Towards abstract and executable multivariate polynomials in Isabelle

ABSTRACT. This work in progress report envisions a library for multivariate polynomials developed jointly by experts from computer theorem proving (CTP) and computer algebra (CA). The urgency of verified algorithms has been recognised in the field of CA, but the cultural gap to CTP is considerable; CA users expect high usability and efficiency. This work collects the needs of CA experts and reports on the design of a proof-of-concept prototype in Isabelle/HOL. The CA requirements have not yet been fully settled, and its development is still at an early stage. The authors hope for lively discussions at the Isabelle Workshop.