Safe Haskell | None |
---|---|
Language | Haskell2010 |
\( \def\lcm{\text{lcm}} \)
Functions from one cyclotomic ring to another that are linear over a common subring.
- data Linear t z e r s
- type ExtendLinIdx e r s e' r' s' = (Fact r, e ~ FGCD r e', r' ~ FLCM r e', e' `Divides` s', s `Divides` s')
- linearDec :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => [Cyc t s z] -> Linear t z e r s
- evalLin :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => Linear t z e r s -> Cyc t r z -> Cyc t s z
- extendLin :: ExtendLinIdx e r s e' r' s' => Linear t z e r s -> Linear t z e' r' s'
Documentation
data Linear t z e r s Source #
An \(E\)-linear function from \(R\) to \(S\).
NFData (Cyc t s z) => NFData (Linear t z e r s) Source # | |
Additive (Cyc t s z) => C (Linear t z e r s) Source # | |
(CElt t zp, CElt t z, (~) * z (LiftOf zp), Lift zp z, Fact s) => Lift' (Linear t zp e r s) Source # | lifts with respect to powerful basis, for best geometry |
(Reduce z zq, Fact s, CElt t z, CElt t zq) => Reduce (Linear t z e r s) (Linear t zq e r s) Source # | |
type LiftOf (Linear t zp e r s) Source # | |
type ExtendLinIdx e r s e' r' s' = (Fact r, e ~ FGCD r e', r' ~ FLCM r e', e' `Divides` s', s `Divides` s') Source #
A convenient constraint synonym for extending a linear function to larger rings.
linearDec :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => [Cyc t s z] -> Linear t z e r s Source #
Construct an \(E\)-linear function given a list of its output values (in \(S\)) on the relative decoding basis of \(R/E\). The number of elements in the list must not exceed the size of the basis.
evalLin :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => Linear t z e r s -> Cyc t r z -> Cyc t s z Source #
Evaluates the given linear function on the input.
extendLin :: ExtendLinIdx e r s e' r' s' => Linear t z e r s -> Linear t z e' r' s' Source #
Extend an \(E\)-linear function \(R\to S\) to an \(E'\)-linear function \(R'\to S'\). (Mathematically, such extension only requires \(\lcm(r,e') | r'\) (not equality), but this generality would significantly complicate the implementation, and for our purposes there's no reason to use any larger \(r'\).)