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