Changes

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a 3-adic ''giving'' relation <math>G \subseteq T \times U \times V</math> with a 2-adic ''loving'' relation <math>L \subseteq U \times W</math> so as to obtain a specialized sort of 3-adic relation <math>(G \circ L) \subseteq T \times W \times V.</math>  The applicable constraints on tuples are shown in Table&nbsp;9.

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a 3-adic ''giving'' relation <math>G \subseteq T \times U \times V</math> with a 2-adic ''loving'' relation <math>L \subseteq U \times W</math> so as to obtain a specialized sort of 3-adic relation <math>(G \circ L) \subseteq T \times W \times V.</math>  The applicable constraints on tuples are shown in Table&nbsp;9.

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| align="center" |

 

{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:70%"

Table 9.  Composite of Triadic and Dyadic Relations

|+ '''Table 9.  Composite of Triadic and Dyadic Relations'''

o---------o---------o---------o---------o---------o

|-

|         #  !1!   |   !1!   |   !1!   |   !1!   |

| style="border-right:1px solid black; border-bottom:1px solid black; width:20%" | &nbsp;

o=========o=========o=========o=========o=========o

| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>

|   G    #    T   |   U   |         |   V   |

| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>

o---------o---------o---------o---------o---------o

| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>

|   L    #        |   U   |   W   |         |

| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>

o---------o---------o---------o---------o---------o

|-

| G o L #    T   |         |   W   |   V   |

| style="border-right:1px solid black" | <math>G\!</math>

| <math>T\!</math>

</pre>

| <math>U\!</math>

| &nbsp;

| <math>V\!</math>

|-

| style="border-right:1px solid black" | <math>L\!</math>

| &nbsp;

| <math>U\!</math>

| <math>W\!</math>

| &nbsp;

|-

| style="border-right:1px solid black" | <math>G \circ L</math>

| <math>T\!</math>

| &nbsp;

| <math>W\!</math>

| <math>V\!</math>

|}

|}

The hypergraph picture of the abstract composition is given in Figure&nbsp;10.

The hypergraph picture of the abstract composition is given in Figure&nbsp;10.