12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Friday November 22, 2024
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
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>
|}
|}
