nLuaCAS

A symbolic math engine for TI-Nspire CX (non-CAS models), written in Lua.

This runs entirely in native Lua without requiring Ndless or OS patches. It parses expressions into ASTs, applies symbolic transformations, and outputs readable results.

Educational tool. Check your institution's assessment policies before use.

Installation

1. Download nLuaCAS.tns
2. Transfer to calculator using TI-Nspire Link or nLink
3. Open from Documents screen
4. Use TAB to navigate between Main, History, Help tabs

Usage Examples

| Operation | Input | Output | |-----------|-------|--------| | Derivative | d/dx(x^2) | 2x | | Integration | int(x^2) | x^3/3 | | Definite integral | int(x^2, 0, 1) | 1/3 | | Equation solving | solve(x^2 - 4 = 0) | x = ±2 | | Simplification | simplify(x + x) | 2x | | Function definition | let f(x) = x^2 + 3 | - | | Function evaluation | f(2) | 7 |

New features:

• series() for Taylor/Maclaurin expansions
• Enhanced int() with integration by parts
• Step-by-step explanations (look for "Explain" button)

Features

Arithmetic & Algebra

• Basic operations: 2 + 3 → 5, x * x^2 → x^3
• Power simplification: (x^2)^3 → x^6
• Binomial expansion: (a + b)^n (up to n=4)

Calculus

• Derivatives of polynomials, trig, exponential, log functions
• Symbolic integration (basic cases)
• Chain rule support (partial)

Trigonometry

• Identity simplification: sin^2(x) + cos^2(x) → 1
• Sign properties: sin(-x) → -sin(x)

Logarithms

• Product rule: log(a*b) → log(a) + log(b)
• Power rule: log(a^b) → b*log(a)

Rational expressions

• Cancellation: x/x → 1
• Cross-cancellation: (a*b)/(b*c) → a/c

Factorials

• Exact values for integers
• Symbolic simplification: x!/(x-1)! → x
• Gamma function for non-integers

Compatibility

• ✅ TI-Nspire CX II (OS 6.2) - tested
• ✅ TI-Nspire CX (non-CAS) - supported
• ❌ Monochrome models - unsupported
• ❌ Ndless - not required

Build System

TI-Nspire Lua executes single .tns files only. The build script merges all source files:

./build.sh

This creates build.lua which you can either:

• Copy into TI Lua editor, or
• Compile to .tns using Luna

Architecture

Parser - Converts input strings to AST representation:

{type="add", args={
  {type="pow", base={type="variable", name="x"}, exp={type="number", value=2}},
  {type="mul", args={{type="number", value=2}, {type="variable", name="x"}}}
}}

Simplifier - Multi-pass rule engine operating on ASTs. Handles canonicalization, algebraic reductions, and identity applications.

Differentiator - Takes AST and variable name, produces derivative AST. Supports polynomial, trigonometric, exponential, and logarithmic functions.

Pretty Printer - Renders AST back to readable math notation.

Data flow:

String → Parser → AST → Simplifier → AST → Pretty Printer → String

What's Missing

• Integration still unreliable
• Advanced chain rule support
• Partial derivatives
• More sophisticated equation solving

Credits

Engine and AST system by d-lta. UI framework adapted from SuperSpire (S²) by Xavier Andréani. Build system concept from Adriweb. Menu concepts from khicas project.

Licensed under MIT. No TI proprietary code used.