The previous post introduces Hermann Klinke’s math input notation, which he developed to speed up entry of equations for real-time note taking in OneNote. The post is followed by a very interesting set of comments comparing high-speed, and yet easy-to-remember, input sequences. Some of these involve hot keys and some can be done with math autocorrect. Both approaches are significantly faster than TeX input. In a future post, I’ll write about possible use of hot keys in math zones, which seems like a really powerful feature (MathType has it). The present post deals with a simple, intuitive way of entering 129 Unicode operators.
Over the years I’ve played with simple keyboard sequences for entering operators, such as +- giving ±. Some such sequences work in math zones of Office 2007/2010. This post gives a table of a larger set of 129 sequences that are reasonably unambiguous. Note that ^ and _ are not used since a user may want to superscript or subscript an operator. Even the case +- giving ± could be ambiguous, since one might want to write a + −b. The user can enter this by typing a+-<undo>b, so counting on undo is a possible way to free up some other natural sequences. An interesting example is <-, which has a mathematical meaning as illustrated by the relation a < −b. Accordingly, the sequence <- isn’t used to produce ←. In contrast, -> has no mathematical meaning and therefore produces → unambiguously. Fortuitously → is much more common in mathematics than ←, since → is used in limit expressions. The +- and -> are included in the math autocorrect file that ships with Microsoft Office. You can add the new ones in this post to your math autocorrect file.
The operator-sequence table given below includes keyboard sequences for operators that can be produced using the ASCII operators !+-./:<=>`' and ~. I couldn’t resist adding the somewhat unintuitive characters `, which transforms < and > into ≺ and ≻, respectively, and ', which transforms < and > into ⊂ and ⊃, respectively. These transformations provide access to 44 additional operators. To input the entire Unicode operator repertoire, one needs a notation that uses additional characters or falls back on TeX notation.
In the present scheme, = usually adds a horizontal bar under the preceding operator. For example, >= produces ≥. An additional = converts ≥ into ≧. For cases where Unicode lacks the single-bar character but has the double-bar character, a single = produces the double-bar character directly. For example, ≷ = → ⪒. Amazingly enough ⪒ actually exists in Unicode! Similarly, ~ puts a ~ under the preceding character, as in ~~ → ≈, etc.
Unicode has 18 negated operators defined by the corresponding unnegated characters followed by the slanted-bar combining mark U+0338 as shown in Table 2.8 of Unicode Technical Report #25 Unicode Support for Mathematics. Table 2.8 also has 18 negated operators that have the vertical bar combining mark U+20D2. It would be easy to add the former to the table, but our current fonts don’t display them very well. Using the vertical bar for the corresponding combining mark can be ambiguous and needs further analysis.
In the table the characters in the shaded cells result from typing the characters in the unshaded cells to their left. Note that the Office formula autobuildup facility automatically replaces the ASCII - by U+2212 (−), so technically there are no entries for the ASCII -. In the table, the shaded characters are followed by their Unicode code points without the U+ prefix for simplicity.
char_{1}
char_{2}
New char
char_{3}
char_{4}
char_{5}
!
‼
203C
*
=
⩮
2A6E
+
−
±
00B1
⩲
2A72
∓
2213
:
∹
2239
≡
2261
≣
2263
>
→
2192
.
∸
2238
≐
2250
≑
⩧
2251
2A67
~
⩪
2A6A
∻
⩭
223B
2A6D
/
<
≮
226E
'
`
≰
≴
≸
⊄
⊀
2270
2274
2278
2284
2280
⊈
2288
≠
2260
≢
2262
≯
226F
≱
≵
≹
⊅
⊁
2271
2275
2279
2285
2281
⊉
2289
≁
2241
≄
≉
2244
2249
≇
2247
∷
2237
⩴
2A74
≔
2254
</
⪇
⋦
2A87
22E6
≨
⪉
2268
2A89
≪
226A
⋘
22D8
≤
2264
≦
⋚
2266
22DA
⪋
2A8B
≶
2276
⪑
2A91
≲
2272
⪅
⪏
2A85
2A8F
⊂
2282
⊂/
⊆
⫕
⫓
⫇
2286
2AD5
2AD3
2AC7
⊊
⫅
⫉
228A
2AC5
2AC9
⫋
2ACB
≺
227A
≺/
⪯
⪻
≾
2AAF
2ABB
227E
⪱
⋨
⪳
⪷
2AB1
22E8
2AB3
2AB7
⪵
⪹
2AB5
2AB9
⋜
22DC
⩵
2A75
⩶
⪙
⪚
⩳
2A76
2A99
2A9A
2A73
⋝
22DD
≕
2255
≂
2242
>/
⪈
⋧
2A88
22E7
≩
⪊
2269
2A8A
≥
2265
≧
⋛
2267
22DB
⪌
2A8C
≫
226B
⋙
22D9
≷
2277
⪒
2A92
⊃
2283
⊃/
⊇
⫔
⫖
⫈
2287
2AD4
2AD6
2AC8
⊋
⫆
⫊
228B
2AC6
2ACA
⫌
2ACC
≻
227B
≻/
⪰
⪼
≿
2AB0
2ABC
227F
⪲
⋩
⪴
⪸
2AB2
22E9
2AB4
2AB8
⪶
⪺
2AB6
2ABA
≳
2273
⪆
⪐
2A86
2A90
~/
≆
2246
⪝
2A9D
⪟
2A9F
≃
2243
≅
⩬
2245
2A6C
⪞
2A9E
⪠
2AA0
≈
2248
≊
≋
224A
224B
⩰
2A70