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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/diagmac2/doc/diagmactest.tex |
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diff --git a/macros/latex/contrib/diagmac2/doc/diagmactest.tex b/macros/latex/contrib/diagmac2/doc/diagmactest.tex new file mode 100644 index 0000000000..a4ee5e99f4 --- /dev/null +++ b/macros/latex/contrib/diagmac2/doc/diagmactest.tex @@ -0,0 +1,403 @@ +%TESTS OF DIAGRAM MACROS - J. C. Reynolds - December 1987 + +%This is an input file for LATEX that inputs the macros in diagmac.tex +%and tests them. A user's manual for these macros is in diagmac.doc + +\documentclass[12pt]{article} +\input diagmac +\oddsidemargin=0in +\evensidemargin=0in +\textwidth=6.5in +\begin{document} + +\thispagestyle{empty} + +\begin{centering} +{\large\bf TESTS OF DIAGRAM MACROS} \\[14 pt] +\today \\[21 pt] +\end{centering} + + +%These are the two examples given in the user's manual. + +$$\diagram{ +\vertex 0,100:{A}{\border{3pt}{4pt}\rect} +\vertex 150,100:{B}{\border{3pt}{4pt}\rect} +\vertex 0,0:{A'}{\border{3pt}{4pt}\rect} +\vertex 150,0:{B'}{\border{3pt}{4pt}\rect} +\setedge 0,100,150,100: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutabove 75:{\textstyle c}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,0,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutbelow 75:{\textstyle c'}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,100,0,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutleft 50:{\textstyle a}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 150,100,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutright 50:{\textstyle b}{\border{2pt}{2pt}\octagon{3pt}} +}$$ + +$$\ctdiagram{ +\ctv 0,100:{A} +\ctv 150,100:{B} +\ctv 0,0:{A'} +\ctv 150,0:{B'} +\ctet 0,100,150,100:{c} +\cteb 0,0,150,0:{c'} +\ctel 0,100,0,0:{a} +\cter 150,100,150,0:{b} +}$$ + +\newpage + +%This gives a thorough workout to the general macros for diagrams. +%The result looks like an eye-chart for Martians. + +$$\diagram{ +\vertex -150,0:{X+Y}{\border{4pt}{3pt}\rorect{2pt}01\outline} +\vertex 0,-50:Y{\border{10pt}{10pt}\hexagon\outline} +\vertex 150,0:\sum{\border{10pt}{10pt}\octagon{10pt}\outline + \border{5pt}{5pt}\octagon{12pt}\thicklines\outline\thinlines} +\vertex -100,150:\alpha{\border{4pt}{3pt}\diamond\outline} +\vertex 100,150:\sum{\border{10pt}{10pt}\rorect{20pt}00\outline + \border{5pt}{5pt}\rorect{24pt}00\thicklines\outline\thinlines} +\vertex 0,200:{X^2+Y^2}{\border{4pt}{3pt}\rect\outline} +\place -150,-150:{X+Y^{Z^2}} + {\leftghost X\symmetrize\borderto{0pt}{0pt}\border{4pt}{3pt}\rect\outline + \setcircle{16pt}{\xcenter}{\bexpr}\drawcircle0110 + \drawcirclehead{0}{-1}1 + \abutcirclebelow{-10pt}\alpha{\border{2pt}{2pt}\rect\outline} + \abutcirclebelow{10pt}\alpha{\border{2pt}{2pt}\rect\outline}} +\placed{150pt}{-150pt}{X+Y} + {\rightghost Y\symmetrize\borderto{0pt}{26pt}\border{4pt}{0pt}\rect\outline + \placed{\lexpr}{\ycenter}{\vrule height3.2pt depth-2.8pt width10pt}{} + \place 0,-3:{\vrule height3.2pt depth-2.8pt width10pt}{\xcenter=\lexpr} + \setcircle{16pt}{\rexpr}{\texpr}\shiftcircle{8pt}{8pt}\drawcircle1101 + \drawcirclehead{0}{-1}1\drawcirclehead{-1}00 + \abutcircleabove{0pt}\alpha{\border{2pt}{2pt}\rect\outline}} +\vertex 0,-150:{}{\setcircle{40pt}{\xcenter}{\ycenter}\drawcircle1111 + \drawcirclehead231\drawcirclehead{-2}30 + \drawcirclehead6{-9}0\drawcirclehead{-4}{-6}1 + \abutcircleleft{0pt}\alpha{\border{2pt}{2pt}\rect\outline} + \abutcircleright{20pt}\alpha{\border{2pt}{2pt}\rect\outline} + \abutcircleright{0pt}\alpha{\border{2pt}{2pt}\rect\outline} + \abutcircleright{-20pt}\alpha{\border{2pt}{2pt}\rect\outline}} +\setedge 0,200,-100,150:\shadeedge\drawsolidedge\drawedgehead{100}10 + \abutleft 185:{\alpha+\beta}{\border{2pt}{2pt}\rorect{5pt}01\outline} +\setedge 0,200,100,150:\shadeedge\drawsolidedge\drawedgehead{100}10 + \abutright 185:{\alpha+\beta}{\border{2pt}{2pt}\rorect{5pt}01\outline} +\setedge -150,0,0,-50:\shadeedge\drawdashedge{11pt}{10pt}01\drawedgehead{80}01 + \abutleftd{-25pt}{\alpha\beta} + {\border{2pt}{2pt}\borderto{25pt}{0pt}\rect\outline} +\setedge -150,0,150,0:\drawedgehead{50}01\shadeedge\drawsolidedge + \abutabove -10:\rho{\border{2pt}{2pt}\diamond\outline} +\setedge -150,0,-100,150:\shadeedge\drawsolidedge\drawedgehead{100}10 + \abutleft 75:\rho{\border{10pt}{10pt}\octagon{10pt}\outline} +\setedge -150,0,100,150:\shadeedge\drawdotedge{7pt}1 + \abutaboved{-100pt}\rho{\border{10pt}{10pt}\hexagon\outline} +\setedge 0,-50,150,0:\shadeedge\drawsolidedge\drawedgehead{20}11 + \abutrightd{-25pt}\rho{\border{2pt}{2pt}\borderto{25pt}{0pt}\rect\outline} +\setedge 0,-50,-100,150:\shadeedge\drawsolidedge +\setedge 0,-50,100,150:\shadeedge\drawsolidedge +\setedge 150,0,-100,150:\shadeedge\drawsolidedge + \abutbelowd{100pt}\rho{\border{10pt}{10pt}\hexagon\outline} +\setedge 150,0,100,150:\shadeedge\drawdashedge{40pt}{40pt}11\drawedgehead000 + \abutleft 75:\rho{\border{10pt}{10pt}\hexagon\outline} + \shiftedge{-10pt}\shadeedge\drawdashedge{30pt}{30pt}10\drawedgehead000 + \shiftedge{-10pt}\shadeedge\drawdashedge{11pt}{5pt}01\drawedgehead000 + \shiftedge{-10pt}\shadeedge\drawdotedge{8pt}0\drawedgehead{100}10 + \abutright 75:\rho{\border{5pt}{5pt}\rorect{5pt}11\outline} +\setedge -100,150,100,150:\drawedgehead{50}11\shadeedge\drawsolidedge + \abutbelow 0:\rho{\border{2pt}{2pt}\rect\outline} +\setedge 0,-50,-150,-150:\thicklines\drawedgehead{50}01\thinlines + \shadeedge\drawdashedge{13pt}{3pt}01\drawedgehead{50}11 + \abutbelow -50:{X \atop Y}{\border{2pt}{2pt}\rorect{5pt}10\outline} +\setedge 0,-50,0,-150:\thicklines\shadeedge\drawsolidedge\thinlines +\setedge 0,-50,150,-150:\shadeedge\drawsolidedge + \abutabove 75:{X \atop Y}{\border{2pt}{2pt}\rorect{5pt}10\outline} +\setedge -175,-50,-175,-100:\drawdashedge{10pt}{31pt}11 +\setedge -165,-100,-165,-50:\drawdashedge{15pt}{15pt}01 +\setedge -155,-50,-155,-100:\drawdashedge{5pt}{5pt}11 +\setedge -145,-100,-145,-50:\drawdotedge{26pt}1 +\setedge -135,-50,-135,-100:\drawdotedge{25pt}1 +\setedge -125,-100,-125,-50:\drawdotedge{5pt}1 +\setedge 125,-50,175,-50:\drawdashedge{10pt}{31pt}11 +\setedge 175,-60,125,-60:\drawdashedge{15pt}{15pt}01 +\setedge 125,-70,175,-70:\drawdashedge{5pt}{5pt}11 +\setedge 175,-80,125,-80:\drawdotedge{26pt}1 +\setedge 125,-90,175,-90:\drawdotedge{25pt}1 +\setedge 175,-100,125,-100:\drawdotedge{5pt}1 +}$$ + +\newpage + +%These three diagrams test the macros for category-theory diagrams. + +$$\ctdiagram{ +\ctvg0,0:{Y'}{\ctlpbl{I_{Y'}}} +\ctvg150,0:{Z=Z_0}{\ctgl{Z}\ctlpbr{I_Z}} +\ctvg0,100:{X_0=X}{\ctgr{X}\ctlptl{I_X}} +\ctvg150,100:{Y}{\ctlptr{I_Y}} +\ctet0,100,150,100:\alpha +\cteb0,0,150,0:{\beta'} +\ctel0,100,0,0:{\alpha'} +\cter150,100,150,0:\beta +\ctetb0,100,150,0:11{\alpha;\beta}{\alpha';\beta'} +}$$ + +$$\ctdiagram{\ctdash +\ctvg0,0:{Y'}{\ctlpblcc{I_{Y'}}} +\ctvg150,0:{Z=Z_0}{\ctgl{Z}\ctlpbrcc{I_Z}} +\ctvg0,100:{X_0=X}{\ctgr{X}\ctlptlcc{I_X}} +\ctvg150,100:{Y}{\ctlptrcc{I_Y}} +\ctet0,100,150,100:\alpha +\ctnohead\cteb0,0,150,0:{\beta'}\cthead +\ctel0,100,0,0:{\alpha'} +\cter150,100,150,0:\beta +\ctelr0,100,150,0:11{\alpha';\beta'}{\alpha;\beta} +}$$ + +$$\ctdiagram{ +\ctv0,0:{Y'} +\ctvg150,0:{Z=Z_0}{\ctgl{Z}} +\ctvg0,100:{X_0=X}{\ctgr{X}} +\ctv150,100:Y +\ctetg0,100,150,100;50:\alpha +\ctebg0,0,150,0;50:{\beta'} +\ctelg0,100,0,0;30:{\alpha'} +\cterg150,100,150,0;30:\beta +\ctetbg0,100,150,0;50,100:10{\rho}{\rho'} +\ctelrg0,0,150,100;70,30:01{\theta}{\theta'} +}$$ + +\newpage + +%The next two diagrams are further tests of the macros for drawing +%double edges. + +$$\ctdiagram{ +\ctv0,0:X +\ctv-100,100:Y\ctv-100,0:Y\ctv-100,-100:Y +\ctv100,100:Z\ctv100,0:Z\ctv100,-100:Z +\ctetb0,0,-100,100:10\alpha\beta +\ctdash\ctetb0,0,-100,0:00\alpha\beta\ctsolid +\ctetb0,0,-100,-100:01\alpha\beta +\ctetb0,0,100,100:10\alpha\beta +\ctdash\ctetb0,0,100,0:11\alpha\beta\ctsolid +\ctetb0,0,100,-100:01\alpha\beta +}$$ + +$$\ctdiagram{ +\ctv0,0:X +\ctv-100,100:Y\ctv0,100:Y\ctv100,100:Y +\ctv-100,-100:Z\ctv0,-100:Z\ctv100,-100:Z +\ctelr0,0,-100,100:10\alpha\beta +\ctelr0,0,0,100:00\alpha\beta +\ctelr0,0,100,100:01\alpha\beta +\ctelr0,0,-100,-100:10\alpha\beta +\ctelr0,0,0,-100:11\alpha\beta +\ctelr0,0,100,-100:01\alpha\beta +}$$ + +\newpage + +%These two diagrams test the usage of \ctinnermid and \ctoutermid. + +$$\ctdiagram{\ctv 0,0:{ +{\displaystyle\sum_{i=0}^{100}x_i\cdot y_i}\over +{\displaystyle\sqrt{\biggl(\sum_{i=0}^{100}x_i^2\biggr) ++\biggl(\sum_{i=0}^{100}y_i^2\biggr)}}} +\ctv0,150:A\ctv150,150:B\ctv150,0:C\ctv150,-150:D +\ctv0,-150:E\ctv-150,-150:F\ctv-150,0:G\ctv-150,150:H +\cter0,0,0,150:A\ctinnermid\cter0,0,0,150:a\ctoutermid +\cter150,150,0,0:B\ctinnermid\cter150,150,0,0:b\ctoutermid +\cteb0,0,150,0:C\ctinnermid\cteb0,0,150,0:c\ctoutermid +\cteb150,-150,0,0:D\ctinnermid\cteb150,-150,0,0:d\ctoutermid +\ctel0,0,0,-150:E\ctinnermid\ctel0,0,0,-150:e\ctoutermid +\ctel-150,-150,0,0:F\ctinnermid\ctel-150,-150,0,0:f\ctoutermid +\ctet0,0,-150,0:G\ctinnermid\ctet0,0,-150,0:g\ctoutermid +\ctet-150,150,0,0:H\ctinnermid\ctet-150,150,0,0:h +}$$ + +$$\ctdiagram{\ctv 0,0:{ +{\displaystyle\sum_{i=0}^{100}x_i\cdot y_i}\over +{\displaystyle\sqrt{\biggl(\sum_{i=0}^{100}x_i^2\biggr) ++\biggl(\sum_{i=0}^{100}y_i^2\biggr)}}} +\ctv-150,150:A\ctv0,150:C\ctv150,150:E\ctv150,0:G +\ctelr0,0,-150,150:11AB\ctinnermid +\ctelr0,0,-150,150:11ab\ctoutermid +\ctelr0,150,0,0:11CD\ctinnermid +\ctelr0,150,0,0:11cd\ctoutermid +\ctetb0,0,150,150:11EF\ctinnermid +\ctetb0,0,150,150:11ef\ctoutermid +\ctetb150,0,0,0:11GH\ctinnermid +\ctetb150,0,0,0:11gh +}$$ + +\newpage + +%This is a ``real'' diagram, relating directed complete relations to +%Scott's inverse limit construction. It is sufficiently crowded +%that it has been necessary to place some of the abutted expressions +%carefully to avoid ambiguity. + +$$\ctdiagram{ +\ctvg0,0:{D_0}{\border{2pt}{0pt}} +\ctv72,0:{D_1} +\ctv144,0:{D_2} +\ctv216,0:{\quad\cdots} +\ctvg288,144:{D_\infty}{\advance\ycenter by 5pt\border{50pt}{10pt}} +\ctv234,36:{\cdots} +\ctetbg0,0,72,0;48,48:10{\phi_0}{\psi_0} +\ctetbg72,0,144,0;114,114:10{\phi_1}{\psi_1} +\ctetb144,0,216,0:10{\phi_2}{\psi_2} +\ctelrg0,0,288,144;42,30:10{\Phi_0}{\Psi_0} +\ctelrg72,0,288,144;42,30:10{\Phi_1}{\Psi_1} +\ctelrg144,0,288,144;42,30:10{\Phi_2}{\Psi_2} +\ctvg0,-72:{D'_0}{\border{2pt}{0pt}} +\ctv72,-72:{D'_1} +\ctv144,-72:{D'_2} +\ctv216,-72:{\quad\cdots} +\ctvg288,-216:{D'_\infty}{\advance\ycenter by -5pt\border{50pt}{10pt}} +\ctv234,-108:{\cdots} +\ctetbg0,-72,72,-72;48,48:10{\phi'_0}{\psi'_0} +\ctetbg72,-72,144,-72;114,114:10{\phi'_1}{\psi'_1} +\ctetb144,-72,216,-72:10{\phi'_2}{\psi'_2} +\ctelrg0,-72,288,-216;-114,-102:10{\Phi'_0}{\Psi'_0} +\ctelrg72,-72,288,-216;-114,-102:10{\Phi'_1}{\Psi'_1} +\ctelrg144,-72,288,-216;-114,-102:10{\Phi'_2}{\Psi'_2} +\cter0,0,0,-72:{\alpha_0} +\cter72,0,72,-72:{\alpha_1} +\cter144,0,144,-72:{\alpha_2} +\ctv216,-36:{\cdots} +\ctdash +\cter288,144,288,-216:{\alpha_\infty} +}$$ + +\newpage + +%This shows how a macro can be defined and then used to give two different +%views of the same diagram. + +\def\testcube#1#2#3#4#5#6#7#8{ +$$\ctdiagram{ +\ctv#1,#3:{A_1} +\ctv#2,#3:{B_1} +\ctv#1,#4:{A_2} +\ctv#2,#4:{B_2} +\ctv#5,#7:{A'_1} +\ctv#6,#7:{B'_1} +\ctv#5,#8:{A'_2} +\ctv#6,#8:{B'_2} +\ctet#1,#3,#2,#3:{\gamma_1} +\ctet#1,#4,#2,#4:{\gamma_2} +\cter#1,#3,#1,#4:{\alpha} +\cter#2,#3,#2,#4:{\beta} +\ctet#5,#7,#6,#7:{\gamma'_1} +\ctet#5,#8,#6,#8:{\gamma'_2} +\cter#5,#7,#5,#8:{\alpha'} +\cter#6,#7,#6,#8:{\beta'} +\cter#1,#3,#5,#7:{a_1} +\cter#2,#3,#6,#7:{b_1} +\cter#1,#4,#5,#8:{a_2} +\cter#2,#4,#6,#8:{b_2} +}$$} + +\testcube{0}{200}{200}{0}{50}{150}{150}{50} + +\testcube{0}{150}{150}{0}{100}{250}{200}{50} + +\newpage + +%An example of a partial ordering with a limit point. + +$${\def\diagramunit{0.25in} +\ctdiagram{\ctnohead +\ctv0,0:{\geq 0} +\ctv2,2:{\geq 1} +\ctv4,4:{\geq 2} +\ctv7,7:\infty +\ctv-2,2:{=0} +\ctv0,4:{=1} +\ctv2,6:{=2} +\cten0,0,2,2: +\cten2,2,4,4: +\cten0,0,-2,2: +\cten2,2,0,4: +\cten4,4,2,6: +\ctdot +\cten4,4,7,7: +}}$$ + +%An example of a binary tree, produced by user macros. + +\newcount\cnx\newcount\cny\newcount\cnxx\newcount\cnyy + +\def\treea#1{\cnxx=\cnx\cnyy=\cny +\ctv\cnx,\cny:{\scriptstyle #1} +\advance\cnx by -1\advance\cny by 4 +\ctdot +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by 2 +\cten\cnxx,\cnyy,\cnx,\cny: +\ctsolid +\cnx=\cnxx\cny=\cnyy} + +\def\treeb#1{\ctv\cnx,\cny:{\scriptstyle #1} +\advance\cnx by -2\advance\cny by 4 +\treea{#10} +\cnxx=\cnx\advance\cnxx by 2\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by 4 +\treea{#11} +\cnxx=\cnx\advance\cnxx by -2\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by -2\advance\cny by -4} + +\def\treec#1{\ctv\cnx,\cny:{\scriptstyle #1} +\advance\cnx by -4\advance\cny by 4 +\treeb{#10} +\cnxx=\cnx\advance\cnxx by 4\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by 8 +\treeb{#11} +\cnxx=\cnx\advance\cnxx by -4\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by -4\advance\cny by -4} + +\def\treed#1{\ctv\cnx,\cny:{\scriptstyle #1} +\advance\cnx by -8\advance\cny by 4 +\treec{#10} +\cnxx=\cnx\advance\cnxx by 8\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by 16 +\treec{#11} +\cnxx=\cnx\advance\cnxx by -8\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by -8\advance\cny by -4} + +\def\tree{\ctv\cnx,\cny:\bot\def\centerheight{2pt} +\advance\cnx by -16\advance\cny by 4 +\treed{0} +\cnxx=\cnx\advance\cnxx by 16\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by 32 +\treed{1} +\cnxx=\cnx\advance\cnxx by -16\cnyy=\cny\advance\cnyy by -4 +\cten\cnxx,\cnyy,\cnx,\cny: +\advance\cnx by -16\advance\cny by -4} + +$${\def\diagramunit{7.5pt} +\ctdiagram{\ctnohead\cnx=0\cny=0\tree}}$$ + +\end{document} |