Compared to the past, RepLAB has a good implementation of exact arithmetic nowadays. Thus, compared with the previous attempt, we could use INTLAB to certify results in targeted places.
This project could proceed as follows.
Use interval arithmetic in targeted places
Add a strict mode to RepLAB. In that mode, all parent representations have an exact representation of their images available. One starts by computing and caching the corresponding interval matrices, which can then be used to certify the error bounds returned by the various equivariant projections.
Then, one can use the returned error bound to validate the decomposition into irreducible representations, and the various places when generic sampling is used in RepLAB to implement primitives.
Generalize the use of interval arithmetic
As a second step, one could have intval as an additional valid argument alongside exact and double / double_sparse . This would require a more clever caching strategy for the internal data of Rep / SubRep etc.
The idea is to add support for interval arithmetic in representations, so that computations can be verified.
Preliminary work was done in the past in the https://github.com/replab/replab/tree/topic/intlab branch.
Compared to the past, RepLAB has a good implementation of exact arithmetic nowadays. Thus, compared with the previous attempt, we could use INTLAB to certify results in targeted places.
This project could proceed as follows.
Add a strict mode to RepLAB. In that mode, all parent representations have an exact representation of their images available. One starts by computing and caching the corresponding interval matrices, which can then be used to certify the error bounds returned by the various equivariant projections.
Then, one can use the returned error bound to validate the decomposition into irreducible representations, and the various places when generic sampling is used in RepLAB to implement primitives.
As a second step, one could have
intvalas an additional valid argument alongsideexactanddouble/double_sparse. This would require a more clever caching strategy for the internal data ofRep/SubRepetc.