This is a lightweight tool for matrices, linear systems and expressions

• Interactive REPL with variable bindings that persist across inputs
• Linear system solver using Gaussian elimination with back-substitution
• Parametric solutions for underdetermined systems — free variables are introduced and propagated symbolically, so the result is a vector of linear expressions rather than a point
• Matrix operations — multiplication and determinant calculation

• help - display available commands
• exit - exit the application
• solve(matrix) – solve a linear system with linear expressions
• det(matrix) – calculate the determinant
• Variable assignment: A = ...
• Expression evaluation: C = A + B * (A+B)/ 3

The CLI processes every input line through a small compiler-style pipeline:

Input ──► Lexer ──► Parser ──► AST ──► Evaluator / Solver ──► Output

• Lexer – tokenizes the input stream (numbers, identifiers, operators, brackets, matrix literals).
• Parser – a handwritten recursive-descent parser that respects operator precedence and associativity, and builds a typed Abstract Syntax Tree.
• AST – node types for scalars, vectors, matrices, variables, binary/unary operations and built-in function calls (solve, det).
• Evaluator – walks the AST, resolves variable bindings from the environment, and dispatches operations based on operand types (scalar × scalar, scalar × matrix, matrix × matrix, …).
• Gauss Solver – performs Gaussian elimination with back-substitution on the augmented matrix. When the system is underdetermined, free variables are introduced and the result is returned as a vector of linear expressions rather than a single numeric solution.

• Language: Java
• Parser strategy: handwritten recursive descent (no parser generator / no external library)
• Symbolic layer: a minimal linear-expression type supports addition, subtraction and scalar multiplication, which is what the Gauss solver needs to express parametric solutions
• Tests: a JUnit test suite covers the lexer, parser, evaluator and solver, including edge cases such as singular matrices, underdetermined systems and nested expressions

Start the CLI application and enter expressions, variables or commands directly.

Type help to see all available commands. Type exit to quit the application.

> A = (1+2)*3
9.0
> B = 15
15.0
> C = A/B
0.6

> solve([[3,11,10,9000], [6,2,2,5000], [150,220,120,194000]])

[600.0, 200.0, 500.0]

> A = [[1, 1, 0, 0, 0, 0, 0, 1],
       [0, 1, 1, 0, 0, 0, 0, 2],
       [0, 0, 1, 1, 0, 0, 0, 3],
       [0, 0, 0, 1, 1, 1, 1, 4]]
       
> solve(A)

[1.0*e + 1.0*f + 1.0*g - 2.0,
 -1.0*e - 1.0*f - 1.0*g + 3.0,
 1.0*e + 1.0*f + 1.0*g - 1.0,
 -1.0*e - 1.0*f - 1.0*g + 4.0,
 1.0*e, 1.0*f, 1.0*g]

> A = [[1,2],[3,4]]
[
  [1.0, 2.0],
  [3.0, 4.0]
]
> B = [[1,2],[3,4]]
[
  [1.0, 2.0],
  [3.0, 4.0]
]
> det(A*B)
4.0

• Scalar expressions in $\mathbb{R}$
• Vectors in $\mathbb{R}^n$
• Matrices in $\mathbb{R}^{n \times m}$
• No symbolic simplification beyond linear expressions
• Expressions evaluation with variables and constants either in $\mathbb{R}$ or $\mathbb{R}^{n \times m}$

Are you curious about the app?

Check out the release on GitHub 🎉