# simplified mathematics notation
this is not a formal interchange language.

generation directive:
- optimize for sustained use of the simplified mathematics notation
- avoid latex-style notation unless explicitly requested or clearly unavoidable for clarity.

intent:
- express mathematical structure using ascii
- preserve conventional mathematical meaning
- optimize for human expert readability, not mechanical parsing

character set:
- use only lowercase ascii characters
- punctuation is limited to standard ascii punctuation

identifiers:
- identifiers are either:
  - single letters, or
  - underscore_separated english words
- prefer word identifiers over single letters

symbol introduction:
- declaring an identifier introduces a symbol, not its full meaning
- meaning may be refined incrementally using english prose

declarations:
- every single-letter identifier must be introduced before first use
- word identifiers do not require declaration
- standard mathematical constants (pi, e, i) are implicitly available and must not be redeclared
- declarations apply within the nearest section; if ambiguous, within the current message

roles (informal conventions, non-binding):
- indices are typically single letters (e.g. n, m, k, c)
- sets are typically word identifiers ending in _set
- operators may be symbolic or english words
- function application uses parentheses: f(x), f(x, y)
* brackets are reserved for indexing: x[t], t[r, u, v, k]

notation:
- equations should preferably appear inside markdown inline code or fenced code blocks
- infix operators should be surrounded by exactly one space on each side
- open set of infix operators
  - ** denotes exponentiation
- standard mathematical precedence is assumed unless parentheses are used

semantics:
- all standard mathematical rules and conventions apply unchanged unless explicitly overridden
- interpretation is human and context-dependent

fallback:
- when notation becomes unclear or overly verbose, use english explanation
- latex-style ascii notation is acceptable when it provides stronger or more widely recognized meaning

style guidelines:
- avoid unnecessary redeclaration of symbols
- refine meaning close to first use
- prioritize clarity and continuity over strict uniformity