12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Sunday April 06, 2025
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)
Revision as of 04:14, 17 June 2009
, 04:14, 17 June 2009→Note 25: convert graphics
Line 3,998:
Line 3,998:
+o---------------------------------------------------------------------o+| |+| X |+| o-------------------o o-------------------o |+| / \ / \ |+| / P o Q \ |+| / / \ \ |+| / / \ \ |+| / / \ \ |+| / / \ \ |
−| / / \ \ |
−| o o (dp) (dq) o o |
−| | | o-->--o | | |
−| | | \ / | | |
−| | (dp) dq | \ / | dp (dq) | |
−| | o----------------->o<-----------------o | |
−| | | ^ | | |
−| | | | | | |
−| | | | | | |
−| o o | o o |
−| \ \ | / / |
−| \ \ | / / |
−| \ \ | / / |
−| \ \ | / / |
−| \ \|/ / |
−| \ | / |
−| \ /|\ / |
−| o-------------------o | o-------------------o |
−| | |
−| dp | dq |
−| | |
−| | |
−| o |
−| |
−o---------------------------------------------------------------------o
−Figure 25-1. Enlargement E[pq] : EX -> B
−
Continuing with the example <math>pq : X \to \mathbb{B},</math> Figure 25-1 shows the enlargement or shift map <math>\operatorname{E}(pq) : \operatorname{E}X \to \mathbb{B}</math> in the same style of differential field picture that we drew for the tacit extension <math>\varepsilon (pq) : \operatorname{E}X \to \mathbb{B}.</math>
Continuing with the example <math>pq : X \to \mathbb{B},</math> Figure 25-1 shows the enlargement or shift map <math>\operatorname{E}(pq) : \operatorname{E}X \to \mathbb{B}</math> in the same style of differential field picture that we drew for the tacit extension <math>\varepsilon (pq) : \operatorname{E}X \to \mathbb{B}.</math>
−{| align="center" cellspacing="10" style="text-align:center"
−{| align="center" cellspacing="10" style="text-align:center; width:90%"
+| [[Image:Field Picture PQ Enlargement Conjunction.jpg|500px]]
+|-
+| <math>\text{Figure 25-1. Enlargement}~ \operatorname{E}(pq) : \operatorname{E}X \to \mathbb{B}</math>
+|-
|
|
−<pre>
+<math>\begin{array}{rcccccc}
−\operatorname{E}(pq)
−& = & p & \cdot & q & \cdot & (\operatorname{d}p)(\operatorname{d}q)
−\\[4pt]
−& + & p & \cdot & (q) & \cdot & (\operatorname{d}p)~\operatorname{d}q~
−\\[4pt]
−& + & (p) & \cdot & q & \cdot & ~\operatorname{d}p~(\operatorname{d}q)
−\\[4pt]
−& + & (p) & \cdot & (q) & \cdot & ~\operatorname{d}p~~\operatorname{d}q~
−\end{array}</math>
−</pre>
|}
|}
