MatrixStructure

algebraeon_rings::matrix

Struct MatrixStructure 

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pub struct MatrixStructure<RS: SetSignature, RSB: BorrowedStructure<RS>> { /* private fields */ }

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impl<FS: ComplexConjugateSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>

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pub fn conjugate(&self, mat: &Matrix<FS::Set>) -> Matrix<FS::Set>

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pub fn conjugate_transpose(&self, mat: &Matrix<FS::Set>) -> Matrix<FS::Set>

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impl<FS: ComplexConjugateSignature + RingSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>

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pub fn inner_product(&self, a: &Matrix<FS::Set>, b: &Matrix<FS::Set>) -> FS::Set

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impl<FS: ComplexConjugateSignature + FieldSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>

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pub fn gram_schmidt_row_orthogonalization_algorithm( &self, mat: Matrix<FS::Set>, ) -> (Matrix<FS::Set>, Matrix<FS::Set>)

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pub fn gram_schmidt_col_orthogonalization_algorithm( &self, mat: Matrix<FS::Set>, ) -> (Matrix<FS::Set>, Matrix<FS::Set>)

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pub fn gram_schmidt_row_orthogonalization( &self, mat: Matrix<FS::Set>, ) -> Matrix<FS::Set>

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pub fn gram_schmidt_col_orthogonalization( &self, mat: Matrix<FS::Set>, ) -> Matrix<FS::Set>

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impl<FS: ComplexConjugateSignature + PositiveRealNthRootSignature + FieldSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>

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pub fn lq_decomposition_algorithm( &self, mat: Matrix<FS::Set>, ) -> (Matrix<FS::Set>, Matrix<FS::Set>)

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pub fn qr_decomposition_algorithm( &self, mat: Matrix<FS::Set>, ) -> (Matrix<FS::Set>, Matrix<FS::Set>)

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pub fn gram_schmidt_row_orthonormalization( &self, mat: Matrix<FS::Set>, ) -> Matrix<FS::Set>

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pub fn gram_schmidt_col_orthonormalization( &self, mat: Matrix<FS::Set>, ) -> Matrix<FS::Set>

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impl<Ring: HermiteAlgorithmSignature, RingB: BorrowedStructure<Ring>> MatrixStructure<Ring, RingB>

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pub fn row_hermite_algorithm( &self, m: Matrix<Ring::Set>, ) -> (Matrix<Ring::Set>, Matrix<Ring::Set>, Ring::Set, Vec<usize>)

Return (H, U, u_det, pivots) such that

  • H is in row hermite normal form, meaning
  • U is invertible
  • UM=H
  • u_det is the determinant of u
  • pivots[r] is the column of the rth pivot
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pub fn col_hermite_algorithm( &self, a: Matrix<Ring::Set>, ) -> (Matrix<Ring::Set>, Matrix<Ring::Set>, Ring::Set, Vec<usize>)

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pub fn det(&self, a: Matrix<Ring::Set>) -> Result<Ring::Set, MatOppErr>

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pub fn rank(&self, a: Matrix<Ring::Set>) -> usize

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impl<Ring: ReducedHermiteAlgorithmSignature, RingB: BorrowedStructure<Ring>> MatrixStructure<Ring, RingB>

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pub fn row_reduced_hermite_algorithm( &self, m: Matrix<Ring::Set>, ) -> (Matrix<Ring::Set>, Matrix<Ring::Set>, Ring::Set, Vec<usize>)

Returns (H, U, u_det, pivots) such that

  • H is in row reduced hermite normal form, meaning entries above pivots have euclidean norm strictly less than the pivot
  • U is invertible
  • UM=H
  • pivots[r] is the column of the rth pivot and pivots.len() == rank(A)
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pub fn row_reduced_hermite_normal_form( &self, m: Matrix<Ring::Set>, ) -> Matrix<Ring::Set>

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pub fn col_reduced_hermite_algorithm( &self, m: Matrix<Ring::Set>, ) -> (Matrix<Ring::Set>, Matrix<Ring::Set>, Ring::Set, Vec<usize>)

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pub fn col_reduced_hermite_normal_form( &self, m: Matrix<Ring::Set>, ) -> Matrix<Ring::Set>

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pub fn inv(&self, a: Matrix<Ring::Set>) -> Result<Matrix<Ring::Set>, MatOppErr>

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pub fn row_span( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn col_span( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn row_kernel( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn col_kernel( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn row_preimage( &self, matrix: &Matrix<Ring::Set>, space: &FinitelyFreeSubmodule<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn col_preimage( &self, matrix: &Matrix<Ring::Set>, space: &FinitelyFreeSubmodule<Ring::Set>, ) -> FinitelyFreeSubmodule<Ring::Set>

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pub fn row_affine_span( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmoduleAffineSubset<Ring::Set>

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pub fn col_affine_span( &self, matrix: Matrix<Ring::Set>, ) -> FinitelyFreeSubmoduleAffineSubset<Ring::Set>

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pub fn row_solve( &self, matrix: Matrix<Ring::Set>, y: &Vec<Ring::Set>, ) -> Option<Vec<Ring::Set>>

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pub fn col_solve( &self, matrix: Matrix<Ring::Set>, y: &Vec<Ring::Set>, ) -> Option<Vec<Ring::Set>>

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pub fn row_solution_set( &self, matrix: Matrix<Ring::Set>, y: &Vec<Ring::Set>, ) -> FinitelyFreeSubmoduleAffineSubset<Ring::Set>

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pub fn col_solution_set( &self, matrix: Matrix<Ring::Set>, y: &Vec<Ring::Set>, ) -> FinitelyFreeSubmoduleAffineSubset<Ring::Set>

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impl<FS: AlgebraicClosureSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>
where PolynomialStructure<FS::BFS, FS::BFS>: FactoringMonoidSignature<FactoredExponent = NaturalCanonicalStructure> + SetSignature<Set = Polynomial<<FS::BFS as SetSignature>::Set>>,

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pub fn eigenvalues_list( &self, mat: Matrix<<FS::BFS as SetSignature>::Set>, ) -> Vec<FS::Set>

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pub fn eigenvalues_unique( &self, mat: Matrix<<FS::BFS as SetSignature>::Set>, ) -> Vec<FS::Set>

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pub fn eigenvalues_powers( &self, mat: Matrix<<FS::BFS as SetSignature>::Set>, ) -> Vec<(FS::Set, usize)>

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pub fn generalized_col_eigenspace( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, eigenvalue: &FS::Set, k: usize, ) -> FinitelyFreeSubmodule<FS::Set>

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pub fn generalized_row_eigenspace( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, eigenvalue: &FS::Set, k: usize, ) -> FinitelyFreeSubmodule<FS::Set>

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pub fn col_eigenspace( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, eigenvalue: &FS::Set, ) -> FinitelyFreeSubmodule<FS::Set>

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pub fn row_eigenspace( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, eigenvalue: &FS::Set, ) -> FinitelyFreeSubmodule<FS::Set>

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pub fn jordan_algorithm( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, ) -> (JordanNormalForm<FS>, Matrix<FS::Set>)

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pub fn jordan_normal_form( &self, mat: &Matrix<<FS::BFS as SetSignature>::Set>, ) -> Matrix<FS::Set>

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impl<RS: SetSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn new(ring: RSB) -> Self

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pub fn ring(&self) -> &RS

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impl<RS: EqSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn equal(&self, a: &Matrix<RS::Set>, b: &Matrix<RS::Set>) -> bool

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impl<RS: ToStringSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn pprint(&self, mat: &Matrix<RS::Set>)

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impl<RS: RingSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn zero(&self, rows: usize, cols: usize) -> Matrix<RS::Set>

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pub fn ident(&self, n: usize) -> Matrix<RS::Set>

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pub fn diag(&self, diag: &[RS::Set]) -> Matrix<RS::Set>

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pub fn join_diag<MatT: Borrow<Matrix<RS::Set>>>( &self, mats: Vec<MatT>, ) -> Matrix<RS::Set>

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pub fn dot(&self, a: &Matrix<RS::Set>, b: &Matrix<RS::Set>) -> RS::Set

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pub fn add_mut( &self, a: &mut Matrix<RS::Set>, b: &Matrix<RS::Set>, ) -> Result<(), MatOppErr>

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pub fn add( &self, a: &Matrix<RS::Set>, b: &Matrix<RS::Set>, ) -> Result<Matrix<RS::Set>, MatOppErr>

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pub fn neg_mut(&self, a: &mut Matrix<RS::Set>)

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pub fn neg(&self, a: Matrix<RS::Set>) -> Matrix<RS::Set>

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pub fn mul( &self, a: &Matrix<RS::Set>, b: &Matrix<RS::Set>, ) -> Result<Matrix<RS::Set>, MatOppErr>

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pub fn apply_row(&self, mat: &Matrix<RS::Set>, row: &[RS::Set]) -> Vec<RS::Set>

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pub fn apply_col(&self, mat: &Matrix<RS::Set>, col: &[RS::Set]) -> Vec<RS::Set>

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pub fn mul_scalar( &self, a: Matrix<RS::Set>, scalar: &RS::Set, ) -> Matrix<RS::Set>

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pub fn mul_scalar_ref( &self, a: &Matrix<RS::Set>, scalar: &RS::Set, ) -> Matrix<RS::Set>

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pub fn det_naive(&self, a: &Matrix<RS::Set>) -> Result<RS::Set, MatOppErr>

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pub fn trace(&self, a: &Matrix<RS::Set>) -> Result<RS::Set, MatOppErr>

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pub fn nat_pow( &self, a: &Matrix<RS::Set>, k: &Natural, ) -> Result<Matrix<RS::Set>, MatOppErr>

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impl<FS: FieldSignature, FSB: BorrowedStructure<FS>> MatrixStructure<FS, FSB>

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pub fn presentation_matrix( &self, m: Matrix<FS::Set>, ) -> Result<Matrix<Polynomial<FS::Set>>, MatOppErr>

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pub fn minimal_polynomial( &self, m: Matrix<FS::Set>, ) -> Result<Polynomial<FS::Set>, MatOppErr>

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pub fn characteristic_polynomial( &self, m: Matrix<FS::Set>, ) -> Result<Polynomial<FS::Set>, MatOppErr>

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impl<RS: GreatestCommonDivisorSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn factor_primitive( &self, mat: Matrix<RS::Set>, ) -> Option<(RS::Set, Matrix<RS::Set>)>

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pub fn primitive_part(&self, mat: Matrix<RS::Set>) -> Option<Matrix<RS::Set>>

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impl<RS: BezoutDomainSignature, RSB: BorrowedStructure<RS>> MatrixStructure<RS, RSB>

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pub fn smith_algorithm( &self, m: Matrix<RS::Set>, ) -> (Matrix<RS::Set>, Matrix<RS::Set>, Matrix<RS::Set>, usize)

Trait Implementations§

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impl<RS: Clone + SetSignature, RSB: Clone + BorrowedStructure<RS>> Clone for MatrixStructure<RS, RSB>

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fn clone(&self) -> MatrixStructure<RS, RSB>

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<RS: Debug + SetSignature, RSB: Debug + BorrowedStructure<RS>> Debug for MatrixStructure<RS, RSB>

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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<RS: PartialEq + SetSignature, RSB: PartialEq + BorrowedStructure<RS>> PartialEq for MatrixStructure<RS, RSB>

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fn eq(&self, other: &MatrixStructure<RS, RSB>) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<RS: SetSignature, RSB: BorrowedStructure<RS>> SetSignature for MatrixStructure<RS, RSB>

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type Set = Matrix<<RS as SetSignature>::Set>

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fn is_element(&self, _x: &Self::Set) -> Result<(), String>

Some instances of Self::Set may not be valid to represent elements of this set. Return true if x is a valid element and false if not.
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impl<RS: Eq + SetSignature, RSB: Eq + BorrowedStructure<RS>> Eq for MatrixStructure<RS, RSB>

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impl<RS: SetSignature, RSB: BorrowedStructure<RS>> Signature for MatrixStructure<RS, RSB>

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impl<RS: SetSignature, RSB: BorrowedStructure<RS>> StructuralPartialEq for MatrixStructure<RS, RSB>

Auto Trait Implementations§

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impl<RS, RSB> Freeze for MatrixStructure<RS, RSB>
where RSB: Freeze,

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impl<RS, RSB> RefUnwindSafe for MatrixStructure<RS, RSB>
where RSB: RefUnwindSafe, RS: RefUnwindSafe,

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impl<RS, RSB> Send for MatrixStructure<RS, RSB>

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impl<RS, RSB> Sync for MatrixStructure<RS, RSB>

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impl<RS, RSB> Unpin for MatrixStructure<RS, RSB>
where RSB: Unpin, RS: Unpin,

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impl<RS, RSB> UnwindSafe for MatrixStructure<RS, RSB>
where RSB: UnwindSafe, RS: UnwindSafe,

Blanket Implementations§

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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<T> CloneToUninit for T
where T: Clone,

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

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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fn equivalent(&self, key: &K) -> bool

Checks if this value is equivalent to the given key. Read more
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impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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fn equivalent(&self, key: &K) -> bool

Compare self to key and return true if they are equal.
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impl<T, U> ExactFrom<T> for U
where U: TryFrom<T>,

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fn exact_from(value: T) -> U

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impl<T, U> ExactInto<U> for T
where U: ExactFrom<T>,

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fn exact_into(self) -> U

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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> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<S> IntoErgonomicSignature for S
where S: SetSignature,

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fn into_ergonomic(&self, elem: Self::Set) -> StructuredElement<Self>

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impl<T, U> OverflowingInto<U> for T
where U: OverflowingFrom<T>,

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fn overflowing_into(self) -> (U, bool)

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impl<T> Pointable for T

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const ALIGN: usize

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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impl<RS> RingMatricesSignature for RS
where RS: SetSignature,

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fn matrices(&self) -> MatrixStructure<Self, &Self>

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fn into_matrices(self) -> MatrixStructure<Self, Self>

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impl<T, U> RoundingInto<U> for T
where U: RoundingFrom<T>,

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fn rounding_into(self, rm: RoundingMode) -> (U, Ordering)

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<T, U> SaturatingInto<U> for T
where U: SaturatingFrom<T>,

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fn saturating_into(self) -> U

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impl<T> ToDebugString for T
where T: Debug,

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fn to_debug_string(&self) -> String

Returns the String produced by Ts Debug implementation.

§Examples
use malachite_base::strings::ToDebugString;

assert_eq!([1, 2, 3].to_debug_string(), "[1, 2, 3]");
assert_eq!(
    [vec![2, 3], vec![], vec![4]].to_debug_string(),
    "[[2, 3], [], [4]]"
);
assert_eq!(Some(5).to_debug_string(), "Some(5)");
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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<RS> ToPolynomialSignature for RS
where RS: Signature,

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fn polynomials(&self) -> PolynomialStructure<Self, &Self>

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fn into_polynomials(self) -> PolynomialStructure<Self, Self>

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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, U> WrappingInto<U> for T
where U: WrappingFrom<T>,

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fn wrapping_into(self) -> U

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impl<Domain, Range, M, BM> BorrowedMorphism<Domain, Range, M> for BM
where Domain: Signature, Range: Signature, M: Morphism<Domain, Range>, BM: Borrow<M> + Clone + Debug + Send + Sync,

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impl<S, BS> BorrowedSet<S> for BS
where BS: Borrow<S> + Clone + Debug + Send + Sync,

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impl<S, BS> BorrowedStructure<S> for BS
where S: Signature, BS: Borrow<S> + Clone + Debug + Eq + Send + Sync,