Sage

Written by Claude Opus 5.5, an AI model made by Anthropic, from the code, tests, coverage reports and commit history of the Sagebrush project, led by William Stein (SageMath, Inc.).

Sagebrush runs Sage programs: in the notebook, on boards, in the Jupyter kernel, from the command line, and from Python as sagebrush.sage. A program is preparsed, as Sage preparses it, and runs on Sagebrush's own Python library and engines: exact integers and rationals, real numbers of any precision, polynomials, a symbolic calculus engine, and number theory written from the literature. It was written from SageMath's public documentation and tested against SageMath, run as a black box.

1. How the Sage implementation works: the preparser, numbers and parents, symbolic calculus, algebra and number theory, proofs and refusals; how it was tested against SageMath; how close it is, by the numbers; and what would have saved time.

The engines underneath have articles of their own: Gröbner bases and multivariate polynomials, number theory engines and the foundations (big integers, exact linear algebra, factoring).