Section: New Results

Efficient normalization of ring/field expressions in Coq

The implementation of Coq's proof commands for manipulation of ring/field expressions has been improved in response to the demand for better efficiency that emerged in the formalization of Apéry's irrationality proof of $\zeta \left(3\right)$. The data structure used for the abstract syntax tree of ring/field expressions has been refined to enable a more efficient and more precise interpretation into concrete ring/field expressions. Moreover the collection of non-nullity conditions for denominators in a field expressions has been speeded up, making the type-checking time of a field normalization proof not be dominated by this collecting phase.