Changes

Table 20 gives the constraint matrix version of the same thing.

Table 20 gives the constraint matrix version of the same thing.

{| align="center" cellspacing="6" width="90%"

| align="center" |

 

<pre>

{| 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 20.  Arrow: J(L(u, v)) = K(Ju, Jv)

|+ <math>\text{Table 20.  Arrow Equation:}~~ J(L(u, v)) = K(Ju, Jv)</math>

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

|-

|         #    J   |   J    |   J   |

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

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

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

|   K    #    X   |   X   |   X   |

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

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

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

|   L    #    Y   |   Y   |   Y   |

|-

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

</pre>

| <math>X\!</math>

| <math>X\!</math>

| <math>X\!</math>

|-

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

| <math>Y\!</math>

| <math>Y\!</math>

| <math>Y\!</math>

|}

|}

One way to read this Table is in terms of the informational redundancies that it schematizes.  In particular, it can be read to say that when one satisfies the constraint in the <math>L\!</math> row, along with all the constraints in the <math>J\!</math> columns, then the constraint in the <math>K\!</math> row is automatically true.  That is one way of understanding the equation:  <math>J(L(u, v)) ~=~ K(Ju, Jv).</math>

One way to read this Table is in terms of the informational redundancies that it schematizes.  In particular, it can be read to say that when one satisfies the constraint in the <math>L\!</math> row, along with all the constraints in the <math>J\!</math> columns, then the constraint in the <math>K\!</math> row is automatically true.  That is one way of understanding the equation:  <math>J(L(u, v)) ~=~ K(Ju, Jv).</math>