Crate bruner 

This script converts between our basis and Bruner’s basis. At the moment, most inputs are hardcoded, and this only works for the sphere.

The script performs the following procedure:

1. Compute our own resolution with the Milnor basis
2. Create Bruner’s resolution as a FiniteChainComplex object
3. Use a ResolutionHomomorphism to lift the identity to a chain map from Bruner’s resolution to our resolution. We should do it in this direction because we have stored the quasi-inverses for our resolution, but not Bruner’s.
4. Read off the transformation matrix we need

The main extra work to put in is step (2), where we have to parse Bruner’s differentials and interpret it as a chain complex. Bruner’s resolution can be found at https://archive.sigma2.no/pages/public/datasetDetail.jsf?id=10.11582/2022.00015 while the descirption of his save file is at https://arxiv.org/abs/2109.13117.