{"action":"created","issue":{"url":"https://api.github.com/repos/wbhart/flint2/issues/366","repository_url":"https://api.github.com/repos/wbhart/flint2","labels_url":"https://api.github.com/repos/wbhart/flint2/issues/366/labels{/name}","comments_url":"https://api.github.com/repos/wbhart/flint2/issues/366/comments","events_url":"https://api.github.com/repos/wbhart/flint2/issues/366/events","html_url":"https://github.com/wbhart/flint2/issues/366","id":249900642,"number":366,"title":"Add support for finite field isomorphisms and embeddings","user":{"login":"defeo","id":1315842,"avatar_url":"https://avatars2.githubusercontent.com/u/1315842?v=4","gravatar_id":"","url":"https://api.github.com/users/defeo","html_url":"https://github.com/defeo","followers_url":"https://api.github.com/users/defeo/followers","following_url":"https://api.github.com/users/defeo/following{/other_user}","gists_url":"https://api.github.com/users/defeo/gists{/gist_id}","starred_url":"https://api.github.com/users/defeo/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/defeo/subscriptions","organizations_url":"https://api.github.com/users/defeo/orgs","repos_url":"https://api.github.com/users/defeo/repos","events_url":"https://api.github.com/users/defeo/events{/privacy}","received_events_url":"https://api.github.com/users/defeo/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":0,"created_at":"2017-08-13T21:37:33Z","updated_at":"2017-08-14T15:35:13Z","closed_at":null,"body":"As discussed at the Hecke/Nemo/Flint workshop, there is a plan to add support for lattices of compatibly embedded finite fields to Nemo/Flint. This issue tracks progress on the subject.\r\n\r\nOn the Flint side, we want to add the basic algorithms for computing and evaluating embeddings of finite fields. See https://arxiv.org/abs/1705.01221 for terminology and theoretical details. The higher level mechanics for compatible lattices will be coded in Nemo, as outlined in ...\r\n\r\nWe have an experimental branch, tracked in #351, where development is happening. We want to complete the following steps before pushing to trunk:\r\n\r\n- [x] Write naive algorithms for computing embeddings;\r\n- [x] Write algorithms to compute embedding matrices;\r\n- [ ] Add a decent implementation of minimal polynomial computation for `fq_*` types;\r\n- [ ] Write Allombert's algorithm as modified in https://arxiv.org/abs/1705.01221 (code can be ported from https://github.com/defeo/ffisom);\r\n- [ ] Write helper functions to facilitate evaluating embeddings without computing matrices;\r\n- [ ] Determine thresholds;\r\n- [ ] Write docs.\r\n\r\nOther useful algorithms that we could eventually add after the first part is merged:\r\n\r\n- [ ] Other embedding algorithms, in particular Rains';\r\n- [ ] Constructions for special families of finite fields (Lenstra-De Smit, De Feo-Doliskani-Schost, ...)."},"comment":{"url":"https://api.github.com/repos/wbhart/flint2/issues/comments/322224149","html_url":"https://github.com/wbhart/flint2/issues/366#issuecomment-322224149","issue_url":"https://api.github.com/repos/wbhart/flint2/issues/366","id":322224149,"user":{"login":"wbhart","id":242598,"avatar_url":"https://avatars1.githubusercontent.com/u/242598?v=4","gravatar_id":"","url":"https://api.github.com/users/wbhart","html_url":"https://github.com/wbhart","followers_url":"https://api.github.com/users/wbhart/followers","following_url":"https://api.github.com/users/wbhart/following{/other_user}","gists_url":"https://api.github.com/users/wbhart/gists{/gist_id}","starred_url":"https://api.github.com/users/wbhart/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/wbhart/subscriptions","organizations_url":"https://api.github.com/users/wbhart/orgs","repos_url":"https://api.github.com/users/wbhart/repos","events_url":"https://api.github.com/users/wbhart/events{/privacy}","received_events_url":"https://api.github.com/users/wbhart/received_events","type":"User","site_admin":false},"created_at":"2017-08-14T15:35:13Z","updated_at":"2017-08-14T15:35:13Z","body":"Thanks for setting this up. I am away for about a week, so it will be a while before I get to look at all this. But I'm looking forward to ticking these off."}}
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