Technical Reports

Fraction Slash and Other Diagonals

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Fraction Slash and Other Diagonals

Unicode has a number of solidi and reverse solidi, which have various mathematical semantics. The most well-known solidus is U+002F / solidus (slash, virgule), which appears on most keyboards. It is used to separate alternatives, to separate fields in URLs (or more generally, in IRIs), and in mathematical contexts to denote division, although U+2215 ∕ division slash is the official division operator. The most well-known reverse solidus is U+005C \ reverse solidus (backslash), which is used in a variety of ways, notably in file path names, TeX macro names, and as a surrogate for mathematical operators such as U+2216 ∖ set minus. Table 2.7 displays various Unicode solidi. In addition there are small form and full-width variants (U+FE68 ﹨, U+FF0F /, U+FF3C \) and the empty-set symbols (U+29B0 ⦰.. U+29B4 ⦴).

Table 2.7 Solidi and Reverse Solidi

002F / Solidus

= slash, virgule

005C \ Reverse Solidus

= backslash

0338 ̸ Combining Long Solidus Overlay

0337 ̷ Combining Short Solidus Overlay

20E5 Combining Reverse Solidus Overlay

2044 ⁄ Fraction Slash

for composing arbitrary fractions

29F5 ⧵ Reverse Solidus Operator

2215 ∕ Division Slash

generic division operator

2216 ∖ Set Minus

233F ⌿ Apl Functional Symbol Slash Bar

2340 ⍀ Apl Functional Symbol Backslash Bar

2341 ⍁ Apl Functional Symbol Quad Slash

2342 ⍂ Apl Functional Symbol Quad Backslash

2298 ⊘ Circled Division Slash

29B8 ⦸ Circled Reverse Solidus

2571 ╱ Box Drawings Light Diagonal Upper Right To Lower Left

might not have 45° slope

not used in math

2572 ╲ Box Drawings Light Diagonal Upper Left To Lower Right

might not have 135° slope

not used in math

27CB ╱ Mathematical Rising Diagonal

= \diagup

must have 45° slope

27CD ╲ Mathematical Falling Diagonal

= \diagdown

must have 135° slope

29C4 ⧄ Squared Rising Diagonal Slash

29C5 ⧅ Squared Falling Diagonal Slash

29F6 ⧶ Solidus With Overbar

29F7 ⧷ Reverse Solidus With Horizontal Bar

29F8 ⧸ Big Solidus

= \xsol

29F9 ⧹ Big Reverse Solidus

= z notation schema hiding

= \xbsol

U+2044 ⁄ FRACTION SLASH is typically used to build up simple skewed fractions in running text. It applies to immediately adjacent sequences of decimal digits, that is, to spans of characters with the General Category property value Nd. For example, 1⁄2 should be displayed as ½. In ordinary plain text, any character other than a digit delimits the numerator or denominator. So 5 1⁄2 should be displayed as 5½ since a space follows the 5. In general mathematical use, a more versatile method for layout of fractions is needed (see, for example, Section 2.1 of [UnicodeMath]), however parsers of mathematical texts should be prepared to handle FRACTION SLASH when it is received from other sources.

U+27CB mathematical rising diagonal and U+27CD mathematical falling diagonal are mathematical symbols for specific uses, to be distinguished from the more widely used solidi and reverse solidi operators as well as from nonmathematical diagonals. U+27CB corresponds to the LaTeX entity \diagup and U+27CD to \diagdown. Their glyphs are invariably drawn with 45° and 135° slopes, respectively, instead of the more upright slants typical for the solidi operators. The diagonals are also to be distinguished from the two box drawing characters U+2571 and U+2572. While in some fonts those characters may be drawn with 45° and 135° slopes, respectively, they are not intended to be used as mathematical symbols. One usage recorded for U+27CB and U+27CD is in the notation for spaces of double cosets.

  1. Other Characters

All remaining Unicode characters may appear in mathematical expressions, typically in spelled-out names for variables in fractions or in simple formulae, but they most commonly appear in ordinary text. An English example is the equation

distance = rate × time,

which uses ordinary ASCII letters to aid in recognizing sequences of letters as words instead of products of individual symbols. Such usage corresponds to identifiers as discussed elsewhere in this report.

The period (U+002E FULL STOP) and U+002C COMMA are widely used as numerical punctuation, however, their meaning depends on local conventions. See [CLDR]. For Arabic, U+066B ARABIC DECIMAL SEPARATOR or U+002C COMMA are used. Note that U+0660 ARABIC-INDIC DIGIT ZERO is easily confused with a period, which leads to the fact that it is often spelled out.

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