linear-algebra-ai999x — offline, verified linear algebra solver with step-by-step answers

Install · Capability guide · Evaluation · AI999X on Hugging Face · Website · Support: Buy Me a Coffee

License: Apache-2.0 · Author: Ibnul Jaif Farabi (creator and engineer) · Organization: AI999X · Version 1.0.0

linear-algebra-ai999x is an offline, deterministic Python solver that answers linear algebra questions with verified results from 89 certified capabilities, gives 399 documented answers identically on Windows and Linux, and refuses rather than guesses when an answer cannot be verified.

linear-algebra-ai999x is a compact, deterministic linear algebra engine for Python. It reads a question in plain English (or a typed call), picks a certified linear algebra capability, computes the answer exactly, checks it, and returns the result with its steps, units, LaTeX and assumptions — or an honest refusal that says what is missing. It runs fully offline on any CPU, needs no GPU, no API key and no internet, and is built to give zero wrong answers: when it is not sure, it refuses instead of guessing.

Highlights

• Verified, not generated. Every answer is computed by a certified linear algebra capability and checked (substituted back, dimension-checked or compared with an independent computation) before it is returned.
• Zero wrong answers by design. Seven explicit outcomes — SOLVED, NEEDS_INPUT, AMBIGUOUS, INVALID_INPUT, OUT_OF_SCOPE, UNRECOGNIZED_FORMAT, INTERNAL_ERROR — never a silent guess. Every one of its 399 documented answers is reproduced exactly on every tested platform.
• Plain-English questions and a guaranteed typed interface. ask() reads documented question forms; solve(capability_id, **inputs) always solves a supported task with valid inputs.
• Explains itself. Steps, formulas in LaTeX, units, assumptions and the model used, ready for notebooks, tutoring apps and homework checkers.
• Small and portable. Pure Python (sympy, mpmath); identical answers on Windows and Linux (Python 3.10, 3.11, 3.12, 3.13, 3.14).
• Coverage: vectors, matrices, determinants, linear systems, eigenvalues, decompositions, least squares, sparse matrices and numerical methods (root finding, interpolation, quadrature).

Model overview

Quickstart

pip install linear-algebra-ai999x

import linear_algebra_ai999x as linear_algebra

linear_algebra.ask("Find the determinant of [[2, 0, 1], [1, 3, 2], [1, 1, 2]].").show()
# -> SOLVED — det = 6  (determinant_3x3)
linear_algebra.ask("Solve the system 2x + 3y = 7, x - y = 1.").show()
# -> SOLVED — solution = [2.0, 1.0], det = -5  (solve_2x2_system)
linear_algebra.ask("Find the eigenvalues of [[2, 1], [1, 2]].").show()
# -> SOLVED — lambda1 = 1, lambda2 = 3  (eigenvalues_2x2)
linear_algebra.ask("Use Newton's method to find a root of x^3 - 2x - 5 starting from x0 = 2.").show()
# -> SOLVED — root = 2.09455  (newton_root)
linear_algebra.solve("qr_decomposition", A="[[3, 1], [4, 2]]").show()
# -> SOLVED — Q = [[0.5999999999999999, -0.7999999999999999], [0.7999999999999999, 0.6000000000000001]], R = [[5.0, 2.1999999999999997], [-0.0, 0.40000000000000013]]  (qr_decomposition)
linear_algebra.ask("Who created you?").message
# -> linear-algebra-ai999x was created and engineered by Ibnul Jaif Farabi at AI999X.

Command line: linear-algebra-ai999x "<question>", linear-algebra-ai999x --capabilities. The outputs above were produced by running this exact code on linear-algebra-ai999x 1.0.0.

Find the right capability, and draw it

linear_algebra.search() finds which certified capability a question is about — across every AI999X model, so a question for another model points you to it. It runs ai999x-encoder, AI999X's own capability encoder (4.7M parameters, a 4.9 MB ONNX model, offline; the root model.safetensors of this repository): pip install "linear-algebra-ai999x[search]". ask(question, suggest=True) adds the same pointers to a question it does not answer; an answer itself never changes.

import linear_algebra_ai999x as linear_algebra

linear_algebra.search("Solve x^2 - 5x + 6 = 0", k=2)
# -> Roots of a quadratic equation (algebra-ai999x, 0.67); Solution of two linear equations in two unknowns (algebra-ai999x, 0.57)

How every answer is verified

1. Reading — the question is turned into typed quantities (value, unit, kind, role) and one asked quantity; every stated number must be used or the question is refused.
2. Planning — only certified capabilities may answer; a capability applies only under the conditions the wording states (for example a pendulum, a liquid at rest, boiling).
3. Computing — exact symbolic or high-precision numeric evaluation.
4. Checking — dimensions, substitution back into the defining equation, and agreement between independent readings; any disagreement becomes a refusal, never a number.

Capabilities are certified before they ship: each must reproduce hand-worked reference cases, reject a deliberately wrong variant (a control), and leave every benchmark answer unchanged.

Capabilities

89 certified procedures. A few of them:

• Procedures: 1-D Poisson equation by finite differences; 2-D Poisson equation on a grid (5-point stencil); Adjugate (classical adjoint) of a matrix; Angle between two vectors; Area of the parallelogram (and triangle) spanned by two vectors; Best rank-k approximation (Eckart-Young); Characteristic polynomial of a matrix; Cholesky decomposition; Clamped cubic spline interpolation; Coefficients of the interpolating polynomial; Column space of a matrix; Composite midpoint rule for a polynomial; Compressed sparse column (CSC) form of a matrix; Compressed sparse row (CSR) form of a matrix; Condition number of a matrix; Conjugate gradient method for Ax = b; Coordinates of a vector in a basis; Cross product of two 3-D vectors; Dense matrix from CSR arrays; Derivative of equally spaced data (finite differences); Determinant of a 2 x 2 matrix; Determinant of a 3 x 3 matrix; Determinant of an n x n matrix; Difference of two matrices …

linear_algebra_ai999x.templates() lists every question form ask() reads; the capability guide (PDF, every example executed) is included in this repository.

Out of scope

• Open-ended explanation, essay writing or tutoring dialogue: it is a solver, not a chatbot.
• Questions outside its certified linear algebra capabilities, and any question whose stated numbers it cannot all use — it refuses with the reason instead.
• High-stakes engineering, medical or legal decisions without independent review.

Limitations

• It answers what its certified capabilities cover (vectors, matrices, determinants, linear systems, eigenvalues, decompositions, least squares, sparse matrices and numerical methods (root finding, interpolation, quadrature)); anything else is refused with a reason.
• ask() reads documented question forms and common phrasings; unusual wording may be refused — use solve() for guaranteed results.
• Results are as correct as the certified relations and their stated conditions; a certified relation is a checked model, not a claim about every physical situation.

Citation

@software{linear_algebra_ai999x_1_0_0,
  title  = {linear-algebra-ai999x: an offline, verified linear algebra solver},
  author = {Farabi, Ibnul Jaif}, organization = {AI999X},
  year   = {2026}, version = {1.0.0},
  url    = {https://huggingface.co/AI999X/linear-algebra-ai999x}
}

Contact

Questions, bug reports and requests: open a discussion on https://huggingface.co/AI999X/linear-algebra-ai999x/discussions or visit https://ai999x.com.

Support the project

linear-algebra-ai999x is free and open source. If it helps you, you can support further development on Buy Me a Coffee.

Created and engineered by Ibnul Jaif Farabi · AI999X · ai999x.com