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Lorentz

diffable::spacetime

Struct Lorentz 

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pub struct Lorentz<R: Real>(/* private fields */);
Expand description

The restricted lorentz group

Trait Implementationsยง

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impl<R: Clone + Real> Clone for Lorentz<R>

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fn clone(&self) -> Lorentz<R>

Returns a duplicate of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<R: Copy + Real> Copy for Lorentz<R>

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impl<R: Debug + Real> Debug for Lorentz<R>

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

Formats the value using the given formatter. Read more
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impl<R: Real> Group for Lorentz<R>

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fn identity() -> Self

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

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fn inverse(&self) -> Self

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fn check_left_identity(&self) -> bool
where Self: PartialEq,

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fn check_right_identity(&self) -> bool
where Self: PartialEq,

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

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fn check_left_inverse(&self) -> bool
where Self: PartialEq + Debug,

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fn check_right_inverse(&self) -> bool
where Self: PartialEq,

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impl<R: Real> LieGroup<SlAlgebra<Complex<R>, 2, 3>> for Lorentz<R>

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

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

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impl<R: PartialEq + Real> PartialEq for Lorentz<R>

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fn eq(&self, other: &Lorentz<R>) -> bool

Equality operator ==. Read more
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fn ne(&self, other: &Rhs) -> bool

Inequality operator !=. Read more
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impl<R: Real> Quotient<Sl<Coords<Complex<R>, 2>, 2>, RootOfUnity<Complex<R>, 2>, SlAlgebra<Complex<R>, 2, 3>> for Lorentz<R>

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

Maps g to the Quotient value representing its coset gH.
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fn lift(&self) -> Sl2c<R>

Recovers a representative of selfโ€™s coset, satisfying new(self.lift()) == self. Read more
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fn embed(h: RootOfUnity<Complex<R>, 2>) -> Sl2c<R>

the subgroup inclusion H โ†ช G
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fn quotient_identity() -> Self

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

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fn quotient_inverse(&self) -> Self

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fn quotient_identity_exp(v: V) -> Self

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

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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.
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impl<R: PartialEq + Real> StructuralPartialEq for Lorentz<R>

Auto Trait Implementationsยง

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impl<R> Freeze for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: Freeze,

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impl<R> RefUnwindSafe for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: RefUnwindSafe,

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impl<R> Send for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: Send,

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impl<R> Sync for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: Sync,

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impl<R> Unpin for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: Unpin,

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impl<R> UnsafeUnpin for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: UnsafeUnpin,

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impl<R> UnwindSafe for Lorentz<R>
where Sl<Coords<Complex<R>, 2>, 2>: UnwindSafe,

Blanket Implementationsยง

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<V, S> Chart<S, V> for S
where V: Tensor, S: Smooth<V>,

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type Global = <S as Smooth<V>>::Global

The result of mapping local coordinates back onto the manifold. Read more
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fn to_local(&self, point: &S) -> Option<V>

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fn to_global(&self, coord: V) -> <S as Smooth<V>>::Global

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fn chart_at(p: &S) -> S

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fn local_distance(&self, other: &P) -> Option<<V::F as Field>::Fixed>
where V: Euclidean,

Calculates the distance between self and other in local coordinates, based at &self.
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fn check_local_inverse(p: &P) -> bool
where P: PartialEq,

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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

๐Ÿ”ฌThis is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<๐’ž, X> Equivalent<๐’ž, X> for X
where ๐’ž: Cat,

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fn project(self) -> X

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fn lift(x: X) -> X

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impl<V, L> ExpMap<L, V> for L
where V: Tensor, L: Smooth<V>,

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fn base_point(&self) -> L

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fn check_base_point_is_origin(&self) -> bool
where V: Form,

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fn check_preservation_of_origin(&self) -> bool
where V: Form,

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fn check_chart_at_base_point(&self) -> bool
where V: Form,

If a chart centred at p exists, chart_at(p) returns it. Formally: chart_at(p).base_point() == p whenever p is the base point of some valid chart in this atlas. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> OptionallyOption<T> for T

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fn into_option(self) -> Option<T>

Converts either permitted representation into Option<T>. Read more
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impl<T> Point for T
where T: Clone + Debug,

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impl<T> Reassociate for T

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fn reassociate<P>( self, ) -> <<Self as ReassociateKernel<P>>::Reassociated as NormalizeWith<Undecorated>>::Normalized
where Self: ReassociateKernel<P>, <Self as ReassociateKernel<P>>::Reassociated: NormalizeWith<Undecorated>,

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impl<V, L> Smooth<V> for L
where V: Tensor, L: LieGroup<V>,

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type Global = L

The result of applying the exponential map. Read more
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fn exp(&self, coord: V) -> L

The exponential map at self: sends a tangent vector v to the point reached by following the geodesic from self in direction v for unit time.
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fn log(&self, point: &L) -> Option<V>

The logarithmic map at self: recovers the tangent vector whose geodesic reaches other, or None at the cut locus (e.g. the antipode on a sphere).
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impl<V, L> TangentBundle<L, V> for L
where V: Tensor, L: Smooth<V>,

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fn check_universal_centring(p: P) -> bool
where V: Form,

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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.