Goal -- Design a specialized p-adic extension type for cyclotomic extensions of Qp and Zp. Design element classes for unramified extensions that take advantage of a Gauss normal basis for faster arithmetic.
Type -- speed improvements, coherence with number fields
Priority -- Medium
Difficulty -- Medium-Hard
Prerequisites -- Cyclotomic fields in general will need to wait on polynomial factoring
Background -- Look at Lercier's talk from Counting Points: Theory, Algorithms and Practice
Contributors -- David Roe, David Lubicz
Progress - not started
Related Tickets --
- Implement Gauss normal basis for finite fields.
- Implement Gauss normal basis for unramified extensions of Zp and Qp.
- Implement elliptic normal basis for finite fields.
- Implement elliptic normal basis for unramified extensions of Zp and Qp.
Implement a special parent for cyclotomic extensions. For totally ramified and unramified cyclotomic extensions this can be done now; in general it will need to wait on polynomial factoring.