Changes

→‎Note 1: convert graphics
Line 38: Line 38:  
Don't think about it — just compute:
 
Don't think about it — just compute:
   −
{| align="center" cellpadding="6" width="90%"
+
{| align="center" cellpadding="10"
| align="center" |
+
| [[Image:Cactus Graph (P,dP)(Q,dQ).jpg|500px]]
<pre>
  −
o-------------------------------------------------o
  −
|                                                 |
  −
|                  dp o  o dq                  |
  −
|                    / \ / \                    |
  −
|                  p o---@---o q                  |
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|                                                |
  −
o-------------------------------------------------o
  −
|                (p, dp) (q, dq)                 |
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o-------------------------------------------------o
  −
</pre>
   
|}
 
|}
   −
To make future graphs easier to draw in ASCII, I will use devices like '''<code>@=@=@</code>''' and '''<code>o=o=o</code>''' to identify several nodes into one, as in this next redrawing:
+
This expression follows because the expression <math>p + \operatorname{d}p,</math> where the plus sign indicates addition in <math>\mathbb{B},</math> that is, addition modulo 2, and thus corresponds to the exclusive disjunction operation in logic, parses to a graph of the following form:
 
  −
{| align="center" cellpadding="6" width="90%"
  −
| align="center" |
  −
<pre>
  −
o-------------------------------------------------o
  −
|                                                |
  −
|                  p  dp q  dq                  |
  −
|                  o---o o---o                  |
  −
|                    \  | |  /                    |
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|                    \ | | /                    |
  −
|                      \| |/                      |
  −
|                      @=@                      |
  −
|                                                |
  −
o-------------------------------------------------o
  −
|                (p, dp) (q, dq)                |
  −
o-------------------------------------------------o
  −
</pre>
  −
|}
  −
 
  −
However you draw it, these expressions follow because the expression <math>p + \operatorname{d}p,</math> where the plus sign indicates addition in <math>\mathbb{B},</math> that is, addition modulo 2, and thus corresponds to the exclusive disjunction operation in logic, parses to a graph of the following form:
      
{| align="center" cellpadding="6" width="90%"
 
{| align="center" cellpadding="6" width="90%"
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