# Gardner–Salinas braille codes

The Gardner–Salinas braille codes are a proposed method of encoding mathematical and scientific notation linearly using braille cells for tactile reading by the visually impaired. The most common form of Gardner–Salinas braille is the 8-cell variety, commonly called GS8. There is also a corresponding 6-cell form called GS6.
The codes were developed as a replacement for Nemeth Braille by John A. Gardner, a physicist at Oregon State University, and Norberto Salinas, an Argentinian mathematician. However, 15 years later Nemeth code was still the standard, with no further change as of 2024.
The Gardner–Salinas braille codes are an example of a compact human-readable markup language. The syntax is based on the LaTeX system for scientific typesetting.

## Table of Gardner–Salinas 8-dot (GS8) braille

The set of lower-case letters, the period, comma, semicolon, colon, exclamation mark, apostrophe, and opening and closing double quotes are the same as in Grade-2 English Braille.

### Digits

| Symbol | 0? | 0? | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Braille | | | | | | | | | | | |
Apart from 0, this is the same as the Antoine notation used in French and Luxembourgish Braille. Sources disagree on 0. Both claimed forms are presented above. The second is the ISO form. Note however that ISO is concerned only with a one-to-one assignment between 8-dot braille and ASCII, and so has no particular connection to Gardner–Salinas braille.

### Upper-case letters

GS8 upper-case letters are indicated by the same cell as standard English braille (and GS8) lower-case letters, with dot #7 added.
| Symbol | A | B | C | D | E | F | G | H | I | J | K | L | M |
| Braille | | | | | | | | | | | | | |
| Symbol | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
| Braille | | | | | | | | | | | | | |
Compare Luxembourgish Braille.

### Greek letters

Dot 8 is added to the letter forms of International Greek Braille to derive Greek letters:
| Symbol | α | β | γ | δ | ε | ζ | η | θ | ι | κ | λ | μ |
| Braille | | | | | | | | | | | | |
| Symbol | ν | ξ | ο | π | ρ | σ | τ | υ | φ | χ | ψ | ω |
| Braille | | | | | | | | | | | | |
| Symbol | Γ | Δ | Θ | Λ | Ξ | Π | Σ | Υ | Φ | Ψ | Ω |
| Braille | | | | | | | | | | | |

### Characters differing from English Braille

| Symbol | Parentheses | Parentheses | Brackets | Brackets | single quote | single quote | |
| Symbol | open | close | open | close | open | close | ? |
| Braille | | | | | | | |
The single quotation marks are the ASCII back tick ` and apostrophe '.

### ASCII symbols and mathematical operators

| Symbol | " | $ | & | @ | \ | ^ | _ | ` | { | } | ~ |
| Braille | | | | | | | | | | | |
| Symbol | # | % | * | + | / | < | = | > | × | · | ÷ |
| Braille | | | | | | | | | | | |

### Text symbols

| Symbol | • | © | † | ‡ | £ |
| Braille | | | | | |

### Math and science symbols

| Symbol | ≈ | ≅ | ≡ | ∝ | |x| (abs. value) | ∞ | ∫ | line ∫ | closed ∫ |
| Braille | | | | | ... | | | | |
| Symbol | 〈 | 〉 | ∇ | ∂ | ... | → | ← | ○ | ℵ | ∈ | ⇌ |
| Braille | | | | | | | | | | | |

### Markup

| Symbol | Superscript | Subscript | Left-superscript | Left-subscript | Begin fraction | Denominator | End fraction | Over * |
| Braille | | | | | | | | |
* Encodes the fraction-slash for the single adjacent digits/letters as numerator and denominator.
| Symbol | √ | complex radicand * | complex radicand * | displayed equation ** | displayed equation ** | math expressions ** | math expressions ** | hyperlink ** | hyperlink ** |
| Symbol | √ | Open | Close | Open | Close | Open | Close | Open | Close |
| Braille | | | | | | | | | |
* Used for any > 1 digit radicand.
** Used for markup to represent inkprint text.
| Symbol | Array | Array | Array | Array | | | |
| Symbol | Begin | End | End element | End line | vert. stack | horiz. combo | superposition |
| Braille | | | | | | | |
| Symbol | Misc. Symbol * | Misc. Symbol * | | | Modifiers | Modifiers | Modifiers | Modifiers |
| Symbol | Begin | End | Quantity | Markup indicator | Inverted | Stroke/Not | Variant | Large |
| Braille | | | | | | | | |

### Typeface indicators

| Symbol | Script | Bold | Italic | Underline | Definable font 1 | Fractur | Roman | Underline |
| Braille | | | | | | | | |
The difference between the two underline markers is not explained.

### Shape symbols

| Symbol | ⊥ | ∥ | ∠ | Open Square | ⊿ |
| Braille | | | | | |

### Set theory

| Symbol | ∪ | ∩ | ⊂ | ⊃ |
| Braille | | | | |