Commit 93fb60d4 authored by Jim Hefferon's avatar Jim Hefferon

jc3 edits

parent 26e5bcf7
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...@@ -66,18 +66,18 @@ beginfig(2); ...@@ -66,18 +66,18 @@ beginfig(2);
% and \\ % and \\
% rank of $t^j$ (below) % rank of $t^j$ (below)
% \end{tabular} etex,OUT); % \end{tabular} etex,OUT);
glabel.bot(btex Power $j$ of the transformation etex,OUT); glabel.bot(btex \small Power $j$ of the transformation etex,OUT);
otick.bot(btex$0$etex,1); otick.bot(btex \scriptsize $0$etex,1);
otick.bot(btex$1$etex,2); otick.bot(btex \scriptsize $1$etex,2);
otick.bot(btex$2$etex,3); otick.bot(btex \scriptsize $2$etex,3);
otick.bot(btex$j$etex,5); otick.bot(btex \scriptsize $j$etex,5);
otick.bot(btex{\ }etex,8); otick.bot(btex{\ }etex,8);
grid.bot(btex$n$etex,9) withcolor .85white; grid.bot(btex$n$etex,9) withcolor .85white;
otick.bot(btex{\ }etex,10); otick.bot(btex{\ }etex,10);
grid.lft(btex$n$etex,8) withcolor .85white; grid.lft(btex \small $n$etex,8) withcolor .85white;
otick.lft(btex{\ }etex,7); otick.lft(btex{\ }etex,7);
otick.lft(btex{\ }etex,6); otick.lft(btex{\ }etex,6);
otick.lft(btex$\text{rank}(t^j)$etex,3); otick.lft(btex$\small \text{rank}(t^j)$etex,3);
otick.lft(btex{\ }etex,1); otick.lft(btex{\ }etex,1);
otick.lft(btex{\ }etex,1); otick.lft(btex{\ }etex,1);
otick.lft(btex{\ }etex,1); otick.lft(btex{\ }etex,1);
...@@ -282,4 +282,71 @@ beginfig(7) % Tower of Hanoi (three disks at start) ...@@ -282,4 +282,71 @@ beginfig(7) % Tower of Hanoi (three disks at start)
endfig; endfig;
beginfig(8) % graph of rank falling and nullity rising
numeric u; %scaling factor
numeric v; %vertical scaling factor
numeric w; %horizontal scaling factor
u:=10pt; v:=u; w:=v; %
% axes
z0=(0w,0v);
z1=(-.5w,0v); z2=(20.5w,0v); % x axis
z3=(0w,-.5v); z4=(0w,9.5v); % y axis
pickup pensquare scaled line_width_light;
draw z1--z2;
draw z3--z4;
label.lrt(btex \small power etex,z2);
% label.ulft(btex \small power of the transformation etex,z2);
% point of interest
z10=(10w,5v);
% ticks
pickup updown_tick;
for i = 1 upto 3:
drawdot (i*w,0v);
endfor
label.bot(btex \scriptsize $0$ etex,(1w,0v));
label.bot(btex \scriptsize $1$ etex,(2w,0v));
label.bot(btex \scriptsize $2$ etex,(3w,0v));
drawdot (x10,0v);
label.bot(btex \scriptsize $j$ etex,(10w,0v));
for i = 17 upto 19:
drawdot (i*w,0v);
endfor
label.bot(btex \scriptsize $k$ etex,(18w,0v));
% label.bot(btex \scriptsize $k+1$ etex,(14w,0v));
pickup sidetoside_tick;
for i = 7 upto 9:
drawdot (0w,i*v);
endfor
label.lft(btex \scriptsize $n$ etex,(0w,9v));
drawdot (0w,y10);
for i = 1 upto 3:
drawdot (0w,i*v);
endfor
label.lft(btex \scriptsize $0$ etex,(0w,1v));
% The points
pickup pencircle scaled line_width_light;
drawpoint(z10);
pickup pensquare scaled line_width_light;
draw (x10,y10+0.5v)--(x10,y4-0.5v) withcolor .8white; % vert line above dot
draw (x10-0.25w,y4-0.5v)--(x10+0.25w,y4-0.5v) withcolor .8white; % whisker at top
draw (x10-0.25w,y10+0.5v)--(x10+0.25w,y10+0.5v) withcolor .8white; % whisker at top
label.rt(btex \scriptsize $\nullity (t^j)$ etex,(x10,.5[y10,y4]));
draw (x10,y10-0.5v)--(x10,1v) withcolor .8white; % vert line below dot
draw (x10-0.25w,y10-0.5v)--(x10+0.25w,y10-0.5v) withcolor .8white; % whisker at top
draw (x10-0.25w,1v)--(x10+0.25w,1v) withcolor .8white; % whisker at bot
label.lft(btex \scriptsize $\rank (t^j)$ etex,(x10,.5[y10,1v]));
pickup pencircle scaled line_width_light;
drawpoint((1w,9v));
drawpoint((2w,7v));
drawpoint((3w,6v));
drawpoint((17w,3v));
drawpoint((18w,2v));
drawpoint((19w,2v));
drawpoint((20w,2v));
endfig;
end end
\ No newline at end of file
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...@@ -169,6 +169,7 @@ ...@@ -169,6 +169,7 @@
% functions % functions
\newcommand{\map}[3]{\mbox{$#1\colon #2\to #3$}} \newcommand{\map}[3]{\mbox{$#1\colon #2\to #3$}}
\newcommand{\mapsunder}[1]{\stackrel{#1}{\longmapsto}} \newcommand{\mapsunder}[1]{\stackrel{#1}{\longmapsto}}
\newcommand{\xmapsunder}[1]{\xmapsto{#1}}
\newcommand{\composed}[2]{#1\mathbin\circ #2} \newcommand{\composed}[2]{#1\mathbin\circ #2}
\newcommand{\identity}{\mbox{id}} \newcommand{\identity}{\mbox{id}}
\newcommand{\restrictionmap}[2]{{#1}\mathpunct\upharpoonright\hbox{}_{#2}} \newcommand{\restrictionmap}[2]{{#1}\mathpunct\upharpoonright\hbox{}_{#2}}
......
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