Struct Sl 

pub struct Sl<V: Tensor<F: CField>, const N: usize>(/* private fields */);

The special linear group SL(V) — automorphisms of V with determinant one.

The determinant-one invariant is maintained by construction: there is no raw constructor. Values arise only from the group operations (the identity, products, inverses) and from exp of the traceless SlAlgebra — all of which preserve det = 1 (det(AB) = det(A)det(B), det(exp X) = e^{tr X} = e^0). Since the Lie algebra has no invalid representations either, every reachable Sl value is genuinely in the group; membership is a theorem about reachability, not a runtime check.

Implementations

impl<V: Tensor<F: CField>, const N: usize> Sl<V, N>

pub fn trace(&self) -> V::F

Returns the trace of the represented special-linear transformation.

Trait Implementations

impl<V: Clone + Tensor<F: CField>, const N: usize> Clone for Sl<V, N>

fn clone(&self) -> Sl<V, N>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<V: Copy + Tensor<F: CField>, const N: usize> Copy for Sl<V, N>

impl<V: Debug + Tensor<F: CField>, const N: usize> Debug for Sl<V, N>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<V: Tensor<F: CField>, const N: usize> Group for Sl<V, N>

fn identity() -> Self

fn compose(&self, other: &Self) -> Self

fn inverse(&self) -> Self

fn check_left_identity(&self) -> bool

where Self: PartialEq,

fn check_right_identity(&self) -> bool

where Self: PartialEq,

fn check_associativity(a: Self, b: Self, c: Self) -> bool

where Self: PartialEq,

fn check_left_inverse(&self) -> bool

where Self: PartialEq + Debug,

fn check_right_inverse(&self) -> bool

where Self: PartialEq,

impl<V: Tensor<F: CField>, const N: usize> Inv for Sl<V, N>

type Output = Sl<V, N>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<F: CField<Characteristic = NatZero>> LieGroup<SlAlgebra<F, 2, 3>> for Sl<Coords<F, 2>, 2>

where Matrix<Coords<F, 2>, 2>: MatrixExponential,

fn identity_exp(v: SlAlgebra<F, 2, 3>) -> Self

fn identity_log(p: &Self) -> Option<SlAlgebra<F, 2, 3>>

impl<V: Tensor<F: CField>, const N: usize> Mul for Sl<V, N>

type Output = Sl<V, N>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<V: Tensor<F: CField>, const N: usize> One for Sl<V, N>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<V: Tensor<F: CField>, const N: usize> PartialEq for Sl<V, N>

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl<R: Real> Quotient<Sl<Coords<Complex<R>, 2>, 2>, RootOfUnity<Complex<R>, 2>, SlAlgebra<Complex<R>, 2, 3>> for Lorentz<R>

fn new(g: Sl2c<R>) -> Self

Maps g to the Quotient value representing its coset gH.

fn lift(&self) -> Sl2c<R>

Recovers a representative of self’s coset, satisfying new(self.lift()) == self.

fn embed(h: RootOfUnity<Complex<R>, 2>) -> Sl2c<R>

the subgroup inclusion H ↪ G

fn quotient_identity() -> Self

fn quotient_compose(&self, other: &Self) -> Self

fn quotient_inverse(&self) -> Self

fn quotient_identity_exp(v: V) -> Self

fn quotient_identity_log(p: &Self) -> Option<V>

fn check_new_respects_coset(g: G, h: H) -> bool

where Self: PartialEq,

The sole independent Quotient axiom: new must not distinguish elements of the same coset. Everything else (group structure, differential structure) follows from this plus the inherited LieGroup axioms.