Goal -- Write new classes of p-adic elements, analogous to IntegerMod_int and IntegerMod_int64 for the case that self.unit or self.value fits into machine precision.
Type -- speed improvements
Priority -- Medium-Low
Difficulty -- Easy
Prerequisites -- None
Background -- understand the inheritance structure for p-adic base rings, take a look at sage.rings.finite_rings.integer_mod
Contributors -- David Roe
Progress - not started
Related Tickets --
Discussion
This will be useful in the following cases:
p |
max precision on 32-bit |
max precision on 64-bit |
2 |
15 |
30 |
3 |
9 |
19 |
5 |
6 |
13 |
7 |
5 |
11 |
11,13 |
4 |
8 |
17,19 |
3 |
7 |
23,29,31 |
3 |
6 |
37-73 |
2 |
5 |
79-211 |
2 |
4 |
223-1289 |
1 |
3 |
1291-46337 |
1 |
2 |
Tasks
Using sage/rings/finite_rings/integer_mod.pyx and sage/rings/padics/padic_(capped_relative_element.pyx AND capped_absolute_element.pyx AND fixed_modulus_element.pyx) as a model, implement Zp and Qp using machine arithmetic.