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diff --git a/Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 b/Master/texmf-dist/doc/latex/diagmac2/README index c884f1df1fa..72936fe1599 100644 --- a/Master/texmf-dist/doc/latex/diagmac2/README.diagmac2 +++ b/Master/texmf-dist/doc/latex/diagmac2/README @@ -1,25 +1,25 @@ +This is the README for diagmac2, Version 2.1 (May 2009) + John Reynolds's diagram macros (available from http://www.cs.cmu.edu/~jcr/ and at CTAN in macros/latex/contrib/misc) have been in use since 1987, particularly for commutative diagrams. Although originally written for use with latex209, they do work with more recent formats such as latex2e and pdflatex, but the diagmac macros -are based on the original picture environment in latex and inherit its +are based on the original picture environment in LaTeX and inherit its limitations on line slopes and circle diameters. diagmac2.sty is a modification of the macros to allow use of the pict2e -package (available at CTAN in macros/latex/contrib) so that there are no -restrictions on line slopes or circle diameters. - -The User's Manual (renamed here diagmac.txt) and the test file -(diagmactest.tex) are as originally released by Reynolds. The -limitations described in the third paragraph of the User's Manual can be -ignored when diagmac2 is used. The diagmac2Example illustrates the use -of line slopes that are not feasible with the original package. +package (available at CTAN in macros/latex/contrib) so that there are +effectively no restrictions on line slopes or circle diameters. Starting +in Version 2.1, some extensions have been added. Also, the User's Manual +has been \TeXified (diagmac2.tex) and expanded, including several +examples. The test file (diagmactest.tex) is as originally released by +Reynolds (but modified to load diagmac2.sty). 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, + These macros are in the public domain, 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 @@ -30,8 +30,7 @@ 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. -I am interpreting Reynolds's statements as putting diagmac into the -public domain. The licence for diagmac2.sty is LPPL. +The licence for diagmac2.sty and diagmac2.tex is LPPL. Bob Tennent School of Computing diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt deleted file mode 100644 index 83cf911debb..00000000000 --- a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac.txt +++ /dev/null @@ -1,779 +0,0 @@ -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/diagmac2.pdf b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2.pdf Binary files differnew file mode 100644 index 00000000000..a9c041255eb --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2.pdf diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2.tex b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2.tex new file mode 100644 index 00000000000..42d4e439fc4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2.tex @@ -0,0 +1,1241 @@ +\documentclass[11pt]{article} +\title{User's Manual for Diagram Macros} +\date{December, 1987\\[2ex] Revised for \texttt{diagmac2.sty}\\by Bob Tennent\\ Version 2.1 May, 2009} +\author{J. C. Reynolds} +\usepackage{fullpage} +\usepackage{url} +\usepackage{diagmac2} +\RequirePackage{amssymb} +\RequirePackage{fancyvrb} +\DefineVerbatimEnvironment{myverb}{Verbatim}{baselinestretch=0.95} +\DefineVerbatimEnvironment{smallverb}{Verbatim}{fontsize=\footnotesize,baselinestretch=0.95} +\RequirePackage{doc} +\MakeShortVerb{\"} % "..." is equivalent to \verb"..." +\PassOptionsToPackage{urlcolor=black,linkcolor=blue,colorlinks}{hyperref} +\RequirePackage{hyperref} +\newcommand{\myurl}[1]{\textcolor{blue}{\underline{\textcolor{black}{\url{#1}}}}} + + +\begin{document} +\sloppy +\maketitle +\thispagestyle{empty} +\tableofcontents + +\section{Introduction} +\begin{list}{}{\setlength{\leftmargin}{0.6in}} +\item +\footnotesize +\begin{flushright} + These macros are in the public domain, 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. +\\ [1ex] +John Reynolds\footnote{\myurl{ftp://ftp.cs.cmu.edu/user/jcr/README}} +\end{flushright} +\end{list} + + + +\enlargethispage*{4ex} +\par\noindent +The file \texttt{diagmac2.sty} 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. + +\texttt{diagmac2.sty} is fully compatible with Reynolds's original \texttt{diagmac}, but +takes advantage of the \texttt{pict2e} implementation of the \texttt{picture} environment +to allow arbitrary slopes for edges and diameters for circles. In +this manual, the sections of the original manual that refered to the +limitations have been deleted. Sections~\ref{extensions} and \ref{examples} are new +in Version~2.1. + +The \LaTeX\ declarations "\thinlines" and "\thicklines" or the "pict2e" declaration +"\linethickness" may be used to vary +the thickness of lines, arrowheads, and circles. + +\cleardoublepage +\section{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: +\begin{itemize} + +\item "\xstart": the $x$-coordinate of the start point +\item "\ystart": the $y$-coordinate of the start point +\item "\xend": the $x$-coordinate of the end point +\item "\yend": the $y$-coordinate of the end point, +\end{itemize} +and two number registers: +\begin{itemize} +\item "\xslope": the $x$-component of the slope +\item "\yslope": the $y$-component of the slope +\end{itemize} +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: +\begin{itemize} +\item "\lexpr": the $x$-coordinate of the left side +\item "\rexpr": the $x$-coordinate of the right side +\item "\texpr": the $y$-coordinate of the top +\item "\bexpr": the $y$-coordinate of the bottom, +\end{itemize} +and a ``center point,'' determined by the two dimension registers: +\begin{itemize} +\item "\xcenter": the $x$-coordinate of the center point +\item "\ycenter": the $y$-coordinate of the center point. +\end{itemize} +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: +\begin{itemize} +\item "\dcircle": the diameter +\item "\xcircle": the $x$-coordinate of the center +\item "\ycircle": the $y$-coordinate of the center. +\end{itemize} +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". + +\cleardoublepage +\section{The General Macros for Diagrams} + +We now describe the general macros for drawing diagrams. The main level +macro is +\begin{myverb} + \diagram{<diagram program>} +\end{myverb} +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: +\begin{myverb} + \vertex<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} +\end{myverb} +"\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. +\begin{myverb} + \place<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \placed{<dimen:x-coord>}{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} +\end{myverb} +"\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. +\begin{myverb} + \setedge<number:x-start-coord>,<number:y-start-coord>, + <number:x-end-coord>,<number:y-end-coord>: +\end{myverb} +"\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". +\begin{myverb} + \shiftedge{<dimen:length>} +\end{myverb} +"\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. +\begin{myverb} + \shadeedge +\end{myverb} +"\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. +\begin{myverb} + \drawsolidedge +\end{myverb} +"\drawsolidedge" draws the current edge as a solid line. +\begin{myverb} + \drawdashedge{<dimen:length>}{<dimen:length>}{<number>}{<number>} +\end{myverb} +"\drawdashedge" draws the current edge as a dashed line. 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. +\begin{myverb} + \drawdotedge{<dimen:length>}{<1 or 0>} +\end{myverb} +"\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. +\begin{myverb} + \drawedgehead{<number:0 to 100>}{<1 or 0>}{<1 or 0>} +\end{myverb} +"\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. +\begin{myverb} + \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>} +\end{myverb} +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 $x$-coordinate. +\begin{myverb} + \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>} +\end{myverb} +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: +\begin{myverb} + \leftghost{<balanced mathematical text>} + + \rightghost{<balanced mathematical text>} +\end{myverb} +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. +\begin{myverb} + \border{<dimen:x-length>}{<dimen:y-length>} + + \borderto{<dimen:x-length>}{<dimen:y-length>} + + \symmetrize +\end{myverb} +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. +\begin{myverb} + \place<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \placed{<dimen:x-coord>}{<dimen:y-coord>} + {<balanced mathematical text>}{<expression program>} +\end{myverb} +These macros can be called from expression programs as well as diagram +programs. They have no effect on the current rectangle or center point. +\begin{myverb} + \rect +\end{myverb} +"\rect" defines the current shadow to be the current rectangle. +\begin{myverb} + \hexagon +\end{myverb} +"\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). +\begin{myverb} + \octagon{<dimen:length>} +\end{myverb} +"\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). +\begin{myverb} + \diamond +\end{myverb} +"\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). +\begin{myverb} + \rorect{<dimen:diameter>}{<1 or 0>}{<1 or 0>} +\end{myverb} +"\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. +\begin{enumerate} + \item \label{one} Take the maximum of: +\begin{enumerate} + \item the first parameter; + \item if the second parameter is 1, then the width of the current + rectangle, else 0; + \item if the third parameter is 1, then the height of the current + rectangle, else 0. +\end{enumerate} + + \item Take the diameter of the smallest printable circle larger or equal + to (\ref{one}), or if no such printable circle exists, take the diameter + of the largest printable circle. +\end{enumerate} +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: +\begin{verse} +\begin{tabular}{lcc} + & if the 2nd parameter is & and the 3rd parameter is\\ +\hline + a rounded rectangle & 0& 0 \\ + a vertical oblong & 1& 0 \\ + a horizontal oblong & 0& 1 \\ + a circle & 1& 1 + +\end{tabular} +\end{verse} +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. +\begin{myverb} + \outline +\end{myverb} +"\outline" draws the current shadow. +\begin{myverb} + \setcircle{<dimen:diameter>}{<dimen:x-coord>}{<dimen:y-coord>} +\end{myverb} +"\setcircle" defines the current circle to have a diameter given by the first +parameter and a center defined by the second and third parameter. +\begin{myverb} + \shiftcircle{<dimen:x-length>}{<dimen:y-length>} +\end{myverb} +"\shiftcircle" displaces the current circle by the vector described by its +parameters. +\begin{myverb} + \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> +\end{myverb} +"\drawcircle" draws the current circle. More precisely, it draws those +quadrants of the current circle for which the corresponding parameter is 1. +\begin{myverb} + \drawcirclehead{<number:x-slope>}{<number:y-slope>}{<1 or 0>} +\end{myverb} +"\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. +\begin{myverb} + \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>} +\end{myverb} +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. + +\paragraph{An Example} + +Consider the simple example in Figure~\ref{example1}. +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. + +\begin{figure}[t] +\begin{smallverb} + \[ + \diagram{ + \vertex 0,100:{A}{\border{3pt}{4pt}\rect} + \vertex 150,100:{B}{\border{3pt}{4pt}\rect} + \vertex 0,0:{A'}{\border{3pt}{4pt}\rect} + \vertex 150,0:{B'}{\border{3pt}{4pt}\rect} + + \setedge 0,100,150,100: + \shadeedge + \drawsolidedge + \drawedgehead{100}10 + \abutabove 75:{\textstyle c}{\border{2pt}{2pt}\octagon{3pt}} + + \setedge 0,0,150,0: + \shadeedge + \drawsolidedge + \drawedgehead{100}10 + \abutbelow 75:{\textstyle c'}{\border{2pt}{2pt}\octagon{3pt}} + + \setedge 0,100,0,0: + \shadeedge + \drawsolidedge + \drawedgehead{100}10 + \abutleft 50:{\textstyle a}{\border{2pt}{2pt}\octagon{3pt}} + + \setedge 150,100,150,0: + \shadeedge + \drawsolidedge + \drawedgehead{100}10 + \abutright 50:{\textstyle b}{\border{2pt}{2pt}\octagon{3pt}} + } + \] +\end{smallverb} +\caption{A Simple Example} +\label{example1} +\end{figure} +The result is as follows: +\[ +\diagram{ +\vertex 0,100:{A}{\border{3pt}{4pt}\rect} +\vertex 150,100:{B}{\border{3pt}{4pt}\rect} +\vertex 0,0:{A'}{\border{3pt}{4pt}\rect} +\vertex 150,0:{B'}{\border{3pt}{4pt}\rect} +\setedge 0,100,150,100: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutabove 75:{\textstyle c}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,0,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutbelow 75:{\textstyle c'}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 0,100,0,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutleft 50:{\textstyle a}{\border{2pt}{2pt}\octagon{3pt}} +\setedge 150,100,150,0: +\shadeedge +\drawsolidedge +\drawedgehead{100}10 +\abutright 50:{\textstyle b}{\border{2pt}{2pt}\octagon{3pt}} +} +\] + +\cleardoublepage +\section{The Macros for Category-Theory Diagrams} + +Now we describe the additional macros oriented towards category-theory +diagrams. The main level program is +\begin{myverb} + \ctdiagram{<diagram program>} +\end{myverb} +"\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): +\begin{myverb} + \ctvg<number:x-coord>,<number:y-coord>: + {<balanced mathematical text>}{<expression program>} + + \ctv<number:x-coord>,<number:y-coord>:{<balanced mathematical text>} +\end{myverb} +"\ctvg" is similar to "\vertex", except that: +\begin{enumerate} + \item The "<balanced mathematical text>" is set in "\ctvertexstyle". + The control symbol "\ctvertexstyle" is defined to be "\displaystyle", + but may be redefined by the user. + + \item 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. +\end{enumerate} +"\ctv" is similar to "\ctvg" except that only the standard expression program +is executed. +\begin{myverb} + \ctsolid + + \ctdash + + \ctdot +\end{myverb} +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 altered by redefining +the macros "\zzctdrawdashedge" and "\zzctdrawdotedge".) +\begin{myverb} + \cthead + + \ctnohead +\end{myverb} +"\cthead" ("\ctnohead") causes subsequent executions of the edge-drawing macros +described below to draw (not to draw) arrowheads. +\begin{myverb} + \cten<number:x-start-coord>,<number:y-start-coord>,<number:x-end-coord>, + <number:y-end-coord>: +\end{myverb} +"\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. +\begin{myverb} + \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>} +\end{myverb} +Each of these macros draws an edge in the same way as "\cten", and then abuts +the "<balanced mathematical text>" to the +\begin{verse} +\begin{tabular}{lll} + top & for & "\ctetg" \\ + bottom & for & "\ctebg" \\ + left & for & "\ctelg" \\ + right & for & "\cterg" \\ +\end{tabular} +\end{verse} +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: +\begin{verse} +\begin{tabular}{lc} + + "\ctabutstyle" & "\textstyle" \\ + "\ctabutborderlr" & 2pt \\ + "\ctabutbordertb" & 2pt \\ + "\ctabutborderinset" & 3pt \\ +\end{tabular} +\end{verse} +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. +\begin{myverb} + \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>} +\end{myverb} +"\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. +\begin{myverb} + \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>} +\end{myverb} +"\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. +\begin{myverb} + \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>} +\end{myverb} +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.) +\begin{myverb} + \ctoutermid + + \ctinnermid +\end{myverb} +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): +\begin{myverb} + \ctgl{<balanced mathematical text>} + + \ctgr{<balanced mathematical text>} +\end{myverb} +These macros are similar to "\leftghost" and "\rightghost" except that the +"<balanced mathematical text>" is set in "\ctvertexstyle". +\begin{myverb} + \ctlptl{<balanced mathematical text>} + + \ctlptr{<balanced mathematical text>} + + \ctlpbr{<balanced mathematical text>} + + \ctlpbl{<balanced mathematical text>} +\end{myverb} +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 +\begin{verse} +\begin{tabular}{lll} + + top left & for & "\ctlptl" \\ + top right & for & "\ctlptr" \\ + bottom right & for & "\ctlpbr" \\ + bottom left & for & "\ctlpbl" +\end{tabular} +\end{verse} +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 +\begin{verse} +\begin{tabular}{lll} + + left & for & "\ctlptl" \\ + right & for & "\ctlptr" \\ + right & for & "\ctlpbr" \\ + left & for & "\ctlpbl" +\end{tabular} +\end{verse} +of the loop, with its center +\begin{verse} +\begin{tabular}{lll} + + above & for & "\ctlptl" \\ + above & for & "\ctlptr" \\ + below & for & "\ctlpbr" \\ + below & for & "\ctlpbl" +\end{tabular} +\end{verse} +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 by "\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". +\begin{myverb} + \ctlptlcc{<balanced mathematical text>} + + \ctlptrcc{<balanced mathematical text>} + + \ctlpbrcc{<balanced mathematical text>} + + \ctlpblcc{<balanced mathematical text>} +\end{myverb} +These macros are similar to their cousins described above, except that a +counterclockwise arrowhead is placed at the counterclockwise end of the loop. + +\paragraph{An Example} + +The following program produces the same display as the previous +example. +\begin{myverb} + \[ + \ctdiagram{ + \ctv 0,100:{A} + \ctv 150,100:{B} + \ctv 0,0:{A'} + \ctv 150,0:{B'} + \ctet 0,100,150,100:{c} + \cteb 0,0,150,0:{c'} + \ctel 0,100,0,0:{a} + \cter 150,100,150,0:{b} + } + \] +\end{myverb} +Less trivial examples of the usage of these macros are found in Section~\ref{examples} and +in "diagmactest.tex". + +\cleardoublepage +\section{Extensions} +\label{extensions} + +This section describes two macros that have been +added to "diagmac2.sty" +by Bob Tennent (and are not in Reynolds's original "diagmac"). + +\begin{myverb} + \drawedgebar +\end{myverb} +"\drawedgebar" draws a bar across the end of the current edge. +\begin{myverb} + \ctec<number:x-start-coord>,<number:y-start-coord>, + <number:x-end-coord>,<number:y-end-coord>, + <number:x-ctrl-coord>,<number:y-ctrl-coord>:{<balanced mathematical text>} +\end{myverb} +"\ctec" draws a bezier-curve edge from the start point to the end point, using the +third point as a control point. The "<balanced mathematical text>" is centered at +the control point. + +\section{Examples} +\label{examples} + +\begin{minipage}[t]{2.9in} + \[ +\ctdiagram{ + \def\diagramunit{0.8pt} + \ctinnermid + \ctv 0,100:{a} + \ctv 150,100:{f(a)} + \ctv 0,0:{g(a)} + \ctv 150,0:{f(g(a))=g(f(a))} + \ctet 0,100,150,100:{f} + \drawedgebar + \cteb 0,0,150,0:{f} + \drawedgebar + \ctel 0,100,0,0:{g} + \drawedgebar + \cter 150,100,150,0:{g} + \drawedgebar +} +\] +\end{minipage} +\qquad +\begin{minipage}[t]{3.0in} +\begin{smallverb} +\[ +\ctdiagram{ + \def\diagramunit{0.8pt} + \ctinnermid + \ctv 0,100:{a} + \ctv 150,100:{f(a)} + \ctv 0,0:{g(a)} + \ctv 150,0:{f(g(a))=g(f(a))} + \ctet 0,100,150,100:{f} + \drawedgebar + \cteb 0,0,150,0:{f} + \drawedgebar + \ctel 0,100,0,0:{g} + \drawedgebar + \cter 150,100,150,0:{g} + \drawedgebar +} +\] +\end{smallverb} +\end{minipage} +\\[4ex] + +\begin{minipage}[t]{3.1in} +\[ +\ctdiagram{ +\def\diagramunit{1.1pt} +\ctv 0,0: {I\otimes v} +\ctv 0,60: {(I\otimes I)\otimes v} +\ctv -80,60: {I\otimes (I\otimes v)} +\ctv 80,60: {I\otimes (I\otimes v)} +\ctelg -80,60,0,0;25:{I\otimes\lambda_v\!} +\cterg 80,60,0,0;25:{\,\lambda{_I\otimes v}} +\ctec -80,60,80,60,0,80:{\mathsf{id}} +\cteb -80,60,0,60:{\alpha^{-1}} +\cteb 0,60,80,60:{\alpha^{-1}} +\ctv 0,36:{\rho_I\otimes v = + \lambda_I\otimes v} +\ctnohead +\cten 0,60,0,36: +\cthead +\cten 0,36,0,0: +} +\] +\end{minipage} +\qquad +\begin{minipage}[t]{3.0in} +\begin{smallverb} +\[ +\ctdiagram{ + \ctv 0,0: {I\otimes v} + \ctv 0,60: {(I\otimes I)\otimes v} + \ctv -80,60: {I\otimes (I\otimes v)} + \ctv 80,60: {I\otimes (I\otimes v)} + \ctelg -80,60,0,0;25:{I\otimes\lambda_v\!} + \cterg 80,60,0,0;25:{\,\lambda{_I\otimes v}} + \ctec -80,60,80,60,0,80:{\mathsf{id}} + \cteb -80,60,0,60:{\alpha^{-1}} + \cteb 0,60,80,60:{\alpha^{-1}} + \ctv 0,36:{\rho_I\otimes v = + \lambda_I\otimes v} + \ctnohead + \cten 0,60,0,36: + \cthead + \cten 0,36,0,0: +} +\] +\end{smallverb} +\end{minipage} + +\clearpage + +\begin{minipage}[t]{3.0in} +\[ +\ctdiagram{ +\ctv -60,0:{V} +\ctv 60,0:{E} +\ctv 0,0: {I} +\cten 0,0,60,0: +\ctnohead +\cten -60,0,0,0: +\ctet -50,20,50,20:{\delta_0} +\setcircle{20pt}{\xstart}{\ystart} +\shiftcircle{0pt}{-10pt} +\drawcircle0001 +\drawcirclehead{-1}{0}{0} +\setcircle{20pt}{\xend}{\yend} +\shiftcircle{0pt}{-10pt} +\drawcircle1000 +\cteb -50,-18,50,-18:{\delta_1} +\setcircle{20pt}{\xstart}{\ystart} +\shiftcircle{0pt}{10pt} +\drawcircle0010 +\drawcirclehead{-1}{0}{1} +\setcircle{20pt}{\xend}{\yend} +\shiftcircle{0pt}{10pt} +\drawcircle0100 +} +\] +\end{minipage} +\qquad +\begin{minipage}[t]{3.0in} +\begin{smallverb} +\[ +\ctdiagram{ + \ctv -60,0:{V} + \ctv 60,0:{E} + \ctv 0,0: {I} + \cten 0,0,60,0: + \ctnohead + \cten -60,0,0,0: + \ctet -50,20,50,20:{\delta_0} + \setcircle{20pt}{\xstart}{\ystart} + \shiftcircle{0pt}{-10pt} + \drawcircle0001 + \drawcirclehead{-1}{0}{0} + \setcircle{20pt}{\xend}{\yend} + \shiftcircle{0pt}{-10pt} + \drawcircle1000 + \cteb -50,-18,50,-18:{\delta_1} + \setcircle{20pt}{\xstart}{\ystart} + \shiftcircle{0pt}{10pt} + \drawcircle0010 + \drawcirclehead{-1}{0}{1} + \setcircle{20pt}{\xend}{\yend} + \shiftcircle{0pt}{10pt} + \drawcircle0100 +} +\] +\end{smallverb} +\end{minipage} +\\[4ex] + +\begin{minipage}[t]{3.0in} +\[ +\ctdiagram{ +\ctv 0,0:{\widetilde{B}} +\ctv 60,0:{B} +\ctv 0,60:{E_b} +\ctv 60,60:{E} +\ctinnermid +\cteb 0,0,60,0:{b} +\cter 0,60,0,0:{q_b} +\cteb 0,60,60,60:{\overline{b}} +\cter 60,60,60,0:{q} +\ctv -40,100: {\widetilde{E}} +\ctec -40,100,0,0,-40,50:{\tilde{q}} +\ctec -40,100,60,60,10,100:{p} +\def\ctvertexborderlr{1pt} +\def\ctvertexbordertb{1pt} +\ctv -20,80:{\hat{p}} +\ctnohead\ctdot +\def\zzctdrawdotedge{\drawdotedge{2.5pt}1} +\cten -40,100,-20,80: +\cthead +\def\zzctdrawdotedge{\drawdotedge{2.5pt}0} +\cten -20,80,-6,66: +\ctv 5,55:{\mbox{\Large$\lrcorner$}} +} +\] +\end{minipage} +\qquad +\begin{minipage}[t]{3.0in} +\begin{smallverb} +\[ +\ctdiagram{ + \ctv 0,0:{\widetilde{B}} + \ctv 60,0:{B} + \ctv 0,60:{E_b} + \ctv 60,60:{E} + \ctinnermid + \cteb 0,0,60,0:{b} + \cter 0,60,0,0:{q_b} + \cteb 0,60,60,60:{\overline{b}} + \cter 60,60,60,0:{q} + \ctv -40,100: {\widetilde{E}} + \ctec -40,100,0,0,-40,50:{\tilde{q}} + \ctec -40,100,60,60,10,100:{p} + \def\ctvertexborderlr{1pt} + \def\ctvertexbordertb{1pt} + \ctv -20,80:{\hat{p}} + \ctnohead\ctdot + \def\zzctdrawdotedge{\drawdotedge{2.5pt}1} + \cten -40,100,-20,80: + \cthead + \def\zzctdrawdotedge{\drawdotedge{2.5pt}0} + \cten -20,80,-6,66: + \ctv 5,55:{\mbox{\Large$\lrcorner$}} +} +\] +\end{smallverb} +\end{minipage} + +\clearpage +\vspace*{-4ex} +\[ +\ctdiagram{ +\ctinnermid +\ctv 0,0: {(I\otimes I) \otimes(v\otimes w)} +\ctv 0,60: {I\otimes \bigl(I\otimes(v\otimes w)\bigr)} +\ctv 0,120: {I\otimes \bigl((I\otimes v)\otimes w\bigr)} +\ctv 80,180: {I\otimes\bigl((v\otimes I)\otimes w\bigr)} +\ctv 200,0: {I\otimes (v\otimes w)} +\ctv 200,180:{I\otimes \bigl(v\otimes(I\otimes w)\bigr)} +\ctv 280,0:{v\otimes w} +\ctv 280,60:{(I\otimes v)\otimes w} +\ctv 280,120: { (I\otimes v)\otimes(I\otimes w)} +\ctel 0,0,0,60:{\alpha^{-1}} +\ctel 0,60,0,120:{I\otimes \alpha^{-1}} +\ctet 0,0,200,0:{\rho_I\otimes(v\otimes v)} +\ctet 200,0,280,0:{\lambda_{v\otimes w}} +\ctelg 0,120,80,180;155:{I\otimes\sigma_{I,v}\otimes w} +\ctet 80,180,200,180:{I\otimes \alpha^{-1}} +\cterg 200,180,280,120;155:{\alpha^{-1}} +\cter 280,120,280,60:{(I\otimes v)\otimes \lambda_w} +\cter 280,60,280,0: {\lambda_v\otimes w} +\ctv 240,30:{\alpha^{-1}} +\ctnohead +\cten 200,0,240,30: +\cthead +\cten 240,30,280,60: +\ctv 100,30:{I\otimes\lambda_{v\otimes w}} +\ctnohead +\cten 0,60,100,30: +\cthead +\cten 100,30,200,0: +\ctv 100,60:{I\otimes(\lambda_v\otimes w)} +\ctnohead +\cten 0,120,100,60: +\cthead +\cten 100,60,200,0: +\ctv 120,120:{I\otimes (\rho_v\otimes w)} +\ctnohead +\cten 80,180,120,120: +\cthead +\cten 120,120,200,0: +\ctv 200,90:{I\otimes (v\otimes \lambda_w)} +\ctnohead +\cten 200,180,200,90: +\cthead +\cten 200,90,200,0: +} +\] +\\ +\begin{smallverb} + \[ + \ctdiagram{\ctinnermid + \ctv 0,0: {(I\otimes I) \otimes(v\otimes w)} + \ctv 0,60: {I\otimes \bigl(I\otimes(v\otimes w)\bigr)} + \ctv 0,120: {I\otimes \bigl((I\otimes v)\otimes w\bigr)} + \ctv 80,180: {I\otimes\bigl((v\otimes I)\otimes w\bigr)} + \ctv 200,0: {I\otimes (v\otimes w)} + \ctv 200,180:{I\otimes \bigl(v\otimes(I\otimes w)\bigr)} + \ctv 280,0:{v\otimes w} + \ctv 280,60:{(I\otimes v)\otimes w} + \ctv 280,120: { (I\otimes v)\otimes(I\otimes w)} + \ctel 0,0,0,60:{\alpha^{-1}} + \ctel 0,60,0,120:{I\otimes \alpha^{-1}} + \ctet 0,0,200,0:{\rho_I\otimes(v\otimes v)} + \ctet 200,0,280,0:{\lambda_{v\otimes w}} + \ctelg 0,120,80,180;155:{I\otimes\sigma_{I,v}\otimes w} + \ctet 80,180,200,180:{I\otimes \alpha^{-1}} + \cterg 200,180,280,120;155:{\alpha^{-1}} + \cter 280,120,280,60:{(I\otimes v)\otimes \lambda_w} + \cter 280,60,280,0: {\lambda_v\otimes w} + \ctv 240,30:{\alpha^{-1}} + \ctnohead\cten 200,0,240,30: + \cthead\cten 240,30,280,60: + \ctv 100,30:{I\otimes\lambda_{v\otimes w}} + \ctnohead\cten 0,60,100,30: + \cthead\cten 100,30,200,0: + \ctv 100,60:{I\otimes(\lambda_v\otimes w)} + \ctnohead\cten 0,120,100,60: + \cthead \cten 100,60,200,0: + \ctv 120,120:{I\otimes (\rho_v\otimes w)} + \ctnohead\cten 80,180,120,120: + \cthead\cten 120,120,200,0: + \ctv 200,90:{I\otimes (v\otimes \lambda_w)} + \ctnohead\cten 200,180,200,90: + \cthead\cten 200,90,200,0: + } + \] +\end{smallverb} + +\clearpage + +\newcommand{\op}{\mathsf{op}} +\newcommand{\vnat}{\Downarrow\mskip-\medmuskip} +\[ +\ctdiagram{ +\ctinnermid +\ctv 0,0:{W^\op\times W^\op} +\ctv 180,0:{S\times S} +\ctv 0,60:{RW^\op} +\ctv 180,60:{RS} +\ctel 0,60,0,0:{\mathit{rw}^\op} +\cter 180,60,180,0:{\mathit{rs}} +\def\ctdoubleedgedisp{6.5pt} +\ctetb 0,60,180,60:11{\widetilde{F}}{\widetilde{G}} +\ctv 98,60:{\vnat\widetilde{\eta}} +\ctetb 0,0,180,0:11{F_0\times F_1}{G_0\times G_1} +\ctv 112,0:{\vnat\eta_0\times\eta_1} +} +\] +\\[4ex] + +\begin{smallverb} + \newcommand{\op}{\mathsf{op}} + \newcommand{\vnat}{\Downarrow\mskip-\medmuskip} + \[ + \ctdiagram{ + \ctinnermid + \ctv 0,0:{W^\op\times W^\op} + \ctv 180,0:{S\times S} + \ctv 0,60:{RW^\op} + \ctv 180,60:{RS} + \ctel 0,60,0,0:{\mathit{rw}^\op} + \cter 180,60,180,0:{\mathit{rs}} + \def\ctdoubleedgedisp{6.5pt} + \ctetb 0,60,180,60:11{\widetilde{F}}{\widetilde{G}} + \ctv 98,60:{\vnat\widetilde{\eta}} + \ctetb 0,0,180,0:11{F_0\times F_1}{G_0\times G_1} + \ctv 112,0:{\vnat\eta_0\times\eta_1} + } + \] +\end{smallverb} + + +See also the examples in Reynolds's "diagmactest". + + + +\end{document} diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf Binary files differdeleted file mode 100644 index 64315d5a87e..00000000000 --- a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex deleted file mode 100644 index 7b4626becde..00000000000 --- a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmac2Example.tex +++ /dev/null @@ -1,52 +0,0 @@ -\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 differindex 266fa28323d..ec4f0136fa4 100644 --- a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.pdf +++ 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 index 2b8fb8fcd15..a4ee5e99f43 100644 --- a/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.tex +++ b/Master/texmf-dist/doc/latex/diagmac2/doc/diagmactest.tex @@ -4,7 +4,7 @@ %and tests them. A user's manual for these macros is in diagmac.doc \documentclass[12pt]{article} -\input{diagmac2.sty} +\input diagmac \oddsidemargin=0in \evensidemargin=0in \textwidth=6.5in diff --git a/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty b/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty index 6c99b11bc1b..5826312c1b0 100644 --- a/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty +++ b/Master/texmf-dist/tex/latex/diagmac2/diagmac2.sty @@ -1,14 +1,43 @@ +%% This is file 'diagmac2.sty' +%% +%% Copyright (C) 1997 J. C. Reynolds, john.reynolds@cs.cmu.edu +%% 2004-09 R. D. Tennent, rdt@cs.queensu.ca +%% +%% This work may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either version 1.3 +%% of this license or (at your option) any later version. +%% The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.3 or later is part of all distributions of LaTeX +%% version 2003/12/01 or later. +%% +%% This work has the LPPL maintenance status "author-maintained". + %MACROS FOR DIAGRAMS - J. C. Reynolds - December 1987 -% Modified to use pict2e.sty by Bob Tennent, February 2004 +% Modified to use pict2e.sty by Bob Tennent % Changes indicated thusly: %%%pict2e +% Changelog: +% +% Version 2.1 May 2009 +% +% Two extensions added: \drawedgebar and \ctec +% User Manual TeXified and expanded +% +% Version 2.0 February 2004 +% +% Modified to use pict2e.sty +% Changes indicated thusly: %%%pict2e + +\ProvidesPackage{diagmac2}[2009/05/09 v2.1 LaTeX style for (category-theory) diagrams] + \AtBeginDocument{\RequirePackage{pict2e}} %%%pict2e \def\slopemax{1000} %%%pict2e slope factor maximum %This file contains general-purpose macros for drawing diagrams in LATEX, %followed by additional macros especially for category-theory diagrams. -%A user's manual is given in the file diagmac.doc, and a test program is +%A user's manual is given in the file diagmac2.tex, and a test program is %%%pict2e %given in the file diagmactest.tex. %GENERAL-PURPOSE MACROS @@ -20,7 +49,7 @@ \def\edgeheaddisp{4pt} \def\circleheaddisp{2pt} \def\diameterlist{1pt,2pt,3pt,4pt,5pt,6pt,7pt,8pt,9pt,10pt,11pt,% -12pt,13pt,14pt,15pt,16pt,20pt,24pt,28pt,32pt,36pt,40pt,} +12pt,13pt,14pt,15pt,16pt,20pt,24pt,28pt,32pt,36pt,40pt,} %%%pict2e: not used %Redefine if circle fonts are different. %The following registers store the representation of diagram and/or @@ -974,3 +1003,57 @@ WITH NO SHADOW}} \def\cthead{\def\zzctdrawhead{\zzctdrawedgehead}} \def\ctnohead{\def\zzctdrawhead{\zzctnodrawedgehead}} + + +% Extensions by Bob Tennent (May 2009): +% +%\drawedgebar draws a bar across the end of the current edge. +% +\def\drawedgebar{\zzdrawedgebara\xend\yend\xstart\ystart{-\xslope}{-\yslope}} +\def\zzdrawedgebara#1#2#3#4#5#6{\zzcheckedge{DRAW ARROWBAR FOR} +\zzcheckslope{#5}{#6}4{ARROWBAR} +\zzdmA=#3\advance\zzdmA by -#1 +\divide\zzdmA by 10\multiply\zzdmA by 100\divide\zzdmA by 10 +\zzdmB=#4\advance\zzdmB by -#2 +\divide\zzdmB by 10\multiply\zzdmB by 100\divide\zzdmB by 10 +\zzdistance{#5}{#6}\zzdmC=0pt +\multiply\zzdmC by 100\divide\zzdmC by \zzglobalcnA\zzdmD=\zzdmC +\multiply\zzdmC by #5\multiply\zzdmD by #6 +\advance\zzdmA by \zzdmC\advance\zzdmB by \zzdmD +\advance\zzdmA by #1\zzcnA=\zzdmA\advance\zzdmB by #2\zzcnB=\zzdmB +\zzmakepicture{\put(\zzcnA,\zzcnB){\line(#6,-#5){140000}} +\zzrecordwidth\zzdmA\zzdmA\zztotheight=\zzdmB\zztotdepth=\zzdmB} +\zzmakepicture{\put(\zzcnA,\zzcnB){\line(-#6,#5){140000}} +\zzrecordwidth\zzdmA\zzdmA\zztotheight=\zzdmB\zztotdepth=\zzdmB} +} + +% \ctec draws a bezier-curve edge from (#1,#2) to (#3,#4) using (#5,#6) as a +% control point; the balanced math text #7 is centered at the control point +% +\def\ctec#1,#2,#3,#4,#5,#6:#7{ +\ctv #5,#6:{#7} +% get and save \xstart,\ystart after shadowing +\setedge#1,#2,#5,#6: +\def\zzprocpoly{\zzcastpoly}\def\zzprocrorect{\zzprocrorecta} +\zzdmA=\xstart\zzdmB=\ystart\zzcnA=\xslope\zzcnB=\yslope +\zzstartshadow\xstart=\zzdmE\ystart=\zzdmF +\zzdmH=\xstart\zzdmI=\ystart +% get \xend, \yend and shadow +\setedge#5,#6,#3,#4: +\def\zzprocpoly{\zzcastpoly}\def\zzprocrorect{\zzprocrorecta} +\zzdmA=\xend\zzdmB=\yend\zzcnA=-\xslope\zzcnB=-\yslope +\zzendshadow\xend=\zzdmE\yend=\zzdmF +% draw head +\zzctdrawhead1 +% restore saved \xstart, \ystart +\xstart=\zzdmH\ystart=\zzdmI +% compute control-point parameters +\zzcnA=#5\zzcnB=#6 +\zzmultdiagramunit\zzdmH\zzcnA\zzmultdiagramunit\zzdmI\zzcnB +\zzcnA=\xstart\zzcnB=\ystart\zzcnC=\xend\zzcnD=\yend\zzcnE=\zzdmH\zzcnF=\zzdmI +% draw bezier curve +\zzmakepicture{\qbezier(\zzcnA,\zzcnB)(\zzcnE,\zzcnF)(\zzcnC,\zzcnD) +\zzrecordwidth\xstart\xstart\zzrecordwidth\xend\xend +\zztotheight=\ystart\zztotdepth=\ystart\zzrecordheight\yend\yend}} + + |