｢‍｣ Lingenic

Mathematics

Pure Unicode math

Core Principle: Math is pure Unicode. Write readable, render beautiful.

Compose uses no special commands for mathematical structure. Authors write mathematics using Unicode characters for everything — symbols, structure, layout. The source is monospace-aligned and readable — exactly as it should be.

Commands

.begin-math
.end-math
begin math block
end math block

Fractions

.begin-math

  𝑎 + 𝑏
  ⎼⎼⎼⎼⎼
  𝑐 + 𝑑

.end-math

𝑎 U+1D44E MATHEMATICAL ITALIC SMALL A
𝑏 U+1D44F MATHEMATICAL ITALIC SMALL B
𝑐 U+1D450 MATHEMATICAL ITALIC SMALL C
𝑑 U+1D451 MATHEMATICAL ITALIC SMALL D
⎼ U+23BC HORIZONTAL SCAN LINE-7

Quadratic Formula

.begin-math

          ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
    −𝑏 ± √ 𝑏² − 4𝑎𝑐
𝑥 = ⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼⎼
          2𝑎

.end-math

⎽ U+23BD HORIZONTAL SCAN LINE-9 (vinculum)
⎼ U+23BC HORIZONTAL SCAN LINE-7 (fraction)
√ U+221A SQUARE ROOT
± U+00B1 PLUS-MINUS SIGN
− U+2212 MINUS SIGN
² U+00B2 SUPERSCRIPT TWO
𝑥 𝑎 𝑏 𝑐 U+1D465 U+1D44E U+1D44F U+1D450

Distance Formula

.begin-math

          ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽
𝑑(𝑃,𝑄) = √ (𝑥₂−𝑥₁)² + (𝑦₂−𝑦₁)²

.end-math

⎽ U+23BD HORIZONTAL SCAN LINE-9 (vinculum)
√ U+221A SQUARE ROOT
𝑑 U+1D451 MATHEMATICAL ITALIC SMALL D
𝑃 U+1D443 MATHEMATICAL ITALIC CAPITAL P
𝑄 U+1D444 MATHEMATICAL ITALIC CAPITAL Q
𝑥 𝑦 U+1D465 U+1D466 MATH ITALIC X Y
₁ ₂ U+2081 U+2082 SUBSCRIPT ONE TWO
² U+00B2 SUPERSCRIPT TWO

Matrices

3×3 Identity Matrix

.begin-math

    ⎡ 1  0  0 ⎤
𝑰 = ⎢ 0  1  0 ⎥
    ⎣ 0  0  1 ⎦

.end-math

𝑰 U+1D470 MATHEMATICAL ITALIC CAPITAL I
⎡ U+23A1 LEFT SQUARE BRACKET UPPER CORNER
⎢ U+23A2 LEFT SQUARE BRACKET EXTENSION
⎣ U+23A3 LEFT SQUARE BRACKET LOWER CORNER
⎤ U+23A4 RIGHT SQUARE BRACKET UPPER CORNER
⎥ U+23A5 RIGHT SQUARE BRACKET EXTENSION
⎦ U+23A6 RIGHT SQUARE BRACKET LOWER CORNER

2×2 Matrix

.begin-math

    ⎡ 𝑎  𝑏 ⎤
𝑴 = ⎢      ⎥
    ⎣ 𝑐  𝑑 ⎦

.end-math

𝑴 U+1D474 MATHEMATICAL ITALIC CAPITAL M
𝑎 U+1D44E MATHEMATICAL ITALIC SMALL A
𝑏 U+1D44F MATHEMATICAL ITALIC SMALL B
𝑐 U+1D450 MATHEMATICAL ITALIC SMALL C
𝑑 U+1D451 MATHEMATICAL ITALIC SMALL D
⎡ ⎢ ⎣ ⎤ ⎥ ⎦ bracket parts

Column Vector

.begin-math

    ⎡ 𝑥 ⎤
𝒗 = ⎢ 𝑦 ⎥
    ⎣ 𝑧 ⎦

.end-math

𝒗 U+1D499 MATHEMATICAL BOLD ITALIC SMALL V
𝑥 U+1D465 MATHEMATICAL ITALIC SMALL X
𝑦 U+1D466 MATHEMATICAL ITALIC SMALL Y
𝑧 U+1D467 MATHEMATICAL ITALIC SMALL Z
⎡ ⎢ ⎣ ⎤ ⎥ ⎦ bracket parts

Cases (Piecewise Functions)

Absolute Value

.begin-math

       ⎧  𝑥   if 𝑥 > 0
|𝑥| =  ⎨  0   if 𝑥 = 0
       ⎩ −𝑥   if 𝑥 < 0

.end-math

𝑥 U+1D465 MATHEMATICAL ITALIC SMALL X
⎧ U+23A7 LEFT CURLY BRACKET UPPER HOOK
⎨ U+23A8 LEFT CURLY BRACKET MIDDLE PIECE
⎩ U+23A9 LEFT CURLY BRACKET LOWER HOOK
− U+2212 MINUS SIGN

Sign Function

.begin-math

          ⎧ −1   if 𝑥 < 0
sign(𝑥) = ⎨  0   if 𝑥 = 0
          ⎩  1   if 𝑥 > 0

.end-math

𝑥 U+1D465 MATHEMATICAL ITALIC SMALL X
⎧ ⎨ ⎩ brace parts
− U+2212 MINUS SIGN

Summation and Products

Modest-sized operators, closer to Euler. Early printed math (1600s-1700s) used what the printer had in the type case. Giant stretchy ∑ is a 19th-century affectation — printers made them bigger because they could, not because it was clearer. Then textbooks copied textbooks. Traditional math typography treats ∑ like a diva. Compose treats it like any other character that showed up for work.

.begin-math

   𝑛
   ∑  𝑘 = 𝑛(𝑛+1)/2
  𝑘=1

.end-math

𝑛 U+1D45B MATHEMATICAL ITALIC SMALL N
∑ U+2211 N-ARY SUMMATION
𝑘 U+1D458 MATHEMATICAL ITALIC SMALL K


.begin-math

   𝑛
   ∏  𝑘 = 𝑛!
  𝑘=1

.end-math

𝑛 U+1D45B MATHEMATICAL ITALIC SMALL N
∏ U+220F N-ARY PRODUCT
𝑘 U+1D458 MATHEMATICAL ITALIC SMALL K

Integrals

.begin-math

 ∞
 ⌠
 ⎮ 𝑒⁻ˣ² d𝑥 = √π
 ⌡
 0

.end-math

∞ U+221E INFINITY
⌠ U+2320 TOP HALF INTEGRAL
⎮ U+23AE INTEGRAL EXTENSION
⌡ U+2321 BOTTOM HALF INTEGRAL
𝑒 U+1D452 MATHEMATICAL ITALIC SMALL E
√ U+221A SQUARE ROOT
π U+03C0 GREEK SMALL LETTER PI
.begin-math

 𝑏
 ⌠
 ⎮ 𝑓(𝑥) d𝑥 = 𝐹(𝑏) − 𝐹(𝑎)
 ⌡
 𝑎

.end-math

𝑎 𝑏 U+1D44E U+1D44F MATH ITALIC A B
𝑓 U+1D453 MATHEMATICAL ITALIC SMALL F
𝐹 U+1D439 MATHEMATICAL ITALIC CAPITAL F
⌠ ⎮ ⌡ integral parts
− U+2212 MINUS SIGN

Limits

.begin-math

       sin(𝑥)
 lim   ⎼⎼⎼⎼⎼⎼ = 1
 𝑥→0     𝑥

.end-math

𝑥 U+1D465 MATHEMATICAL ITALIC SMALL X
⎼ U+23BC HORIZONTAL SCAN LINE-7
→ U+2192 RIGHTWARDS ARROW

Symbol Reference

Operators

×
÷
−
±
·
U+00D7 MULTIPLICATION SIGN
U+00F7 DIVISION SIGN
U+2212 MINUS SIGN
U+00B1 PLUS-MINUS SIGN
U+00B7 MIDDLE DOT

Relations

=
≠
≤
≥
≈
U+003D EQUALS SIGN
U+2260 NOT EQUAL TO
U+2264 LESS-THAN OR EQUAL TO
U+2265 GREATER-THAN OR EQUAL TO
U+2248 ALMOST EQUAL TO

Greek Letters

α
β
γ
δ
θ
λ
π
σ
φ
ω
Σ
Π
U+03B1 GREEK SMALL LETTER ALPHA
U+03B2 GREEK SMALL LETTER BETA
U+03B3 GREEK SMALL LETTER GAMMA
U+03B4 GREEK SMALL LETTER DELTA
U+03B8 GREEK SMALL LETTER THETA
U+03BB GREEK SMALL LETTER LAMDA
U+03C0 GREEK SMALL LETTER PI
U+03C3 GREEK SMALL LETTER SIGMA
U+03C6 GREEK SMALL LETTER PHI
U+03C9 GREEK SMALL LETTER OMEGA
U+03A3 GREEK CAPITAL LETTER SIGMA
U+03A0 GREEK CAPITAL LETTER PI

Variables (Mathematical Italic)

𝑎
𝑏
𝑐
𝑑
𝑒
𝑓
𝑖
𝑗
𝑘
𝑚
𝑛
𝑥
𝑦
𝑧
U+1D44E MATHEMATICAL ITALIC SMALL A
U+1D44F MATHEMATICAL ITALIC SMALL B
U+1D450 MATHEMATICAL ITALIC SMALL C
U+1D451 MATHEMATICAL ITALIC SMALL D
U+1D452 MATHEMATICAL ITALIC SMALL E
U+1D453 MATHEMATICAL ITALIC SMALL F
U+1D456 MATHEMATICAL ITALIC SMALL I
U+1D457 MATHEMATICAL ITALIC SMALL J
U+1D458 MATHEMATICAL ITALIC SMALL K
U+1D45A MATHEMATICAL ITALIC SMALL M
U+1D45B MATHEMATICAL ITALIC SMALL N
U+1D465 MATHEMATICAL ITALIC SMALL X
U+1D466 MATHEMATICAL ITALIC SMALL Y
U+1D467 MATHEMATICAL ITALIC SMALL Z

Roots

√
∛
∜
U+221A SQUARE ROOT
U+221B CUBE ROOT
U+221C FOURTH ROOT

Other Symbols

∞
∂
∇
∴
∵
U+221E INFINITY
U+2202 PARTIAL DIFFERENTIAL
U+2207 NABLA
U+2234 THEREFORE
U+2235 BECAUSE

Superscripts

⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹
⁺ ⁻ ⁼ ⁽ ⁾
ⁿ ⁱ
U+2070–U+2079 SUPERSCRIPT DIGITS
U+207A–U+207E SUPERSCRIPT OPERATORS
U+207F U+2071 SUPERSCRIPT LETTERS

Subscripts

₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉
₊ ₋ ₌ ₍ ₎
ₐ ₑ ₕ ᵢ ⱼ ₖ ₗ ₘ ₙ ₒ ₚ ᵣ ₛ ₜ ᵤ ᵥ ₓ
U+2080–U+2089 SUBSCRIPT DIGITS
U+208A–U+208E SUBSCRIPT OPERATORS
U+2090–U+209C SUBSCRIPT LETTERS

Structure Characters

Horizontal Rules

⎼
⎽
U+23BC HORIZONTAL SCAN LINE-7 (fraction bar)
U+23BD HORIZONTAL SCAN LINE-9 (vinculum for √)

Compose-Terminal font shifts content down to clear the vinculum automatically.

Brackets

⎡
⎢
⎣
⎤
⎥
⎦
U+23A1 LEFT SQUARE BRACKET UPPER CORNER
U+23A2 LEFT SQUARE BRACKET EXTENSION
U+23A3 LEFT SQUARE BRACKET LOWER CORNER
U+23A4 RIGHT SQUARE BRACKET UPPER CORNER
U+23A5 RIGHT SQUARE BRACKET EXTENSION
U+23A6 RIGHT SQUARE BRACKET LOWER CORNER

Braces

⎧
⎨
⎩
⎫
⎬
⎭
U+23A7 LEFT CURLY BRACKET UPPER HOOK
U+23A8 LEFT CURLY BRACKET MIDDLE PIECE
U+23A9 LEFT CURLY BRACKET LOWER HOOK
U+23AB RIGHT CURLY BRACKET UPPER HOOK
U+23AC RIGHT CURLY BRACKET MIDDLE PIECE
U+23AD RIGHT CURLY BRACKET LOWER HOOK

Parentheses

⎛
⎜
⎝
⎞
⎟
⎠
U+239B LEFT PARENTHESIS UPPER HOOK
U+239C LEFT PARENTHESIS EXTENSION
U+239D LEFT PARENTHESIS LOWER HOOK
U+239E RIGHT PARENTHESIS UPPER HOOK
U+239F RIGHT PARENTHESIS EXTENSION
U+23A0 RIGHT PARENTHESIS LOWER HOOK

Integrals

⌠
⎮
⌡
U+2320 TOP HALF INTEGRAL
U+23AE INTEGRAL EXTENSION
U+2321 BOTTOM HALF INTEGRAL

Summation and Product

∑
∏
U+2211 N-ARY SUMMATION
U+220F N-ARY PRODUCT

Expression Evaluation

.set-variable 𝑟 5
Circumference: .calculate 2 × π × 𝑟
𝑟 U+1D45F MATHEMATICAL ITALIC SMALL R
× U+00D7 MULTIPLICATION SIGN
π U+03C0 GREEK SMALL LETTER PI

Built-in Constants

π = 3.14159265359
𝐞 = 2.71828182846
U+03C0 GREEK SMALL LETTER PI
U+1D41E MATHEMATICAL BOLD SMALL E

Functions

sin  cos  tan
asin acos atan
log  exp
abs  floor  ceil  round
min  max
sqrt
trigonometric
inverse trigonometric
natural log, exponential
rounding
minimum, maximum
square root

Design Philosophy

Compose renders math in monospace. Math is a formal technical language — like code. Code moved to monospace decades ago; math just did. For antique calligraphic rendering, embed LaTeX.