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, 18:27, 3 July 2007→Taking Aim at Higher Dimensional Targets: wiki table
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<pre>+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+| Operand | F = <F_1, F_2> | F_i : <|u,v|> -> B | F : [u, v] -> [x, y] |+| | | | |+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+| | (U%->X%)->(EU%->dX%) | B^n x D^n -> D | [B^n x D^n]->[D^k] |+o--------------o----------------------o--------------------o----------------------o+o--------------o----------------------o--------------------o----------------------o+| | U%->EU%, X%->EX%, | | [u, v, du, dv] -> |+| | (U%->X%)->(EU%->EX%) | | [x, y, dx, dy], |+| | | | |+| | | | [B^k x D^k] |+| | | | |+o--------------o----------------------o--------------------o----------------------o+| | | | |+| Secant | $E$ = <!e!, E> : | | $E$F : |+| Operator | | | |+| | U%->EU%, X%->EX%, | | [u, v, du, dv] -> |+| | (U%->X%)->(EU%->EX%) | | [x, y, dx, dy], |+| | | | |+| | | | [B^n x D^n] -> |+| | | | [B^k x D^k] |+| | | | |+o--------------o----------------------o--------------------o----------------------o+| | | | |+| Chord | $D$ = <!e!, D> : | | $D$F : |+| Operator | | | |+| | U%->EU%, X%->EX%, | | [u, v, du, dv] -> |+| | (U%->X%)->(EU%->EX%) | | [x, y, dx, dy], |+| | | | |+| | | | [B^n x D^n] -> |+| | | | [B^k x D^k] |+| | | | |+o--------------o----------------------o--------------------o----------------------o+| | | | |+| Tangent | $T$ = <!e!, d> : | dF_i : | $T$F : |+| Functor | | | |+| | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u, v, du, dv] -> |+| | (U%->X%)->(EU%->EX%) | | [x, y, dx, dy], |+| | | | |+| | | B^n x D^n -> D | [B^n x D^n] -> |+| | | | [B^k x D^k] |+| | | | |+o--------------o----------------------o--------------------o----------------------o+
|}<br>
|}<br>
−{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
−Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes
+|+ '''Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes'''
−|- style="background:paleturquoise"
−| | Operator | Proposition | Transformation |
+|
−| | or | or | or |
+| align="center" | '''Operator<br>or<br>Operand'''
−| | Operand | Component | Mapping |
+| align="center" | '''Proposition<br>or<br>Component'''
−| align="center" | '''Transformation<br>or<br>Mapping'''
−| | | | |
+|-
−| valign="top" | Operand
−| | | | |
+| valign="top" |
−| | F = <f, g> : U -> X | F_i : B^n -> B | F : B^n -> B^k |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| ''F'' = ‹''F''<sub>1</sub>, ''F''<sub>2</sub>›
−|-
−| | | | |
+| ''F'' = ‹''f'', ''g''› : ''U'' → ''X''
−| Tacit | !e! : | !e!F_i : | !e!F : |
+|}
−| Extension | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> B | [u,v,du,dv]->[x, y] |
+| valign="top" |
−| | (U%->X%)->(EU%->X%) | B^n x D^n -> B | [B^n x D^n]->[B^k] |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| | | | |
+| ''F''<sub>''i''</sub> : 〈''u'', ''v''〉 → '''B'''
−|-
−| | | | |
+| ''F''<sub>''i''</sub> : '''B'''<sup>''n''</sup> → '''B'''
−| Trope | !h! : | !h!F_i : | !h!F : |
+|}
−| Extension | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx,dy] |
+| valign="top" |
−| | (U%->X%)->(EU%->dX%) | B^n x D^n -> D | [B^n x D^n]->[D^k] |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100"
−| | | | |
+| ''F'' : [''u'', ''v''] → [''x'', ''y'']
−|-
−| | | | |
+| ''F'' : '''B'''<sup>''n''</sup> → '''B'''<sup>''k''</sup>
−| Enlargement | E : | EF_i : | EF : |
+|}
−| Operator | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx,dy] |
+|-
−| | (U%->X%)->(EU%->dX%) | B^n x D^n -> D | [B^n x D^n]->[D^k] |
+|
−| | | | |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| Tacit
−| | | | |
+|-
−| Difference | D : | DF_i : | DF : |
+| Extension
−| Operator | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx,dy] |
+|}
−| | (U%->X%)->(EU%->dX%) | B^n x D^n -> D | [B^n x D^n]->[D^k] |
+|
−| | | | |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| <math>\epsilon</math> :
−| | | | |
+|-
−| Differential | d : | dF_i : | dF : |
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
−| Operator | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx,dy] |
+|-
−| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → ''X''<sup> •</sup>)
−| | | | |
+|}
−|
−| | | | |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| Remainder | r : | rF_i : | rF : |
+| <math>\epsilon</math>''F''<sub>''i''</sub> :
−| Operator | U%->EU%, X%->EX%, | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx,dy] |
+|-
−| | (U%->X%)->(EU%->dX%) | B^n x D^n -> D | [B^n x D^n]->[D^k] |
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''B'''
−| | | | |
+|-
−| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''B'''
−| | | | |
+|}
−| Radius | $e$ = <!e!, !h!> : | | $e$F : |
+|
−| Operator | | | |
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| <math>\epsilon</math>''F'' :
−|-
−| [''u'', ''v'', d''u'', d''v''] → [''x'', ''y'']
−| | | | [B^n x D^n] -> |
+|-
−| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''B'''<sup>''k''</sup>]
−|}
−|-
−|
−{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| Trope
−|-
−| Extension
−|}
−|
−{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| <math>\eta</math> :
−|-
−| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
−|-
−| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → d''X''<sup> •</sup>)
−|}
−|
−{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| <math>\eta</math>''F''<sub>''i''</sub> :
−|-
−| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
−|-
−| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
−|}
−|
−{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
−| <math>\eta</math>''F'' :
−|-
−| [''u'', ''v'', d''u'', d''v''] → [d''x'', d''y'']
−|-
−| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''D'''<sup>''k''</sup>]
−|}
−</pre>
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Enlargement
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| E :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → d''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| E''F''<sub>''i''</sub> :
+|-
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
+|-
+| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| E''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Difference
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| D :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → d''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| D''F''<sub>''i''</sub> :
+|-
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
+|-
+| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| D''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Differential
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| d :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → d''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| d''F''<sub>''i''</sub> :
+|-
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
+|-
+| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| d''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Remainder
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| r :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → d''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| r''F''<sub>''i''</sub> :
+|-
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
+|-
+| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| r''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Radius
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''e'''</font> = ‹<math>\epsilon</math>, <math>\eta</math>› :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → E''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+|
+|-
+|
+|-
+|
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''e'''</font>''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [''x'', ''y'', d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Secant
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''E'''</font> = ‹<math>\epsilon</math>, E› :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → E''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+|
+|-
+|
+|-
+|
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''E'''</font>''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [''x'', ''y'', d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Chord
+|-
+| Operator
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''D'''</font> = ‹<math>\epsilon</math>, D› :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → E''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+|
+|-
+|
+|-
+|
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''D'''</font>''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [''x'', ''y'', d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
+|}
+|-
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| Tangent
+|-
+| Functor
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''T'''</font> = ‹<math>\epsilon</math>, d› :
+|-
+| ''U''<sup> •</sup> → E''U''<sup> •</sup> , ''X''<sup> •</sup> → E''X''<sup> •</sup> ,
+|-
+| (''U''<sup> •</sup> → ''X''<sup> •</sup>) → (E''U''<sup> •</sup> → E''X''<sup> •</sup>)
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| d''F''<sub>''i''</sub> :
+|-
+| 〈''u'', ''v'', d''u'', d''v''〉 → '''D'''
+|-
+| '''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup> → '''D'''
+|}
+|
+{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
+| <font face=georgia>'''T'''</font>''F'' :
+|-
+| [''u'', ''v'', d''u'', d''v''] → [''x'', ''y'', d''x'', d''y'']
+|-
+| ['''B'''<sup>''n''</sup> × '''D'''<sup>''n''</sup>] → ['''B'''<sup>''k''</sup> × '''D'''<sup>''k''</sup>]
+|}
+|}<br>
===Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>===
===Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>===
