| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Noether.Algebra.Vector.Tags
Documentation
data VectorLift Source #
data UVectorLift Source #
Instances
| (Unbox b, KnownNat n, ActsK k lr op a b s) => ActsK k lr op a (UVector n b) (ActsTagged UVectorLift s) Source # | Actions of a on b extend to actions of a on 'UVector n b'. |
| (Unbox v, KnownNat n, NeutralK k op v s) => NeutralK k op (UVector n v) (NeutralTagged UVectorLift s) Source # | Neutral elements for addition and multiplication. |
| (Unbox v, MagmaK k op v s) => MagmaK k op (UVector n v) (MagmaTagged UVectorLift s) Source # | Lifting addition and multiplication coordinatewise (Hadamard?) |
| (Unbox v, KnownNat n, CancellativeK k op v s) => CancellativeK k op (UVector n v) (CancellativeTagged UVectorLift s) Source # | Pointwise negation and inversion. Note that v^n has (a lot of) nontrivial zerodivisors even if v does not. The zerodivisors are all elements with a zero(divisor) in some coordinate, e.g. (1,0) and (0,1) are zerodivisors in R^2. (This corresponds to the idea that the Spec of a product ring is disconnected!) |
data BVectorLift Source #
Instances
| ActsK k1 lr op a b s => ActsK k1 lr op a (BVector k n b) (ActsTagged BVectorLift s) Source # | Actions of a on b extend to actions of a on 'BVector n b'. |
| (KnownNat n, NeutralK k op v s) => NeutralK k op (BVector Nat n v) (NeutralTagged BVectorLift s) Source # | Neutral elements for addition and multiplication. |
| MagmaK k1 op v s => MagmaK k1 op (BVector k n v) (MagmaTagged BVectorLift s) Source # | Lifting addition and multiplication coordinatewise (Hadamard?) |
| CancellativeK k1 op v s => CancellativeK k1 op (BVector k n v) (CancellativeTagged BVectorLift s) Source # | Pointwise negation and inversion. Note that v^n has (a lot of) nontrivial zerodivisors even if v does not. The zerodivisors are all elements with a zero(divisor) in some coordinate, e.g. (1,0) and (0,1) are zerodivisors in R^2. (This corresponds to the idea that the Spec of a product ring is disconnected!) |
data SVectorLift Source #
data MVectorLift Source #
data SMVectorLift Source #
data UMVectorLift Source #