# Mathematical Annotation in R

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### Description

If the text argument to one of the text-drawing functions (text, mtext, axis, legend) in R is an expression, the argument is interpreted as a mathematical expression and the output will be formatted according to TeX-like rules. Expressions can also be used for titles, subtitles and x- and y-axis labels (but not for axis labels on persp plots).

In most cases other language objects (names and calls, including formulas) are coerced to expressions and so can also be used.

### Details

A mathematical expression must obey the normal rules of syntax for any R expression, but it is interpreted according to very different rules than for normal R expressions.

It is possible to produce many different mathematical symbols, generate sub- or superscripts, produce fractions, etc.

The output from demo(plotmath) includes several tables which show the available features. In these tables, the columns of grey text show sample R expressions, and the columns of black text show the resulting output.

The available features are also described in the tables below:

 Syntax Meaning x + y x plus y x - y x minus y x*y juxtapose x and y x/y x forwardslash y x %+-% y x plus or minus y x %/% y x divided by y x %*% y x times y x %.% y x cdot y x[i] x subscript i x^2 x superscript 2 paste(x, y, z) juxtapose x, y, and z sqrt(x) square root of x sqrt(x, y) yth root of x x == y x equals y x != y x is not equal to y x < y x is less than y x <= y x is less than or equal to y x > y x is greater than y x >= y x is greater than or equal to y x %~~% y x is approximately equal to y x %=~% y x and y are congruent x %==% y x is defined as y x %prop% y x is proportional to y x %~% y x is distributed as y plain(x) draw x in normal font bold(x) draw x in bold font italic(x) draw x in italic font bolditalic(x) draw x in bolditalic font symbol(x) draw x in symbol font list(x, y, z) comma-separated list ... ellipsis (height varies) cdots ellipsis (vertically centred) ldots ellipsis (at baseline) x %subset% y x is a proper subset of y x %subseteq% y x is a subset of y x %notsubset% y x is not a subset of y x %supset% y x is a proper superset of y x %supseteq% y x is a superset of y x %in% y x is an element of y x %notin% y x is not an element of y hat(x) x with a circumflex tilde(x) x with a tilde dot(x) x with a dot ring(x) x with a ring bar(xy) xy with bar widehat(xy) xy with a wide circumflex widetilde(xy) xy with a wide tilde x %<->% y x double-arrow y x %->% y x right-arrow y x %<-% y x left-arrow y x %up% y x up-arrow y x %down% y x down-arrow y x %<=>% y x is equivalent to y x %=>% y x implies y x %<=% y y implies x x %dblup% y x double-up-arrow y x %dbldown% y x double-down-arrow y alpha -- omega Greek symbols Alpha -- Omega uppercase Greek symbols theta1, phi1, sigma1, omega1 cursive Greek symbols Upsilon1 capital upsilon with hook aleph first letter of Hebrew alphabet infinity infinity symbol partialdiff partial differential symbol nabla nabla, gradient symbol 32*degree 32 degrees 60*minute 60 minutes of angle 30*second 30 seconds of angle displaystyle(x) draw x in normal size (extra spacing) textstyle(x) draw x in normal size scriptstyle(x) draw x in small size scriptscriptstyle(x) draw x in very small size underline(x) draw x underlined x ~~ y put extra space between x and y x + phantom(0) + y leave gap for "0", but don't draw it x + over(1, phantom(0)) leave vertical gap for "0" (don't draw) frac(x, y) x over y over(x, y) x over y atop(x, y) x over y (no horizontal bar) sum(x[i], i==1, n) sum x[i] for i equals 1 to n prod(plain(P)(X==x), x) product of P(X=x) for all values of x integral(f(x)*dx, a, b) definite integral of f(x) wrt x union(A[i], i==1, n) union of A[i] for i equals 1 to n intersect(A[i], i==1, n) intersection of A[i] lim(f(x), x %->% 0) limit of f(x) as x tends to 0 min(g(x), x > 0) minimum of g(x) for x greater than 0 inf(S) infimum of S sup(S) supremum of S x^y + z normal operator precedence x^(y + z) visible grouping of operands x^{y + z} invisible grouping of operands group("(",list(a, b),"]") specify left and right delimiters bgroup("(",atop(x,y),")") use scalable delimiters group(lceil, x, rceil) special delimiters group(lfloor, x, rfloor) special delimiters

The supported ‘scalable delimiters’ are | ( [ {, lceil, lfloor and their right-hand versions. "." is equivalent to "": the corresponding delimiter will be omitted. Delimiter || is supported but has the same effect as |.

The symbol font uses Adobe Symbol encoding so, for example, a lower case mu can be obtained either by the special symbol mu or by symbol("m"). This provides access to symbols that have no special symbol name, for example, the universal, or forall, symbol is symbol("\042"). To see what symbols are available in this way use TestChars(font=5) as given in the examples for points: some are only available on some devices.

Note to TeX users: TeX's \Upsilon is Upsilon1, TeX's \varepsilon is close to epsilon, and there is no equivalent of TeX's \epsilon. TeX's \varpi is close to omega1. vartheta, varphi and varsigma are allowed as synonyms for theta1, phi1 and sigma1.

sigma1 is also known as stigma, its Unicode name.

Control characters (e.g., \n) are not interpreted in character strings in plotmath, unlike normal plotting.

The fonts used are taken from the current font family, and so can be set by par(family=) in base graphics, and gpar(fontfamily=) in package grid.

Note that bold, italic and bolditalic do not apply to symbols, and hence not to the Greek symbols such as mu which are displayed in the symbol font. They also do not apply to numeric constants.

### Other symbols

On many OSes and some graphics devices many other symbols are available as part of the standard text font, and all of the symbols in the Adobe Symbol encoding are in principle available via changing the font face or (see ‘Details’) plotmath: see the examples section of points for a function to display them. (‘In principle’ because some of the glyphs are missing from some implementations of the symbol font.) Unfortunately, postscript and pdf have support for little more than European (not Greek) and CJK characters and the Adobe Symbol encoding (and in a few fonts, also Cyrillic characters).

In a UTF-8 locale any Unicode character can be entered, perhaps as a \uxxxx or \Uxxxxxxxx escape sequence, but the issue is whether the graphics device is able to display the character. The widest range of characters is likely to be available in the X11 device using cairo: see its help page for how installing additional fonts can help. This can often be used to display Greek letters in bold or italic.

In non-UTF-8 locales there is normally no support for symbols not in the languages for which the current encoding was intended.

### References

Murrell, P. and Ihaka, R. (2000) An approach to providing mathematical annotation in plots. Journal of Computational and Graphical Statistics, 9, 582–599.

The symbol codes can be found in octal in the Adobe reference manuals, e.g. for Postscript https://www.adobe.com/products/postscript/pdfs/PLRM.pdf or PDF https://www.adobe.com/devnet/acrobat/pdfs/pdf_reference_1-7.pdf and in decimal, octal and hex at http://www.stat.auckland.ac.nz/~paul/R/CM/AdobeSym.html.

demo(plotmath), axis, mtext, text, title, substitute quote, bquote
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 require(graphics) x <- seq(-4, 4, len = 101) y <- cbind(sin(x), cos(x)) matplot(x, y, type = "l", xaxt = "n", main = expression(paste(plain(sin) * phi, " and ", plain(cos) * phi)), ylab = expression("sin" * phi, "cos" * phi), # only 1st is taken xlab = expression(paste("Phase Angle ", phi)), col.main = "blue") axis(1, at = c(-pi, -pi/2, 0, pi/2, pi), labels = expression(-pi, -pi/2, 0, pi/2, pi)) ## How to combine "math" and numeric variables : plot(1:10, type="n", xlab="", ylab="", main = "plot math & numbers") theta <- 1.23 ; mtext(bquote(hat(theta) == .(theta)), line= .25) for(i in 2:9) text(i, i+1, substitute(list(xi, eta) == group("(",list(x,y),")"), list(x = i, y = i+1))) ## note that both of these use calls rather than expressions. ## text(1, 10, "Derivatives:", adj = 0) text(1, 9.6, expression( " first: {f * minute}(x) " == {f * minute}(x)), adj = 0) text(1, 9.0, expression( " second: {f * second}(x) " == {f * second}(x)), adj = 0) plot(1:10, 1:10) text(4, 9, expression(hat(beta) == (X^t * X)^{-1} * X^t * y)) text(4, 8.4, "expression(hat(beta) == (X^t * X)^{-1} * X^t * y)", cex = .8) text(4, 7, expression(bar(x) == sum(frac(x[i], n), i==1, n))) text(4, 6.4, "expression(bar(x) == sum(frac(x[i], n), i==1, n))", cex = .8) text(8, 5, expression(paste(frac(1, sigma*sqrt(2*pi)), " ", plain(e)^{frac(-(x-mu)^2, 2*sigma^2)})), cex = 1.2) ## some other useful symbols plot.new(); plot.window(c(0,4), c(15,1)) text(1, 1, "universal", adj = 0); text(2.5, 1, "\\042") text(3, 1, expression(symbol("\042"))) text(1, 2, "existential", adj = 0); text(2.5, 2, "\\044") text(3, 2, expression(symbol("\044"))) text(1, 3, "suchthat", adj = 0); text(2.5, 3, "\\047") text(3, 3, expression(symbol("\047"))) text(1, 4, "therefore", adj = 0); text(2.5, 4, "\\134") text(3, 4, expression(symbol("\134"))) text(1, 5, "perpendicular", adj = 0); text(2.5, 5, "\\136") text(3, 5, expression(symbol("\136"))) text(1, 6, "circlemultiply", adj = 0); text(2.5, 6, "\\304") text(3, 6, expression(symbol("\304"))) text(1, 7, "circleplus", adj = 0); text(2.5, 7, "\\305") text(3, 7, expression(symbol("\305"))) text(1, 8, "emptyset", adj = 0); text(2.5, 8, "\\306") text(3, 8, expression(symbol("\306"))) text(1, 9, "angle", adj = 0); text(2.5, 9, "\\320") text(3, 9, expression(symbol("\320"))) text(1, 10, "leftangle", adj = 0); text(2.5, 10, "\\341") text(3, 10, expression(symbol("\341"))) text(1, 11, "rightangle", adj = 0); text(2.5, 11, "\\361") text(3, 11, expression(symbol("\361")))