Summary of qsymbols

Kristoffer H. Rose^{∗}

Version 1.12 ⟨1997/01/07⟩

Abstract

qsymbols is a L^{A}TEX [1] package defining systematic mnemonic abbreviations, starting with a single open quote ` for symbols, and in double quotes " … " for arrows, for characters from the amssymb and stmaryrd fonts. Optionally a very large class of arrows can be typeset using the XY-pic package.

Contents

1 Introduction 1

2 Simple symbols 2 2.1 Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Common symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Circled and Boxed Symbols . . . . . . . . . . . . . . . . . . . . . 2 2.4 Bold symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.5 Adding new symbols . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Orderings 3

4 Arrows 3 4.1 Canned arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4.2 Labelling arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4.3 Adding new arrows . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4.4 Using XY-pic for arrows . . . . . . . . . . . . . . . . . . . . . . . . 4 4.5 Using qsymbols arrows in XY-pic diagrams . . . . . . . . . . . . . 6

1 Introduction

qsymbols sets up a number of mnemonic and compact abbreviations for math symbols from L^{A}TEX and the packages amssymb and stmaryrd, which it loads. The abbreviations all start with the backquote character ` except for arrows that are of the form "->". Some are a single characters, some a more complicated pattern, but always the idea is to use abbreviations that hint at the visual appearance of the symbol. Finally it is possible for the user to add more abbreviations of the simpler categories.

∗E-mail: krisdiku.dk, W3 URL: http://www.diku.dk/users/kris/.

You can retrieve qsymbols as well as the amssymb and stmaryrd packages by anonymous ftp from all CTAN archives in directory /tex-archive/macros/ latex/contrib/supported/^{1} (each package has its own subdirectory).

2 Simple symbols

2.1 Greek letters

All the standard greek letters used in math are available as ` followed by a letter: either lowercase:

        x a b c d e f g h i j k l m n p q r s t u v w x y z

`x α β χ δ ϵ ϕ γ η ι ψ κ λ μ ν π θ ρ σ τ ϱ φ ω ξ υ ζ

or uppercase:

              X D  F  G  J  L  P  Q  S  W  X  Y

`X Δ Φ Γ Ψ Λ Π Θ Σ Ω Ξ Υ

2.2 Common symbols

Simple symbols are available using ` followed by a symbolic representation of the symbol. The most common have single character representations:

\begin{aligned}x & + & * & : & ; & / & U & C & _ & T & o & . & = & ~ & E & A & ! & ^ & V \\ `x & ± & × & ∈ & ∉ & \ & ∪ & ∁ & ⊥ & ⊤ & ∘ & · & ≡ & ≃ & ∃ & ∀ & ¬ & ∧ & ∨ \end{aligned}

2.3 Circled and Boxed Symbols

These are represented using round and square brackets, respectively:

    x  +  - `* / | `/ `. * `o `^`V <  > ? ! :-  R  C  a

`(x) ◯ ⊕ ⊖ ⊗ ⊘ ⦶ ⍉ ⊙ ⊛ ⊚  ⧀ ⧁ ∘ • ◯_{¨⌣} ® \begin{matrix}c \\ ◯ \end{matrix} ◯^{a}
`[x] □ ⊞ ⊟ ⊠ ⧄ ◫ ⧅ ⊡ ⧆ ⧇ □^{∧} □^{∨} □^{<} □^{>} ◯_{¨⌢} □^{R} □^{C} □^{a}
`<x> ♢  ⋄ ◯_{¨−}
`{x} ∅  ◯_{¨∼}

As it can be seen, ‘undefined’ codes of the forms `(a) and `[a] result in the contents being circled and boxed, respectively.

2.4 Bold symbols

The AMS-L^{A}TEX \boldsymbol command is available by using the special abbreviation `@x for the bold version x of x as well as `@`x where x is on one of the forms described in this section, i.e., `@`a gives α.

2.5 Adding new symbols

Symbols of all the above forms can be added using the form

                  \newqsymbol {`code} {expansion}

which makes `code behave as expansion in math mode. code should be either a single character or some characters enclosed in (), [], <>, or {}.

1The ‘home’ of qsymbols is ftp.diku.dk in directory /diku/users/kris/TeX/qsymbols/.

3 Orderings

Two to four consecutive `s indicate an ordering relation:

   ϵ, ϶ ``ϵ ``/ϵ ``ϵ= ``/ϵ= ```ϵ ````ϵ ``϶ ``/϶ ``϶= ``/϶= ```϶ ````϶

<, > < ≮ ≤ ≰ ∧ ⋀  > ≯ ≥ ≱ ∨ ⋁
(,) ⊂ ⊄ ⊆ ⊈ ∩ ⋂  ⊃ ⊅ ⊇ ⊉ ∪ ⋃
[,] ⊏ ⊏̸ ⊑ ⋢ ⊓ ⨅  ⊐ ⊐̸ ⊒ ⋣ ⊔ ⨆
\{, \} ≺ ⊀ ⪯ ⪯̸ ⋏ ⋏  ≻ ⊁ ⪰ ⪰̸ ⋎ ⋎
\<, \> ◁ ⋪ ⊴ ⋬ △ △  ▷ ⋫ ⊵ ⋭ ▽ ▽
~, \~ ∼ ≁ ≃ ≄  ≀  ∽ ∽̸ ⋍ ⋍̸ ∫  ∫
(-, -) ∈ ∉  ⋔  ∋
(+, +) ⪿ ⪿̸  ⫀̸ ⫀̸  ⊎̸ ⨄

Some abbreviations are provided for convenience:

                        \begin{matrix}x & U & V & S & P \\ ``x & ⋃ & ⋁ & ∑ & ∏ \end{matrix}

There is no simple way to add more orderings.

4 Arrows

Double quotes " … " make it possible to typeset arrows. On some systems " is reserved for other uses, in that case you can use `" … " instead.

4.1 Canned arrows

The available arrows are shown in figure 1 where ! means that the arrow is available in a long version by adding a ! just after the stem character (one of -=), and ? means that it stretches to accomodate labels (when no !s are given, see below).

4.2 Labelling arrows

Inserting {^s} or {_s}, where s is a legal super- or subscript, respectively, will typeset these as limits, and even grows it in those cases where the arrow is marked with a “@” in the table.

x

             -{_1}>

                     3>{^{`a`.`b}}

                                    <|-|>{_{\mbox{push}}}

"x"     [figure: 1]  ≡ ; ≡ ; ≡ ; ⇛^{α·β}  ⇽ ; − ; − ; − ; ⇾ ; push

4.3 Adding new arrows

You can add more ‘canned’ arrows of this kind with commands

                 \newqsymbol {"arrow"} {expansion}

which makes "arrow" behave as expansion in math mode.

[figure: "<-"; !@; "<->"; !; "->"; !@]
"<=" ⇐ !@ "<=>" ⇔ ! "=>" ⇒ !@
"<3" ⇚ @  "3>" ⇛ @
[figure: "</-"; "</->"; "-/>"]
"</=" ⇍  "</=>" ⇎  "=/>" ⇏
[figure: "^<-"; "^->"]
[figure: "_<-"; "_->"]
[figure: "<-|"; !@; "|->"; !@]
"<=|" ⤆ !@  "|=>" ⤇ !@
[figure: "<-'"; @; "`->"; @]
[figure: "<-<"; ">->"]
"<|-" ⇽ @ "<|-|>" ⇿ @ "-|>" ⇾ @
                                 "-o" ⊸ @
"<--" ←−−  "-->" −−→
                 "<~>" ↭  "~>" ⇝
[figure: "<<-"; @; "->>"; @]
"<<=" ⇐ ⇐ @  "=>>" ⇒ ⇒ @
"|-" ⊢  "|/-" ⊬  "-|" ⊣
"|=" ⊨  "|/=" ⊭
"||-" ⊩  "||/-" ⊮

Figure 1: Standard ‘canned’ arrow symbols.

Similarly, you can add stretchable arrows using commands of the form

         \newqsymbol {"arrow@"} {filler}

which makes "arrow" stretch under long labels as filler dictates: this should behave as the plain TEX command \rightarrowfill or use the macro

      \genericarrowfill{tail}{leader}{head}

qsymbols includes, for example, the declaration

\newqsymbol{"3>@"}{\genericarrowfill\equiv\equiv\Rrightarrow}

4.4 Using XY-pic for arrows

If the option [xy] is used in the \usepackage command, or if XY-pic [3]^{2} is already loaded, then the XY-pic arrow feature (with the ‘cmtip’ extension) is used to allow a much more general class of arrows.

First, all blank entries in figure 1 are filled; if the option [purexy] is used instead of [xy] then all the entries of the table are replaces with XY-pic generated arrows (this gives a somewhat more homogenous look and avoids loading of ams and stmary arrows).

Second, general arrows can be constructed according to the following rules:

• Basic arrows are composed by combining the variants 23^_, the tips <>|xo`', and the connectors -=.:~.

2XY-pic version 3 is needed for this to work.

• The character / ‘negates’ the arrow (once or twice) similar to the way \not does for relations:

                       \begin{matrix}x & `-/> & =//!> \\ "x" & [figure] & [figure] \end{matrix}

• Each ! character makes the arrow a bit longer.

                  \begin{matrix}x & -> & -!> & -!!> & -!!!> \\ "x" & [figure] & [figure] & [figure] & [figure] \end{matrix}

Note: Some arrows are automatically made a bit longer, e.g., the <~> arrow shown above.

• The form *object inserts the XY-pic object which will be used for the tail, shaft, or tip as indicated by the position. Here are some examples:

                 \begin{matrix}x & *\{x\}-*\{y\}! & *\{\}*\{*\}|!! \\ "x" & x y &  ; \begin{aligned}& & & ∗ \\ & & ∗ \\ & ∗ \\ ∗ \end{aligned} \end{matrix}

as in the examples it is recommended to specify all three of tail, shaft, and head, when using this, in particular an empty tail when the shaft is specified with * because otherwise it is taken as the tail.

• The forms (x) and [x] insert a break with x in a circle and box, respectively:

                      \begin{matrix}x & (1)> & [1]>> \\ "x" & [figure: ◯^{1}] & [figure: □^{1}] \end{matrix}

• The special code {ℓ} adds the ℓ material to the end of the XY-pic arrow: All XY-pic ⟨labels⟩ can be used as described in [3, §16], for example,

                      \begin{matrix}x & =\{|\{`b\}\}!!|> \\ "x" & [figure: β] \end{matrix}

Use this with care!

• Similarly the special code @{ℓ} adds the @ℓ material (note the omission of the braces) to the beginning of the XY-pic arrow: all XY-pic arrow ⟨form⟩s can be used ¡form¿ to the beginning of the arrow specification; this can be used to as described in [3, §16], for example,

             \begin{matrix}x & |-@\{/^/\}!!!>| & ->!!!!@\{(dr,ul)\} \\ "x" & [figure] & [figure] \end{matrix}

Use this with care!

4.5 Using qsymbols arrows in XY-pic diagrams

Finally it is possible to some extent to use qsymbols arrows in XY-pic matrices (as described in the XY-pic User’s Guide [2]) and graphs (as described in the XY-pic Reference Manual [3, §19]). First notice that you should always use the `" … " form. Second, the entire `" … " construction behaves as an arrow made with \ar for matrices and : for graphs, that is, you must add a ‘target address’ for the arrow after it. Further information of this can be found

Here is the canonical pull-back example diagram from category theory typeset using qsymbols:

    \xymatrix{
     U `"->"@/_/[ddr]_y `".>"[dr]|-{(x,y)} `"->"@/^/[drr]^x \\
      & X \times_Z Y `"=>"[d]^q `"=>"[r]_p & X `"=>"[d]_f   \\
      & Y `"=>"[r]^g                       & Z              }

typesets

[figure: U; y; (x,y); x; X ×_{Z} Y; q; p; X; f; Y; g; Z]

As you can see, XY-pic is loaded by qsymbols and as a convenience XY-pic options may be passed to qsymbols.

References

[1] Leslie Lamport. L^{A}TEX—A Document Preparation System. Addison-Wesley, 2nd edition, 1994.

[2] Kristoffer H. Rose. XY-pic user’s guide. Mathematics Report 94–148, MPCE, Macquarie University, NSW 2109, Australia, June 1994. For version 2.10+.

   Latest version available with URL ftp://ftp.diku.dk/diku/users/kris/
   TeX/xy/xyguide.ps.

[3] Kristoffer H. Rose and Ross Moore. XY-pic reference manual. Mathematics Report 94–155, MPCE, Macquarie University, NSW 2109, Australia, June 1994. For version 2.10+. Latest version available by anonymous ftp in

   ftp.diku.dk:  /diku/users/kris/TeX/xyrefer.ps.Z.