMA> <!-- b < 1 --> <OMS cd="list1" name="list"/> <OMSTR> b </OMSTR> <OMA> <OMS cd="list1" name="list"/> <OMSTR> 1 </OMSTR> </OMA> </OMA> <OMA> <!-- c < 1 --> <OMS cd="list1" name="list"/> <OMSTR> c </OMSTR> <OMA> <OMS cd="list1" name="list"/> <OMSTR> 1 </OMSTR> </OMA> </OMA> </OMA> </OMOBJ> </Example> </CDDefinition> </CD>