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author | Karl Berry <karl@freefriends.org> | 2009-04-22 17:09:04 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2009-04-22 17:09:04 +0000 |
commit | 66c43c768dd459a054b014c5cb6652c87895d682 (patch) | |
tree | 1685008c59da813ca88c59be7fe5fcda14a403de /Master/texmf-dist/doc/latex/diagmac2 | |
parent | 27c36765240572fc41d9ca8c69b99e0a41493674 (diff) |
new latex package diagmac2 (20apr09)
git-svn-id: svn://tug.org/texlive/trunk@12792 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/diagmac2')
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 | 38 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt | 779 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf | bin | 0 -> 19988 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex | 52 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.pdf | bin | 0 -> 54918 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.tex | 403 |
6 files changed, 1272 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 b/Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 new file mode 100644 index 00000000000..0c40b231acd --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 @@ -0,0 +1,38 @@ +diagmac2.sty is a small modification of the diagmac macros written +by John Reynolds (http://www.cs.cmu.edu/~jcr/) in 1987 and available +from his ftp site (ftp://ftp.cs.cmu.edu/user/jcr) since 2002. The only +modifications to the original package is that restrictions on line +slopes have been removed, on the assumption that the pict2e.sty package +(http://www.ctan.org/get/macros/latex/contrib/pict2e.zip) is being +used. The User's Manual (renamed here diagmac.txt) and the test file +(diagmactest.tex) are as originally released by Reynolds, except for the +replacement of + +\input diagmac + +by + +\input{diagmac2.sty} + +in the latter. The limitations on line slopes described in the third +paragraph of the User's Manual can be ignored with diagmac2. + +At Reynolds's ftp site, there is the following disclaimer: + + These macros are intended for public usage and have not changed in + many years. Acknowledgement of their usage is not necessary. However, + neither I nor CMU accept any responsibility for the consequences of + errors in these macros or their documentation. This is more than the + usual disclaimer; TEX is a beastly language for programming anything + complex, and I am not an expert in its use, so that there are probably + errors lurking in the macros. + +In fact, after more than 20 years of intensive use by dozens of +enthusiastic users, it seems that not a single error has been +discovered. + +Bob Tennent +School of Computing +Queen's University +Kingston, Canada K7L 3N6 +rdt@cs.queensu.ca diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt new file mode 100644 index 00000000000..83cf911debb --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt @@ -0,0 +1,779 @@ +USER'S MANUAL FOR DIAGRAM MACROS - J. C. Reynolds - December 1987 + +The file diagmac.tex contains TEX macros for producing various kinds of +diagrams. It consists of two parts: a collection of general macros for +producing a wide variety of diagrams, and a second collection of macros +(which call upon the first) that are specifically oriented to category-theory +diagrams. + +A second file diagmactest.tex is an input file for LATEX that tests the +macros in diagmac.tex. + +USE OF THE LATEX PICTURE FACILITY + +These macros use the LATEX picture facility to draw lines, arrows, and +circles. Thus all lines and arrowheads are subject to the limitations of +this facility. In particular, the slope of any solid or dashed line must be +a pair of integers whose magnitudes, after division by their greatest common +divisor, are no more than six. When an arrowhead is placed on a line or a +circular arc, the slope of the line (or the tangent to the arc) +must be a pair of integers whose magnitudes, after division by their +greatest common divisor, are no more than four. Also, lines (or dashes in +dashed lines) that are not either horizontal or vertical will not appear +unless they are longer than a minimum length, which is about 10 to 15 points. + +Since circles and circular arcs are also drawn via the LATEX picture +facility, they are limited to a fixed variety of diameters. A list of these +diameters is the meaning of the control symbol \diameterlist, which should +be changed if a different circle font is used. (Note that it is a list +of dimensions in increasing order that ends with a comma.) + +The latex declarations \thinlines and \thicklines may be used to vary +the thickness of lines, arrowheads, and circles. + +PROGRAMS AND STATES + +Certain parameters to these macros are ``programs''. A program is a +TEX text that does not directly produce any output but causes state changes +by calling macros. For example, in LATEX, the text read in picture mode, +i.e. the text between \begin{picture} and \end{picture} commands, is a +program that causes state changes by calling the macro \put. (Internally, +such macros cause state changes by assigning to hidden registers and +redefining hidden control symbols. As a consequence, a program cannot +call state-changing macros within a group.) + +The diagram-producing macros use two kinds of program, called diagram +programs and expression programs. The state manipulated by a diagram +program, called a diagram state, is a plane containing symbols, lines, +and circles. Locations on this plane are specified by an x,y-coordinate +system, in which x specifies horizontal distance, with increasing values +to the right, and y specifies vertical distance, with increasing values +upwards. The diagram state also contains a ``vertex list'', which is a +list of points (i.e. x,y-coordinate pairs) paired with polygonal regions +called ``shadows''. + +The diagram state may also contain a ``current edge'', which is a +(perhaps invisible) directed line segment. When the current edge is defined, +it is determined by four dimension registers: + + \xstart: the x-coordinate of the start point + \ystart: the y-coordinate of the start point + \xend: the x-coordinate of the end point + \yend: the y-coordinate of the end point, + +and two number registers: + + \xslope: the x-component of the slope + \yslope: the y-component of the slope + +giving the slope of the edge, reduced to lowest terms. A diagram program may +refer to any of these quantities, and may also alter the dimension registers +explicitly (as well as by calling diagram macros), providing this alteration +preserves the slope of the edge. + +The state manipulated by an expression program, called an expression state, +is also a plane, containing an expression and other symbols, etc., +upon which is imposed an x,y-coordinate system. This state contains an +invisible ``current rectangle'', determined by the four dimension registers: + + \lexpr: the x-coordinate of the left side + \rexpr: the x-coordinate of the right side + \texpr: the y-coordinate of the top + \bexpr: the y-coordinate of the bottom, + +and a ``center point'', determined by the two dimension registers: + + \xcenter: the x-coordinate of the center point + \ycenter: the y-coordinate of the center point. + +An expression program may refer to or alter these six dimension registers +explicitly (as well as by calling various macros). + +The expression state may also contain a (perhaps invisible) polygon called +the ``current shadow'', and a (perhaps invisible) circle called the +``current circle''. When the current circle is defined, it is determined +by three dimension registers: + + \dcircle: the diameter + \xcircle: the x-coordinate of the center + \ycircle: the y-coordinate of the center. + +An expression program may refer to or alter these three dimension registers +explicitly (as well as by calling various macros). + +The qualification ``perhaps invisible'' is meant to indicate that the +position, shape, and size of edges, shadows, and circles are established +by one group of macros (e.g. \setedge, \rect, \octagon, \setcircle), but +that these entities are actually drawn, i.e. made to appear on the plane +of the diagram or expression state, by another group of macros (e.g. +\drawsolidedge, \outline, \drawcircle). + +In calls of the diagram macros, a coordinate is sometimes specified by a +dimension, but often it is specified by a number (i.e. integer) that gives +the coordinate as a multiple of the dimension that is the meaning of the +control symbol \diagramunit. This control symbol is defined to be 1pt, +but the user may redefine it to be some other dimension, either in his main +program or at the beginning of a diagram program. + +In addition to the control symbols discussed in this description, this +collection of macros defines a large number of control symbols that are +normally no concern of the user. To avoid the accidental redefinition +of these symbols by the user, they are all given names beginning with \zz. + +THE GENERAL MACROS FOR DIAGRAMS + +We now describe the general macros for drawing diagrams. The main level +macro is + + \diagram{<diagram program>} + +It executes the diagram program that is its only parameter, and then issues +the final state produced by this program as a horizontal box whose height, +width, and depth are just enough to enclose all of the symbols and lines +in this state, plus the origin (0,0) of the coordinate system. The height +(depth) will be the distance from the horizontal line y=0 to the highest +(lowest) extent of any symbol or line. + +Within a diagram program, one can call the following macros: + + \vertex<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + +\vertex sets the <balanced mathematical text> in math mode, with text style, +and creates an expression state containing the resulting expression, with +the current rectangle just enclosing the expression. The center point is +placed midway between the left and right sides of the current rectangle, +at a height above the baseline of the expression given by the control +symbol \centerheight, which is defined to be 3pt. (The effect is to place +the center point on the axis of the expression. However, the user may need +to change the definition of \centerheight if he is using unusual fonts or +script style.) The reference point of the expression will lie at the +origin of the coordinate system. + +Next, \vertex executes the <expression program> to modify the expression +state. Then the material in the expression state is placed in the +current diagram state, at a position so that the center point lies at +the point <number:x-coord>,<number:y-coord>. Finally, if the expression +state contains a current shadow, the point <number:x-coord>,<number:y-coord> +is paired with the shadow and placed on the vertex list. + + \place<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \placed{<dimen:x-coord>}{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} + +\place behaves the same way as \vertex, except that nothing is placed on the +vertex list. \placed behaves the same way as \place, except that the +coordinates at which the center point is placed are expressed by dimensions +rather than numbers. + + \setedge<number:x-start-coord>,<number:y-start-coord>, + <number:x-end-coord>,<number:y-end-coord>: + +\setedge makes the current edge a directed line segment from the point +``start'' given by its first two parameters to the point ``end'' given +by its last two parameters. This line segment is invisible (until it +is drawn by one of the macros discussed below). + +\setedge also examines the vertex list to obtain any shadows that have been +associated with the start or end points by prior executions of \vertex. + + \shiftedge{<dimen:length>} + +\shiftedge displaces the current edge by a vector whose length is determined +by the <dimen:length> parameter, and whose direction is obtained by rotating +the current edge 90 degrees counterclockwise. + + \shadeedge + +\shadeedge changes the extent of the current edge, without displacing +or rotating it, to exclude the portions of the edge lying within shadows +associated with its start and end points. If the execution of \setedge that +established the current edge found a shadow associated with the start point, +then \shadedge will shorten (or conceivably lengthen) the current edge +so that its start point lies on the boundary of the shadow. (If this is +not possible, the start point will be adjusted to be as close as possible +to the shadow.) The end point is adjusted similarly. + + \drawsolidedge + +\drawsolidedge draws the current edge as a solid line. It is subject to +the constraints of the LATEX picture facility. + + \drawdashedge{<dimen:length>}{<dimen:length>}{<number>}{<number>} + +\drawdashedge draws the current edge as a dashed line. It is subject to +the constraints of the LATEX picture facility (particularly regarding the +minimum length of printable dashes for lines that are not horizontal or +vertical). The dashed line will always begin and end with a dash. The +number of dashes will be as large as possible subject to the constraint +that, if one or more blanks occur, the dashes will be at least as long +as the first parameter and the blanks will be at least as long as the +second parameter. If one or more blanks occur, the excess length of the +dashes and of the blanks will be proportional to the third and fourth +parameters respectively. The first two parameters must be positive +dimensions, and the last two parameters must be nonnegative numbers whose +sum is positive. + + \drawdotedge{<dimen:length>}{<1 or 0>} + +\drawdotedge draws the current edge as a dotted line. The number of dots +will be the largest number such that the distance between dots is at least +as large as the first parameter, which must be a positive dimension. +A dot will always appear at the start point, and will appear at the end +point if the second parameter is 1. If the second parameter is 0 then +the final dot will be omitted. + + \drawedgehead{<number:0 to 100>}{<1 or 0>}{<1 or 0>} + +\drawedgehead draws an arrowhead on the current edge at a distance from +the start point of p times the length of the edge, where p is the first +parameter divided by 100. The arrowhead will point to the end point if +the second parameter is 1, or to the start point if the second parameter +is 0. If the third parameter is 1, the arrowhead will be advanced towards +its tip by the value of the control symbol \edgeheaddisp, which is defined +to be 4pt, but may be redefined by the user. + + \abutleft<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \abutright<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \abutbelow<number:x-coord>: + {<balanced mathematical text>}{<expression program>} + + \abutabove<number:x-coord>: + {<balanced mathematical text>}{<expression program>} + +Each of these macros uses the <balanced mathematical text> to initialize +an expression state (in the same way as \vertex) and then executes +the <expression program>, which must establish a shadow. The material in +the expression state is then placed in the diagram state, at a location +such that the shadow touches the current edge (or its extension as an +infinite line), and lies to the left (or to the right, below, or above, +as determined by the macro name). For \abutleft and \abutright, which +must not be used when the current edge is horizontal, the first parameter +gives the y-coordinate of the point at which the center point is to be +located. For \abutbelow and \abutabove, which must not be used when the +current edge is vertical, the first parameter gives the x-ccordinate. + + \abutleftd{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} + + \abutrightd{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} + + \abutbelowd{<dimen:x-coord>} + {<balanced mathematical text>}{<expression program>} + + \abutaboved{<dimen:x-coord>} + {<balanced mathematical text>}{<expression program>} + +Each of these macros behaves the same way as its cousin, described above, +except that the first parameter is a dimension instead of a number. + +Within an expression program, one can call the following macros: + + \leftghost{<balanced mathematical text>} + + \rightghost{<balanced mathematical text>} + +These macros change \xcenter (the x-coordinate of the center point). +The <balanced mathematical text> is set in an hbox, using math mode, +text style, which is ignored except for its width. \leftghost sets +\xcenter to the left of the current rectangle plus half the width of +the hbox. \rightghost sets \xcenter to the right of the current rectangle +minus half the width of the hbox. The effect is to place the ``ghost +expression'' (invisibly) within the current rectangle at the left or +right side, and to move the center point horizontally to the midpoint of +the ghost expression. + + \border{<dimen:x-length>}{<dimen:y-length>} + + \borderto{<dimen:x-length>}{<dimen:y-length>} + + \symmetrize + +These macros enlarge the current rectangle. \border moves the left and +right sides outwards by its first parameter, and raises the top and lowers +the bottom by its second parameter. (If either parameter is negative, +the rectangle will contract.) \borderto enlarges the current rectangle +so that its width is at least the first parameter and its height (including +depth) is at least the second parameter. (Equal amounts will be added at +the left and right, and at the top and bottom.) \symmetrize raises the top +or lowers the bottom so that they are equally distant from the center point. + + \place<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \placed{<dimen:x-coord>}{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} + +These macros can be called from expression programs as well as diagram +programs. They have no effect on the current rectangle or center point. + + \rect + +\rect defines the current shadow to be the current rectangle. + + \hexagon + +\hexagon defines the current shadow to be a hexagon with two horizontal +sides identical with the top and bottom of the current rectangle, and +four sides of slope (+ or - 1), (+ or - 2). + + \octagon{<dimen:length>} + +\octagon defines the current shadow to be an octagon inscribed in the +current rectangle. The horizontal sides and vertical sides are shorter than +those of the current rectangle by twice the parameter, and the remaining +sides have slope (+ or - 1), (+ or - 1). + + \diamond + +\diamond defines the current shadow to be a square, just large enough to +enclose the current rectangle, whose sides have slope (+ or - 1), (+ or - 1). + + \rorect{<dimen:diameter>}{<1 or 0>}{<1 or 0>} + +\rorect defines the current shadow to be a rectangle with rounded (i.e. +quarter-circle) corners. The diameter of the corners is determined as +follows: + + (1) Take the maximum of: + (a) The first parameter, + (b) If the second parameter is 1, then the width of the current + rectangle, else 0, + (c) If the third parameter is 1, then the height of the current + rectangle, else 0. + + (2) Take the diameter of the smallest printable circle larger or equal + to (1), or if no such printable circle exists, take the diameter + of the largest printable circle. + +The shadow is then the smallest rounded rectangle with corners of this +diameter such that the corresponding true (unrounded) rectangle encloses +the current rectangle. + +The effect (if there is a sufficiently large printable circle) is to produce: + + A rounded rectangle 00 + A vertical oblong if the second and third parameters are 10 + A horizontal oblong 01 + A circle 11 + +If the shadow is drawn (using \outline, as described below) its shape will +be the rounded rectangle just described. However, if the shadow is used +to shade an edge or to abut an expression to an edge or circle, then a +slight fudge occurs: the shadow is taken to be the smallest octagon +(with the same shape as that produced by \octagon) enclosing the specified +rounded rectangle. + + \outline + +\outline draws the current shadow. + + \setcircle{<dimen:diameter>}{<dimen:x-coord>}{<dimen:y-coord>} + +\setcircle defines the current circle to have a diameter given by the first +parameter and a center defined by the second and third parameter. + + \shiftcircle{<dimen:x-length>}{<dimen:y-length>} + +\shiftcircle displaces the current circle by the vector described by its +parameters. + + \drawcircle<1 or 0:upper right quadrant><1 or 0:lower right quadrant> + <1 or 0:lower left quadrant><1 or 0:upper left quadrant> + +\drawcircle draws the current circle. More precisely, it draws those +quadrants of the current circle for which the corresponding parameter is 1. + + \drawcirclehead{<number:x-slope>}{<number:y-slope>}{<1 or 0>} + +\drawcirclehead draws an arrowhead on the current circle, at the +intersection with a directed line segment starting at the center with a +slope determined by the first two parameters. If the third parameter +is 1 (0) the arrowhead will point in a clockwise (counterclockwise) +direction. The arrowhead will be advanced towards its tip by the distance +\circleheaddisp. This control symbol is defined to be 2pt, but may be +redefined by the user. + + \abutcircleleft{<dimen:y-length>} + {<balanced mathematical text>}{<expression program>} + + \abutcircleright{<dimen:y-length>} + {<balanced mathematical text>}{<expression program>} + + \abutcirclebelow{<dimen:x-length>} + {<balanced mathematical text>}{<expression program>} + + \abutcircleabove{<dimen:x-length>} + {<balanced mathematical text>}{<expression program>} + +Each of these macros uses the <balanced mathematical text> to initialize +an expression state (in the same way as \vertex) and then executes the +<expression program>, which must establish a shadow. The material in the +final expression state produced by this program is then placed in the +expression state of the expression program containing the call of +\abutcircle... , at a location such that shadow touches the current circle +on the outside of this circle. For \abutcircleleft and \abutcircleright +the first parameter gives the y-coordinate of the point at which the center +is to be located. For \abutcirclebelow and \abutcircleabove the first +parameter gives the x-coordinate. + +Actually, the abutment is approximate. For \abutcircleabove, the shadow +is abutted against three tangents to the current circle, that touch at the +top of the circle and at the two points 45 degrees to the left and right +of the top, and is then given the lowest of the three positions obtained +by these abutments. The other three macros behave similarly. + +AN EXAMPLE + +As a simple example, consider + +$$\diagram{ +\vertex 0,100:{A}{\border{3pt}{4pt}\rect} +\vertex 150,100:{B}{\border{3pt}{4pt}\rect} +\vertex 0,0:{A'}{\border{3pt}{4pt}\rect} +\vertex 150,0:{B'}{\border{3pt}{4pt}\rect} +\setedge 0,100,150,100: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutabove 75:{\textstyle c}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,0,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutbelow 75:{\textstyle c'}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,100,0,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutleft 50:{\textstyle a}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 150,100,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutright 50:{\textstyle b}{\border{2pt}{2pt}\octagon{3pt}} +}$$ + +This call of \diagram contains a diagram program in which the four calls +of \vertex place the expressions A, B, A', and B' at the four corners of +a 100pt by 150pt rectangle. Then come four groups of five calls that +draw edges along the sides of this rectangle and abut expressions to +the middles of these edges. + +In each group, \setedge determines the position of the edge, \shadeedge +adjusts the end points to exclude the shadows of the expressions that +have been placed at these points by \vertex, \drawsolidedge draws the +edge as a solid line, and \drawedgehead places an arrowhead at the end +of the edge. Then \abut... places an expression above, below, to the +left, or to the right of the midpoint of the edge, so that its shadow +touches the edge. + +In the calls of \vertex, {\border{3pt}{4pt}\rect} is an expression program +that enlarges the current rectangle by 3pt at the left and right and by 4pt +at the top and bottom, and then establishes this expanded rectangle as the +shadow. In the calls of \abut... , {\border{2pt}{2pt}\octagon{3pt}} is an +expression program that enlarges the current rectangle by 2pt on each side +and then defines the shadow to be an octagon inscribed in this expanded +rectangle, with slanted edges of length 4.24pt. + +The result is a display that looks approximately like: + + c + A --------------------> B + | | + | | + | | + a| |b + | | + | | + V V + A'--------------------> B' + c' + +(except, of course that the arrows are solid). + +THE MACROS FOR CATEGORY-THEORY DIAGRAMS + +Now we describe the additional macros oriented towards category-theory +diagrams. The main level program is + + \ctdiagram{<diagram program>} + +\ctdiagram is similar to \diagram, except that it executes \ctsolid, +\cthead, and \ctoutermid (described below) before the <diagram program>, +so that the category-theory macros for drawing edges will draw solid edges +with arrowheads and will calculate midpoints of edges before shading or +displacement. + +Within a diagram program, one can call the following macros (in addition +to the general macros described previously): + + \ctvg<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \ctv<number:x-coord>,<number:y-coord>:{<balanced mathematical text>} + +\ctvg is similar to \vertex, except that: + + (1) The <balanced mathematical text> is set in \ctvertexstyle. + The control symbol \ctvertexstyle is defined to be \displaystyle, + but may be redefined by the user. + + (2) The execution of the <expression program> is followed by a + ``standard expression program'' that enlarges the current rectangle + by \ctvertexborderlr on the left and right and by \ctvertexbordertb + on the top and bottom, and then creates a rectangular shadow of the + same size. The control symbols \ctvertexborderlr and \ctvertexbordertb + are defined to be 3pt and 4pt respectively, but may be redefined + by the user. + +\ctv is similar to \ctvg except that only the standard expression program +is executed. + + \ctsolid + + \ctdash + + \ctdot + +These macros cause subsequent executions of the edge-drawing macros described +below to draw solid, dashed, or dotted edges respectively. Horizontal and +vertical dashed edges are drawn by \drawdashedge{7pt}{7pt}11, but other +dashed edges are drawn by \drawdashedge{15pt}{7pt}01. Dotted edges are +drawn by \drawdotedge{8pt}1. (These conventions can be alter by redefining +the macros \zzctdrawdashedge and \zzctdrawdotedge.) + + \cthead + + \ctnohead + +\cthead (\ctnohead) causes subsequent executions of the edge-drawing macros +described below to draw (not to draw) arrowheads. + + \cten<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>: + +\cten draws an edge from x-start to x-end, after shading the start and end +points with any shadows associated with these points on the vertex list. +The edge will be solid, dashed, or dotted depending upon whether \ctsolid, +\ctdash, or \ctdot was called last. An arrowhead will or will not be placed +at the end point depending upon whether \cthead or \ctnohead was called last. + + \ctetg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:x-coord>:{<balanced mathematical text>} + + \ctebg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:x-coord>:{<balanced mathematical text>} + + \ctelg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:y-coord>:{<balanced mathematical text>} + + \cterg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:y-coord>:{<balanced mathematical text>} + +Each of these macros draws an edge in the same way as \cten, and then abuts +the <balanced mathematical text> to the + + top \ctetg + bottom for \ctebg + left \ctelg + right \cterg + +of the edge, with its center placed at the x-coordinate (for \ctetg or +\ctebg) or y-coordinate (for \ctelg or \cterg) specified by the fifth +parameter. The abutted expression is set in \ctabutstyle, with an octagonal +shadow (of the shape produced by \octagon). This octagon will be inscribed +in a rectangle obtained by bordering the expression by \ctabutborderlr +on the left and right, and by \ctabutbordertb on the top and bottom; +the length of the slanted sides of the octagon will be \ctabutborderinset +times the square root of 2. + +The relevant control symbols are defined to be: + + \ctabutstyle \textstyle + \ctabutborderlr 2pt + \ctabutbordertb 2pt + \ctabutborderinset 3pt + +These symbols may be redefined by the user, but \ctabutborderinsetdouble +must also be redefined so that its value is twice \ctabutborderinset. + +\ctetg and \ctebg should not be used to draw a vertical edge; \ctelg and +\cterg should not be used to draw a horizontal edge. + + \ctetbg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:x-coord>,<number:x-coord>: + {<1 or 0>}{<1 or 0>} + {<balanced mathematical text>}{<balanced mathematical text>} + +\ctetbg draws a pair of edges in the same manner as \cten and then abuts +the first <balanced mathematical text> above the pair, in the same manner +as \ctetg, with its center placed at the x-coordinate specified by the +fifth parameter, and abuts the second <balanced mathematical text> below +the pair, in the same manner as \ctebg, with its center placed at the +x-coordinate specified by the sixth parameter. If the seventh parameter +is 1 (and \cthead has been called most recently), the arrowhead on the upper +edge will occur at the end point; otherwise it will occur (pointing +backwards) at the start point. The eighth parameter controls the arrowhead +on the lower edge similarly. The distance between the edges will be twice +the control symbol \ctdoubleedgedisp, which is defined to be 2pt, but may +be redefined by the user. + +\ctetbg should not be used to draw a vertical edge. + + \ctelrg<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>;<number:y-coord>,<number:y-coord>: + {<1 or 0>}{<1 or 0>} + {<balanced mathematical text>}{<balanced mathematical text>} + +\ctelrg draws a pair of edges in the same manner as \cten and then abuts +the first <balanced mathematical text> to the left, in the same manner +as \ctetg, with its center placed at the y-coordinate specified by the +fifth parameter, and abuts the second <balanced mathematical text> to +the right, in the same manner as \ctebg, with its center placed at the +y-coordinate specified by the sixth parameter. If the seventh parameter +is 1 (and \cthead has been called most recently), the arrowhead on the left +edge will occur at the end point; otherwise it will occur (pointing +backwards) at the start point. The eighth parameter controls the arrowhead +on the right edge similarly. The distance between the edges will be twice +the control symbol \ctdoubleedgedisp, which is defined to be 2pt, but may +be redefined by the user. + +\ctelrg should not be used to draw a horizontal edge. + + \ctet<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<balanced mathematical text>} + + \cteb<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<balanced mathematical text>} + + \ctel<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<balanced mathematical text>} + + \cter<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<balanced mathematical text>} + + \ctetb<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<1 or 0>}{<1 or 0>} + {<balanced mathematical text>}{<balanced mathematical text>} + + \ctelr<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>:{<1 or 0>}{<1 or 0>} + {<balanced mathematical text>}{<balanced mathematical text>} + +These macros behave similarly to their cousins described above, except that +the fifth parameter (and also the sixth parameter in the case of \ctetb and +\ctelr) is omitted. In its place, these macros use the x- or y-coordinate +of the midpoint between the start and end points of the edge. If \ctoutermid +(described below) has been called most recently, then the midpoint will +be calculated from the start and end coordinates given as parameters to the +macros. If \ctinnermid (described below) has been called most recently, +then the midpoint will be computed after displacement and shading, so that +it will be the midpoint of the actual line segment that is printed. +(In the case of \ctetb and \ctelr, this midpoint will be calculated +separately for the two edges that are printed.) + + \ctoutermid + + \ctinnermid + +These macros control the calculation of edge midpoints as described above. + +Within a expression program, one can call the following macros (in addition +to the general macros described previously): + + \ctgl{<balanced mathematical text>} + + \ctgr{<balanced mathematical text>} + +These macros are similar to \leftghost and \rightghost except that the +<balanced mathematical text> is set in \ctvertexstyle. + + \ctlptl{<balanced mathematical text>} + + \ctlptr{<balanced mathematical text>} + + \ctlpbr{<balanced mathematical text>} + + \ctlpbl{<balanced mathematical text>} + +These macros print a loop (three quarters of a circle) of diameter +\ctloopdiameter on the exterior of the current rectangle, with its center +at the + + top left \ctlptl + top right for \ctlptr + bottom right \ctlpbr + bottom left \ctlpbl + +corner of the current rectangle, and with a clockwise arrowhead at the +clockwise end of the loop. Then the <balanced mathematical text> is +abutted to the + + left \ctlptl + right for \ctlptr + right \ctlpbr + left \ctlpbl + +of the loop, with its center + + above \ctlptl + above for \ctlptr + below \ctlpbr + below \ctlpbl + +the center of the loop by the distance \ctabutcircledisp. + +The control symbols \ctloopdiameter and \ctabutcircledisp are defined to be +20pt and 5pt respectively, but may be redefined by the user. + +The current rectangle is expanded by \ctvertexborderlr at the left and right +and and \ctvertexbordertb at the top and bottom before the loop center +is determined, and is contracted to its original size afterwards. Thus +the loop center will lie at a corner of the shadow that will be produced +by the ``standard expression program'' executed by \ctvg. (Actually, the +loop center is displaced by \circleheaddisp, so that the tip of the +arrowhead will just touch the shadow.) The arrowhead is always printed, +regardless of the use of \cthead and \ctnohead. + +The <balanced mathematical text> is set in \ctabutstyle, and is given an +octagonal shadow in the same manner as by \ctetg. The abutment to the loop +is similar to that performed by \abutcircleleft or \abutcircleright. + + \ctlptlcc{<balanced mathematical text>} + + \ctlptrcc{<balanced mathematical text>} + + \ctlpbrcc{<balanced mathematical text>} + + \ctlpblcc{<balanced mathematical text>} + +These macros are similar to their cousins described above, except that a +counterclockwise arrowhead is placed at the counterclockwise end of the loop. + +AN EXAMPLE + +For example, the following produces the same display as the previous +example: + +$$\ctdiagram{ +\ctv 0,100:{A} +\ctv 150,100:{B} +\ctv 0,0:{A'} +\ctv 150,0:{B'} +\ctet 0,100,150,100:{c} +\cteb 0,0,150,0:{c'} +\ctel 0,100,0,0:{a} +\cter 150,100,150,0:{b} +}$$ + +Less trivial examples of the usage of these macros are found in the file +diagmactest.tex. + diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf Binary files differnew file mode 100644 index 00000000000..64315d5a87e --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex new file mode 100644 index 00000000000..7b4626becde --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex @@ -0,0 +1,52 @@ +\documentclass{minimal} +\usepackage{diagmac2} +\begin{document} +\[ +\ctdiagram{ +\ctinnermid +\ctv 0,0: {(I\otimes I) \otimes(v\otimes w)} +\ctv 0,60: {I\otimes \bigl(I\otimes(v\otimes w)\bigr)} +\ctv 0,120: {I\otimes \bigl((I\otimes v)\otimes w\bigr)} +\ctv 80,180: {I\otimes\bigl((v\otimes I)\otimes w\bigr)} +\ctv 200,0: {I\otimes (v\otimes w)} +\ctv 200,180:{I\otimes \bigl(v\otimes(I\otimes w)\bigr)} +\ctv 280,0:{v\otimes w} +\ctv 280,60:{(I\otimes v)\otimes w} +\ctv 280,120: { (I\otimes v)\otimes(I\otimes w)} +\ctel 0,0,0,60:{\alpha^{-1}} +\ctel 0,60,0,120:{I\otimes \alpha^{-1}} +\cteb 0,0,200,0:{\rho_I\otimes(v\otimes v)} +\cteb 200,0,280,0:{\lambda_{v\otimes w}} +\ctelg 0,120,80,180;155:{I\otimes\sigma_{I,v}\otimes w} +\ctet 80,180,200,180:{I\otimes \alpha^{-1}} +\cterg 200,180,280,120;155:{\alpha^{-1}} +\cter 280,120,280,60:{(I\otimes v)\otimes \lambda_w} +\cter 280,60,280,0: {\lambda_v\otimes w} +\ctv 240,30:{\alpha^{-1}} +\ctnohead +\cten 200,0,240,30: +\cthead +\cten 240,30,280,60: +\ctv 100,30:{I\otimes\lambda_{v\otimes w}} +\ctnohead +\cten 0,60,100,30: +\cthead +\cten 100,30,200,0: +\ctv 100,60:{I\otimes(\lambda_v\otimes w)} +\ctnohead +\cten 0,120,100,60: +\cthead +\cten 100,60,200,0: +\ctv 140,90:{I\otimes (\rho_v\otimes w)} +\ctnohead +\cten 80,180,140,90: +\cthead +\cten 140,90,200,0: +\ctv 200,90:{I\otimes (v\otimes \lambda_w)} +\ctnohead +\cten 200,180,200,90: +\cthead +\cten 200,90,200,0: +} +\] +\end{document} diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.pdf b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.pdf Binary files differnew file mode 100644 index 00000000000..266fa28323d --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.pdf diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.tex b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.tex new file mode 100644 index 00000000000..2b8fb8fcd15 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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{diagmac2.sty} +\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} |