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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 01:24, 19 June 2008

7,533 bytes added ,  01:24, 19 June 2008
→‎Work Area: prep tables of differential forms
Line 5,020: Line 5,020:  
| <math>1 + 1 = 0\!</math>
 
| <math>1 + 1 = 0\!</math>
 
| <math>1 + 1 = 0\!</math>
 
| <math>1 + 1 = 0\!</math>
 +
|}
 +
<br>
 +
 +
==Differential Forms==
 +
 +
===Expanded on a Logical Basis===
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 +
|+ '''Orbit Table Template'''
 +
|- style="background:ghostwhite; height:36px"
 +
| &nbsp;
 +
| <math>f\!</math>
 +
| <math>\operatorname{F}f|_{xy}</math>
 +
| <math>\operatorname{F}f|_{x(y)}</math>
 +
| <math>\operatorname{F}f|_{(x)y}</math>
 +
| <math>\operatorname{F}f|_{(x)(y)}</math>
 +
|- style="height:36px"
 +
| <math>f_{0}\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{1}\!</math>
 +
|-
 +
| height="36px" | <math>f_{2}\!</math>
 +
|-
 +
| height="36px" | <math>f_{4}\!</math>
 +
|-
 +
| height="36px" | <math>f_{8}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)(y)\!</math>
 +
|-
 +
| height="36px" | <math>(x)\ y\!</math>
 +
|-
 +
| height="36px" | <math>x\ (y)\!</math>
 +
|-
 +
| height="36px" | <math>x\ y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{3}\!</math>
 +
|-
 +
| height="36px" | <math>f_{12}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)\!</math>
 +
|-
 +
| height="36px" | <math>x\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{6}\!</math>
 +
|-
 +
| height="36px" | <math>f_{9}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x,\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x,\ y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{5}\!</math>
 +
|-
 +
| height="36px" | <math>f_{10}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(y)\!</math>
 +
|-
 +
| height="36px" | <math>y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{7}\!</math>
 +
|-
 +
| height="36px" | <math>f_{11}\!</math>
 +
|-
 +
| height="36px" | <math>f_{13}\!</math>
 +
|-
 +
| height="36px" | <math>f_{14}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x\ y)\!</math>
 +
|-
 +
| height="36px" | <math>(x\ (y))\!</math>
 +
|-
 +
| height="36px" | <math>((x)\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x)(y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|- style="height:36px"
 +
| <math>f_{15}\!</math>
 +
| <math>((~))\!</math>
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
|}
 +
<br>
 +
 +
===Expanded on an Algebraic Basis===
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
 +
|+ '''Orbit Table Template'''
 +
|- style="background:ghostwhite; height:36px"
 +
| &nbsp;
 +
| <math>f\!</math>
 +
| <math>\operatorname{F}f|_{xy}</math>
 +
| <math>\operatorname{F}f|_{x(y)}</math>
 +
| <math>\operatorname{F}f|_{(x)y}</math>
 +
| <math>\operatorname{F}f|_{(x)(y)}</math>
 +
|- style="height:36px"
 +
| <math>f_{0}\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
| <math>(~)\!</math>
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{1}\!</math>
 +
|-
 +
| height="36px" | <math>f_{2}\!</math>
 +
|-
 +
| height="36px" | <math>f_{4}\!</math>
 +
|-
 +
| height="36px" | <math>f_{8}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)(y)\!</math>
 +
|-
 +
| height="36px" | <math>(x)\ y\!</math>
 +
|-
 +
| height="36px" | <math>x\ (y)\!</math>
 +
|-
 +
| height="36px" | <math>x\ y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{3}\!</math>
 +
|-
 +
| height="36px" | <math>f_{12}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x)\!</math>
 +
|-
 +
| height="36px" | <math>x\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{6}\!</math>
 +
|-
 +
| height="36px" | <math>f_{9}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x,\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x,\ y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{5}\!</math>
 +
|-
 +
| height="36px" | <math>f_{10}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(y)\!</math>
 +
|-
 +
| height="36px" | <math>y\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|-
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>f_{7}\!</math>
 +
|-
 +
| height="36px" | <math>f_{11}\!</math>
 +
|-
 +
| height="36px" | <math>f_{13}\!</math>
 +
|-
 +
| height="36px" | <math>f_{14}\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" | <math>(x\ y)\!</math>
 +
|-
 +
| height="36px" | <math>(x\ (y))\!</math>
 +
|-
 +
| height="36px" | <math>((x)\ y)\!</math>
 +
|-
 +
| height="36px" | <math>((x)(y))\!</math>
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|
 +
{| align="center"
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|-
 +
| height="36px" |
 +
|}
 +
|- style="height:36px"
 +
| <math>f_{15}\!</math>
 +
| <math>((~))\!</math>
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 
|}
 
|}
 
<br>
 
<br>
Jon Awbrey
12,080

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/67882"

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