Changeset 111

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• docs/trunk/omega-test-slides/equality-2.gnu

  r110	r111
  2	2
  3	3	set title "Two Equations"
  4	(削除) (削除ここまで)
  5	(削除) set pm3d depthorder (削除ここまで)
  6	4
  7	5	#3x - y + z = 30

• docs/trunk/omega-test-slides/equality-3.gnu

  r110	r111
  2	2
  3	3	set title "Two Equations"
  4	(削除) (削除ここまで)
  5	(削除) set pm3d depthorder (削除ここまで)
  6	4
  7	5	#3x - y + z = 30
  …	…
  33	31
  34	32	set style fill transparent solid 0.5 noborder
  33	(追記) (追記ここまで)
  34	(追記) #4x + y + 6z = 110 (追記ここまで)
  35	(追記) #u = x (追記ここまで)
  36	(追記) #v = y (追記ここまで)
  37	(追記) #z = (110 - 4u - v) / 6 (追記ここまで)
  38	(追記) set palette defined (0 'blue',1 'blue') (追記ここまで)
  39	(追記) splot u, v, (110 - 4*u - v) / 6 with pm3d (追記ここまで)
  40	(追記) (追記ここまで)
  35	41	set palette defined (0 'red',1 'red')
  36	42	splot (30 + u - v)/3, u, v with pm3d
  …	…
  46	52	set style fill transparent solid 0 noborder
  47	53
  48	splot 0,0,0 title "{/*1.5 x + y + 3z = 50}" with lines, 0,0,0 title "{/*1.5 3x - y + z = 30}" with lines(削除) (削除ここまで)
  54	splot 0,0,0 title "{/*1.5 x + y + 3z = 50}" with lines, 0,0,0 title "{/*1.5 3x - y + z = 30}" with lines(追記) , 0,0,0 title "{/*1.5 4x + y + 6z = 110}" with lines (追記ここまで)

• docs/trunk/omega-test-slides/omega-test.tex

  r109	r111
  76	76	%TODO mention that we want integer solutions
  77	77
  78	(追記) %TODO point out that the equation must be linear (追記ここまで)
  79	(追記) (追記ここまで)
  78	80	\section{Terms, etc}
  79	81
  …	…
  134	136	\begin{frame}[fragile]
  135	137	\biggraph{Inconsistent Equality}{equality-1-par}
  138	(追記) (追記ここまで)
  136	139	Rule: Identical coeffs but different constant $\implies$ unsolveable.
  137	140	\end{frame}
  …	…
  143	146	\end{frame}
  144	147
  145	%TODO Show a graph with three planes intersecting in a line:
  148	%Show a graph with three planes intersecting in a line:
  149
  150	\begin{frame}[fragile]
  151	\fullframegraph{Equalities}{equality-3}
  152	\end{frame}
  146	153
  147	154	%This is the maths of the three planes intersecting in a line:
  …	…
  149	156	\begin{frame}[fragile]
  150	157	\frametitle{The Maths}
  151	3x - y + z = 30
  152	x + y + 3z = 50
  158	$\begin{array}{rrcr}
  159	3x - y + & z & = & 30 \\
  160	x + y + & 3z & = & 50 \\
  153	161	%goes to: 4x + 4z = 80, x + z = 20, z = 20 - x. y = 3x + z - 30
  154	162	% Two points this line goes through are: (10,10,10) + (11,12,9)
  155	163	% Therefore (10,10,10) + t(1,2,-1), or (5,0,15) + t(1,2,-1)
  156	% Another random point: (25,10,0).
  157	\end{frame}
  164	% Another random point: (25,10,0), therefore another vector in the plane
  165	% is (3,0,-2)
  166
  167	%Therefore another plane that contains this line satisfies:
  168	% 5 + t + 3u = x
  169	% 2t = y
  170	% 15 - t - 2u = z
  171	% gives:
  172	% t = y/2, u = x + z - 20
  173	% So the plane is:
  174	% 5 + y/2 + 3x + 3z - 60 = x
  175	% 4x + y + 6z = 110
  176	4x + y + & 6z & = & 110
  177	\end{array}$
  178
  179	Subst. $y = 3x + z - 30$ into latter two:
  180
  181	$\begin{array}{rrcr}
  182	4x + & 4z & = & 80 \\
  183	7x + & 7z & = & 140
  184	\end{array}$
  185
  186	After normalisation, equations are identical $\therefore$ redundant.
  187
  188	\end{frame}
  189
  190	%TODO show what happens when you don't yet have a unit coefficient
  158	191
  159	192	\section{Inequalities}
  …	…
  161	194	%TODO probably best shown in two dimensions
  162	195
  196	(追記) \section{Tricky Parts} (追記ここまで)
  197	(追記) (追記ここまで)
  198	(追記) %TODO mention picking out i*j as a variable if possible (追記ここまで)
  199	(追記) (追記ここまで)
  200	(追記) \section{Code to Equations} (追記ここまで)
  201	(追記) (追記ここまで)
  163	202
  164	203	\end{document}

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