detexpX

detexpX is a software framework for computing and manipulating determinants of square matrices within symbolic and numerical linear algebra workflows. It focuses on providing efficient determinant-related operations for large or sparse matrices and emphasizes interoperability with computer algebra systems and numerical libraries.

The core method combines symbolic expansion by minors with structure-aware shortcuts and recurrence relations, supplemented by numerical stabilization techniques when exact results are expensive. The design supports parallel execution and can target multiple backends, including CPU and GPU, to optimize performance on large-scale problems.

Features include support for dense and sparse matrices, exact arithmetic via arbitrary-precision integers or rationals, and high-level interfaces for common languages. It also provides fallbacks to numerical det approximations with error bounds, as well as export to standard formats for downstream computation.

Applications span computational algebra, polynomial system solving, invariant computation in algebraic geometry, and teaching tools for linear algebra. The project emphasizes reproducibility and transparency, with publicly available documentation and example notebooks, aimed at researchers, educators, and students.

DetexpX originated as an open community project in the early 2020s to explore determinant-centric methods beyond traditional LU-based approaches. It collects contributions from developers and researchers and is described in public release notes and user guides.