Struct qsym2::group::MagneticRepresentedGroup

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pub struct MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol>, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,
{ /* private fields */ }
Expand description

Structure for managing groups with magnetic corepresentations.

Such a group consists of two types of elements in equal numbers: those that are unitary represented and those that are antiunitary represented. This division of elements affects the class structure of the group via an equivalence relation defined in Newmarch, J. D. & Golding, R. M. The character table for the corepresentations of magnetic groups. Journal of Mathematical Physics 23, 695–704 (1982), DOI.

Implementations§

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impl<T, UG, RowSymbol> MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol>, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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pub fn unitary_subgroup(&self) -> &UG

Returns a shared reference to the unitary subgroup of this group.

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impl<T, UG, RowSymbol> MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Serialize + DeserializeOwned, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, <UG as CharacterProperties>::CharTab: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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pub fn new( name: &str, elements: Vec<T>, unitary_subgroup: UG, ) -> Result<Self, Error>

Constructs a magnetic-represented group from its elements and the unitary subgroup.

§Arguments
  • name - A name to be given to the magnetic-reprented group.
  • elements - A vector of all group elements.
  • unitary_subgroup - The unitary subgroup of the magnetic-represented group. All elements of this must be present in elements.
§Returns

A magnetic-represented group with its Cayley table constructed and conjugacy classes determined.

Trait Implementations§

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impl<T, RowSymbol, UG> CharacterProperties for MagneticRepresentedGroup<T, UG, RowSymbol>
where RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Serialize + DeserializeOwned, T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder<Int = u32> + Pow<i32, Output = T>, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, UG: Clone + GroupProperties<GroupElement = T> + ClassProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, <UG as CharacterProperties>::CharTab: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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type RowSymbol = RowSymbol

Type of the row-labelling symbols in the associated character table.
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type CharTab = CorepCharacterTable<<MagneticRepresentedGroup<T, UG, RowSymbol> as CharacterProperties>::RowSymbol, <UG as CharacterProperties>::CharTab>

Type of the associated character table whose row-labelling symbol type is constrained to be the same as Self::RowSymbol.
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fn character_table(&self) -> &Self::CharTab

Returns a shared reference to the character table of this group.
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fn unitary_represented(&self) -> bool

Returns a boolean indicating if this character table contains irreducible representations of a unitary-represented group. Read more
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impl<T, UG, RowSymbol> ClassProperties for MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, <Self as GroupProperties>::GroupElement: Inv, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Serialize + DeserializeOwned, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, <UG as CharacterProperties>::CharTab: Serialize + DeserializeOwned,

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fn compute_class_structure(&mut self) -> Result<(), Error>

Compute the class structure of this magnetic-represented group that is induced by the following equivalence relation:

    g \sim h \Leftrightarrow
    \exists u : h = u g u^{-1}
    \quad \textrm{or} \quad
    \exists a : h = a g^{-1} a^{-1},

where $u$ is unitary-represented and $a$ is antiunitary-represented in the group.

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type ClassSymbol = <UG as ClassProperties>::ClassSymbol

The type of class symbols.
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fn get_cc_index(&self, cc_idx: usize) -> Option<&HashSet<usize>>

Given a class index, returns an optional shared reference to the set containing the indices of all elements in that class. Read more
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fn get_cc_of_element_index(&self, e_idx: usize) -> Option<usize>

Given an element index, returns an optional index of the conjugacy class to which the element belongs. Read more
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fn get_cc_transversal(&self, cc_idx: usize) -> Option<Self::GroupElement>

Given a class index, returns an optional representative element of that conjugacy class. Read more
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fn get_index_of_cc_symbol(&self, cc_sym: &Self::ClassSymbol) -> Option<usize>

Given a conjugacy class symbol, returns the index of the corresponding conjugacy class. Read more
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fn get_cc_symbol_of_index(&self, cc_idx: usize) -> Option<Self::ClassSymbol>

Given a class index, returns its conjugacy class symbol, if any. Read more
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fn filter_cc_symbols<P: FnMut(&Self::ClassSymbol) -> bool>( &self, predicate: P, ) -> Vec<Self::ClassSymbol>

Given a predicate, returns conjugacy class symbols satisfying it. Read more
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fn set_class_symbols(&mut self, cc_symbols: &[Self::ClassSymbol])

Sets the conjugacy class symbols for this group. Read more
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fn get_inverse_cc(&self, cc_idx: usize) -> Option<usize>

Given a class index, returns an index for its inverse. Read more
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fn class_number(&self) -> usize

Returns the number of conjugacy classes in the group.
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fn class_size(&self, cc_idx: usize) -> Option<usize>

Given a class index, returns its size. Read more
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fn class_matrix( &self, ctb_opt: Option<&Array2<usize>>, r: usize, ) -> Array2<usize>

The class matrix $\mathbf{N}_r$ for the conjugacy classes in the group. Read more
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impl<T, UG, RowSymbol> Clone for MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder + Clone, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Clone, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties + Clone, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned, UG::CharTab: Clone,

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fn clone(&self) -> MagneticRepresentedGroup<T, UG, RowSymbol>

Returns a copy 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<'de, T, UG, RowSymbol> Deserialize<'de> for MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder + Deserialize<'de>, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Deserialize<'de>, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties + Deserialize<'de>, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>
where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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impl<T, UG, RowSymbol> GroupProperties for MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol>, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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type GroupElement = T

The type of the elements in the group.
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type ElementCollection = IndexSet<T>

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fn name(&self) -> String

Returns the name of the group.
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fn finite_subgroup_name(&self) -> Option<&String>

Returns the finite subgroup name of this group, if any.
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fn get_index(&self, index: usize) -> Option<Self::GroupElement>

Given an index, returns the element associated with it, or None if the index is out of range.
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fn get_index_of(&self, g: &Self::GroupElement) -> Option<usize>

Given an element, returns its index in the group, or None if the element does not exist in the group.
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fn contains(&self, g: &Self::GroupElement) -> bool

Checks if an element is a member of the group.
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fn elements(&self) -> &Self::ElementCollection

Returns an iterable collection of the elements in the group.
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fn is_abelian(&self) -> bool

Checks if this group is abelian.
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fn order(&self) -> usize

Returns the order of the group.
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fn cayley_table(&self) -> Option<&Array2<usize>>

Returns the Cayley table of the group, if any.
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impl<T, UG, RowSymbol> HasUnitarySubgroup for MagneticRepresentedGroup<T, UG, RowSymbol>
where T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol>, UG: Clone + GroupProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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fn check_elem_antiunitary(&self, element: &T) -> bool

Checks if a given element is antiunitary-represented in this group.

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element - A reference to an element to be checked.

§Returns

Returns true if element is antiunitary-represented in this group.

§Panics

Panics if element is not in the group.

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type UnitarySubgroup = UG

The type of the unitary halving subgroup.
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fn unitary_subgroup(&self) -> &Self::UnitarySubgroup

Returns a shared reference to the unitary subgroup associated with this group.
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impl<T, RowSymbol, UG> IrcorepCharTabConstruction for MagneticRepresentedGroup<T, UG, RowSymbol>
where RowSymbol: ReducibleLinearSpaceSymbol<Subspace = UG::RowSymbol> + Serialize + DeserializeOwned, T: Mul<Output = T> + Inv<Output = T> + Hash + Eq + Clone + Sync + Debug + FiniteOrder<Int = u32> + Pow<i32, Output = T>, for<'a, 'b> &'b T: Mul<&'a T, Output = T>, UG: Clone + GroupProperties<GroupElement = T> + ClassProperties<GroupElement = T> + CharacterProperties, <UG as ClassProperties>::ClassSymbol: Serialize + DeserializeOwned, <UG as CharacterProperties>::CharTab: Serialize + DeserializeOwned, CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: Serialize + DeserializeOwned,

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fn set_ircorep_character_table(&mut self, chartab: Self::CharTab)

Sets the ircorep character table internally.
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fn construct_ircorep_character_table(&mut self)

Constructs the ircorep character table for this group. Read more
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impl<T, UG, RowSymbol> Serialize for MagneticRepresentedGroup<T, UG, RowSymbol>

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fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>
where __S: Serializer,

Serialize this value into the given Serde serializer. Read more
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impl SymmetryGroupProperties for MagneticRepresentedGroup<SymmetryOperation, UnitaryRepresentedGroup<SymmetryOperation, MullikenIrrepSymbol, SymmetryClassSymbol<SymmetryOperation>>, MullikenIrcorepSymbol>

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fn from_molecular_symmetry( sym: &Symmetry, infinite_order_to_finite: Option<u32>, ) -> Result<Self, Error>

Constructs a magnetic-represented group from molecular symmetry elements (not operations).

§Arguments
  • sym - A molecular symmetry struct.
  • infinite_order_to_finite - Interpret infinite-order generating elements as finite-order generating elements to create a finite subgroup of an otherwise infinite group.
§Returns

A magnetic-represented group of the symmetry operations generated by sym.

§Panics

Panics if sym generates no antiunitary operations.

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fn to_double_group(&self) -> Result<Self, Error>

Constructs the double group of this magnetic-represented group.

Note that the unitary subgroup of the magnetic-represented double group is not necessarily the same as the double group of the unitary subgroup. This difference can manifest when there are binary rotations or reflections and the positive hemisphere of the magnetic-represented group might be different from the positive hemisphere of the unitary subgroup.

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The magnetic-represented double group.

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fn canonicalise_character_table(&mut self)

Reorders and relabels the rows and columns of the constructed character table using symmetry-specific rules and conventions. Read more
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fn deduce_finite_group_name(&mut self) -> String

Deduces the group name in Schönflies notation of a finite subgroup of an infinite molecular symmetry group.
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fn all_unitary(&self) -> bool

Returns true if all elements in this group are unitary.
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fn is_double_group(&self) -> bool

Returns true if all elements in this group are in $\mathsf{SU}'(2)$ or false if they are all in $\mathsf{O}(3)$. Read more
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fn group_type(&self) -> GroupType

Determines whether this group is an ordinary (double) group, a magnetic grey (double) group, or a magnetic black-and-white (double) group.
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fn class_symbols_from_symmetry( &mut self, ) -> Vec<SymmetryClassSymbol<SymmetryOperation>>

Returns the conjugacy class symbols in this group based on molecular symmetry.

Auto Trait Implementations§

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impl<T, UG, RowSymbol> Freeze for MagneticRepresentedGroup<T, UG, RowSymbol>
where CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: for<'de> Sized, <UG as ClassProperties>::ClassSymbol: for<'de> Sized, UG: Freeze, <UG as CharacterProperties>::CharTab: Freeze,

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impl<T, UG, RowSymbol> RefUnwindSafe for MagneticRepresentedGroup<T, UG, RowSymbol>

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impl<T, UG, RowSymbol> Send for MagneticRepresentedGroup<T, UG, RowSymbol>
where CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: for<'de> Sized, <UG as ClassProperties>::ClassSymbol: for<'de> Sized + Send, UG: Send, <UG as CharacterProperties>::CharTab: Send, T: Send, RowSymbol: Send,

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impl<T, UG, RowSymbol> Sync for MagneticRepresentedGroup<T, UG, RowSymbol>
where CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: for<'de> Sized, <UG as ClassProperties>::ClassSymbol: for<'de> Sized + Sync, UG: Sync, <UG as CharacterProperties>::CharTab: Sync, RowSymbol: Sync,

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impl<T, UG, RowSymbol> Unpin for MagneticRepresentedGroup<T, UG, RowSymbol>
where CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: for<'de> Sized, <UG as ClassProperties>::ClassSymbol: for<'de> Sized + Unpin, UG: Unpin, <UG as CharacterProperties>::CharTab: Unpin, T: Unpin, RowSymbol: Unpin,

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impl<T, UG, RowSymbol> UnwindSafe for MagneticRepresentedGroup<T, UG, RowSymbol>
where CorepCharacterTable<RowSymbol, <UG as CharacterProperties>::CharTab>: for<'de> Sized, <UG as ClassProperties>::ClassSymbol: for<'de> Sized + UnwindSafe, UG: UnwindSafe, <UG as CharacterProperties>::CharTab: UnwindSafe, T: UnwindSafe, RowSymbol: UnwindSafe,

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🔬This is a nightly-only experimental API. (clone_to_uninit)
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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> TryConv for T

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fn try_conv<T>(self) -> Result<T, Self::Error>
where Self: TryInto<T>,

Attempts to convert self into T using TryInto<T>. 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.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> WithSubscriber for T

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fn with_subscriber<S>(self, subscriber: S) -> WithDispatch<Self>
where S: Into<Dispatch>,

Attaches the provided Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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fn with_current_subscriber(self) -> WithDispatch<Self>

Attaches the current default Subscriber to this type, returning a [WithDispatch] wrapper. Read more
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impl<T> DeserializeOwned for T
where T: for<'de> Deserialize<'de>,

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impl<T> Ungil for T
where T: Send,