MultiPolynomialStructure

algebraeon_rings::polynomial

Struct MultiPolynomialStructure 

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pub struct MultiPolynomialStructure<RS: RingEqSignature, RSB: BorrowedStructure<RS>> { /* private fields */ }

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> MultiPolynomialStructure<RS, RSB>

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pub fn coeff_ring(&self) -> &RS

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impl<RS: UniqueFactorizationMonoidSignature<FactoredExponent = NaturalCanonicalStructure> + GreatestCommonDivisorSignature + CharZeroRingSignature + FiniteUnitsSignature + 'static, RSB: BorrowedStructure<RS> + 'static> MultiPolynomialStructure<RS, RSB>
where MultiPolynomialStructure<RS, RSB>: SetSignature<Set = MultiPolynomial<RS::Set>> + UniqueFactorizationMonoidSignature<FactoredExponent = NaturalCanonicalStructure>, PolynomialStructure<RS, RSB>: SetSignature<Set = Polynomial<RS::Set>> + UniqueFactorizationMonoidSignature<FactoredExponent = NaturalCanonicalStructure>, for<'a> PolynomialStructure<Self, &'a Self>: SetSignature<Set = Polynomial<MultiPolynomial<RS::Set>>> + UniqueFactorizationMonoidSignature<FactoredExponent = NaturalCanonicalStructure>,

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pub fn factor_by_yuns_and_kroneckers_inductively( &self, factor_coeff: Rc<dyn Fn(&RS::Set) -> Factored<RS::Set, Natural>>, factor_poly: Rc<dyn Fn(&Polynomial<RS::Set>) -> Factored<Polynomial<RS::Set>, Natural>>, mpoly: &<Self as SetSignature>::Set, ) -> Factored<MultiPolynomial<RS::Set>, Natural>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> MultiPolynomialStructure<RS, RSB>

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pub fn reduce(&self, p: MultiPolynomial<RS::Set>) -> MultiPolynomial<RS::Set>

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pub fn var_pow(&self, v: Variable, k: usize) -> MultiPolynomial<RS::Set>

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pub fn var(&self, v: Variable) -> MultiPolynomial<RS::Set>

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pub fn as_constant(&self, p: &MultiPolynomial<RS::Set>) -> Option<RS::Set>

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pub fn degree(&self, p: &MultiPolynomial<RS::Set>) -> Option<usize>

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pub fn split_by_degree( &self, p: MultiPolynomial<RS::Set>, ) -> HashMap<usize, MultiPolynomial<RS::Set>>

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pub fn homogenize( &self, p: &MultiPolynomial<RS::Set>, v: &Variable, ) -> MultiPolynomial<RS::Set>

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pub fn expand( &self, p: &MultiPolynomial<RS::Set>, v: &Variable, ) -> Polynomial<MultiPolynomial<RS::Set>>

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pub fn partial_evaluate( &self, poly: &MultiPolynomial<RS::Set>, values: HashMap<Variable, impl Borrow<RS::Set>>, ) -> MultiPolynomial<RS::Set>

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pub fn evaluate( &self, poly: &MultiPolynomial<RS::Set>, values: HashMap<Variable, impl Borrow<RS::Set>>, ) -> RS::Set

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impl<RS: IntegralDomainSignature, RSB: BorrowedStructure<RS>> MultiPolynomialStructure<RS, RSB>
where MultiPolynomialStructure<RS, RSB>: SetSignature<Set = MultiPolynomial<RS::Set>> + ToStringSignature,

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pub fn is_symmetric( &self, vars: Vec<impl Borrow<Variable>>, poly: &MultiPolynomial<RS::Set>, ) -> bool

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pub fn elementary_symmetric( &self, n: usize, vars: &[impl Borrow<Variable>], ) -> MultiPolynomial<RS::Set>

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pub fn as_elementary_symmetric_polynomials_unchecked( &self, vars: Vec<impl Borrow<Variable>>, poly: &MultiPolynomial<RS::Set>, ) -> (Vec<Variable>, MultiPolynomial<RS::Set>)

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pub fn as_elementary_symmetric_polynomials( &self, vars: Vec<impl Borrow<Variable>>, poly: &MultiPolynomial<RS::Set>, ) -> Option<(Vec<Variable>, MultiPolynomial<RS::Set>)>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> AdditionSignature for MultiPolynomialStructure<RS, RSB>

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fn add(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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fn add_mut(&self, a: &mut Self::Set, b: &Self::Set)

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> AdditiveGroupSignature for MultiPolynomialStructure<RS, RSB>

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fn neg(&self, a: &Self::Set) -> Self::Set

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fn sub(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> AdditiveMonoidSignature for MultiPolynomialStructure<RS, RSB>

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fn sum(&self, vals: Vec<impl Borrow<Self::Set>>) -> Self::Set

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> CancellativeAdditionSignature for MultiPolynomialStructure<RS, RSB>

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fn try_sub(&self, a: &Self::Set, b: &Self::Set) -> Option<Self::Set>

Return the unique x such that a = b + x, or None if no such x exists.
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impl<RS: IntegralDomainSignature, RSB: BorrowedStructure<RS>> CancellativeMultiplicationSignature for MultiPolynomialStructure<RS, RSB>

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fn try_divide(&self, a: &Self::Set, b: &Self::Set) -> Option<Self::Set>

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fn divisible(&self, a: &Self::Set, b: &Self::Set) -> bool

return true iff a is divisible by b
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impl<RS: CharZeroRingSignature + EqSignature, RSB: BorrowedStructure<RS>> CharZeroRingSignature for MultiPolynomialStructure<RS, RSB>

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fn try_to_int(&self, x: &Self::Set) -> Option<Integer>

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impl<RS: CharacteristicSignature + RingEqSignature, RSB: BorrowedStructure<RS>> CharacteristicSignature for MultiPolynomialStructure<RS, RSB>

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fn characteristic(&self) -> Natural

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impl<RS: Clone + RingEqSignature, RSB: Clone + BorrowedStructure<RS>> Clone for MultiPolynomialStructure<RS, RSB>

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fn clone(&self) -> MultiPolynomialStructure<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 + RingEqSignature, RSB: Debug + BorrowedStructure<RS>> Debug for MultiPolynomialStructure<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: RingEqSignature, RSB: BorrowedStructure<RS>> EqSignature for MultiPolynomialStructure<RS, RSB>

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fn equal(&self, a: &Self::Set, b: &Self::Set) -> bool

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impl<B: BorrowedStructure<IntegerCanonicalStructure> + 'static> FactoringMonoidSignature for MultiPolynomialStructure<IntegerCanonicalStructure, B>

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fn factor_unchecked(&self, p: &Self::Set) -> Factored<Self::Set, Natural>

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fn is_irreducible(&self, a: &Self::Set) -> bool

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fn factor( &self, a: &Self::Set, ) -> Factored<Self::Set, <Self::FactoredExponent as SetSignature>::Set>

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impl<RS: FavoriteAssociateSignature + IntegralDomainSignature, RSB: BorrowedStructure<RS>> FavoriteAssociateSignature for MultiPolynomialStructure<RS, RSB>

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fn factor_fav_assoc(&self, mpoly: &Self::Set) -> (Self::Set, Self::Set)

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fn fav_assoc(&self, a: &Self::Set) -> Self::Set

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fn is_fav_assoc(&self, a: &Self::Set) -> bool

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impl<RS: GreatestCommonDivisorSignature, RSB: BorrowedStructure<RS>> GreatestCommonDivisorSignature for MultiPolynomialStructure<RS, RSB>
where for<'a> PolynomialStructure<MultiPolynomialStructure<RS, RSB>, &'a Self>: SetSignature<Set = Polynomial<MultiPolynomial<RS::Set>>>,

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fn gcd(&self, x: &Self::Set, y: &Self::Set) -> Self::Set

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fn gcd_list(&self, elems: Vec<impl Borrow<Self::Set>>) -> Self::Set

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fn lcm(&self, x: &Self::Set, y: &Self::Set) -> Self::Set

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fn lcm_list(&self, elems: Vec<impl Borrow<Self::Set>>) -> Self::Set

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impl<RS: IntegralDomainSignature, RSB: BorrowedStructure<RS>> IntegralDomainSignature for MultiPolynomialStructure<RS, RSB>

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fn try_from_rat(&self, x: &Rational) -> Option<Self::Set>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> MultiplicationSignature for MultiPolynomialStructure<RS, RSB>

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fn mul(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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fn mul_mut(&self, a: &mut Self::Set, b: &Self::Set)

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> MultiplicativeMonoidSignature for MultiPolynomialStructure<RS, RSB>

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fn product(&self, vals: Vec<impl Borrow<Self::Set>>) -> Self::Set

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fn nat_pow(&self, a: &Self::Set, n: &Natural) -> Self::Set

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> OneSignature for MultiPolynomialStructure<RS, RSB>

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fn one(&self) -> Self::Set

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impl<RS: PartialEq + RingEqSignature, RSB: PartialEq + BorrowedStructure<RS>> PartialEq for MultiPolynomialStructure<RS, RSB>

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fn eq(&self, other: &MultiPolynomialStructure<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: RingEqSignature, RSB: BorrowedStructure<RS>> RingSignature for MultiPolynomialStructure<RS, RSB>

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fn is_reduced(&self) -> Result<bool, String>

Determine whether the ring is reduced. Read more
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fn bracket(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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fn from_int(&self, x: impl Into<Integer>) -> Self::Set

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fn inbound_principal_integer_map(&self) -> PrincipalIntegerMap<Self, &Self>

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fn into_inbound_principal_integer_map(self) -> PrincipalIntegerMap<Self, Self>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> RinglikeSpecializationSignature for MultiPolynomialStructure<RS, RSB>

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fn try_ring_restructure( &self, ) -> Option<impl EqSignature<Set = Self::Set> + RingSignature>

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fn try_char_zero_ring_restructure( &self, ) -> Option<impl EqSignature<Set = Self::Set> + CharZeroRingSignature>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> SemiRingSignature for MultiPolynomialStructure<RS, RSB>

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fn from_nat(&self, x: impl Into<Natural>) -> Self::Set

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> SetSignature for MultiPolynomialStructure<RS, RSB>

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type Set = MultiPolynomial<<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: RingEqSignature + ToStringSignature, RSB: BorrowedStructure<RS>> ToStringSignature for MultiPolynomialStructure<RS, RSB>

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fn to_string(&self, p: &Self::Set) -> String

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> TryNegateSignature for MultiPolynomialStructure<RS, RSB>

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fn try_neg(&self, a: &Self::Set) -> Option<Self::Set>

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impl<RS: IntegralDomainSignature, RSB: BorrowedStructure<RS>> TryReciprocalSignature for MultiPolynomialStructure<RS, RSB>

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fn try_reciprocal(&self, a: &Self::Set) -> Option<Self::Set>

b such that a*b=1 and b*a=1 or None if no such b exists.
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fn is_unit(&self, a: &Self::Set) -> bool

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fn units(&self) -> MultiplicativeMonoidUnitsStructure<Self, &Self>

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fn into_units(self) -> MultiplicativeMonoidUnitsStructure<Self, Self>

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impl<RS: UniqueFactorizationMonoidSignature + IntegralDomainSignature, RSB: BorrowedStructure<RS>> UniqueFactorizationMonoidSignature for MultiPolynomialStructure<RS, RSB>

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type FactoredExponent = NaturalCanonicalStructure

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fn factorization_exponents(&self) -> &Self::FactoredExponent

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fn into_factorization_exponents(self) -> Self::FactoredExponent

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fn try_is_irreducible(&self, _a: &Self::Set) -> Option<bool>

This should determine whether a is irreducible without factoring it. Factoring a is not allowed because this function is used by factorizations to validate their state.
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fn factorization_pow(&self, a: &Self::Set, k: &Natural) -> Self::Set

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fn factorizations( &self, ) -> FactoringStructure<Self, &Self, Self::FactoredExponent, &Self::FactoredExponent>

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fn into_factorizations( self, ) -> FactoringStructure<Self, Self, Self::FactoredExponent, Self::FactoredExponent>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> ZeroSignature for MultiPolynomialStructure<RS, RSB>

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fn zero(&self) -> Self::Set

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> CommutativeMultiplicationSignature for MultiPolynomialStructure<RS, RSB>

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impl<RS: Eq + RingEqSignature, RSB: Eq + BorrowedStructure<RS>> Eq for MultiPolynomialStructure<RS, RSB>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> LeftDistributiveMultiplicationOverAddition for MultiPolynomialStructure<RS, RSB>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> MultiplicativeAbsorptionMonoidSignature for MultiPolynomialStructure<RS, RSB>

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impl<RS: IntegralDomainSignature, RSB: BorrowedStructure<RS>> MultiplicativeIntegralMonoidSignature for MultiPolynomialStructure<RS, RSB>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> RightDistributiveMultiplicationOverAddition for MultiPolynomialStructure<RS, RSB>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> Signature for MultiPolynomialStructure<RS, RSB>

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impl<RS: RingEqSignature, RSB: BorrowedStructure<RS>> StructuralPartialEq for MultiPolynomialStructure<RS, RSB>

Auto Trait Implementations§

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

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

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

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

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

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impl<RS, RSB> UnwindSafe for MultiPolynomialStructure<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<S> AreAssociateMultiplicationSignature for S
where S: CancellativeMultiplicationSignature + ZeroEqSignature,

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fn are_associate(&self, a: &Self::Set, b: &Self::Set) -> bool

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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<S> FactoringMonoidNaturalExponentSignature for S
where S: FactoringMonoidSignature<FactoredExponent = NaturalCanonicalStructure>,

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fn gcd_by_factor(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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fn lcm_by_factor(&self, a: &Self::Set, b: &Self::Set) -> Option<Self::Set>

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fn is_squarefree(&self, a: &Self::Set) -> bool

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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<RS> InfiniteSignature for RS
where RS: CharZeroRingSignature + 'static,

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fn generate_distinct_elements( &self, ) -> Box<dyn Iterator<Item = <RS as SetSignature>::Set>>

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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<S> LeftCancellativeMultiplicationSignature for S
where S: CancellativeMultiplicationSignature,

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fn try_left_divide( &self, a: &<S as SetSignature>::Set, b: &<S as SetSignature>::Set, ) -> Option<<S as SetSignature>::Set>

Try to find x such that a = b * x.
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impl<S> MultiplicativeMonoidTryInverseSignature for S
where S: MultiplicativeMonoidSignature + TryReciprocalSignature,

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fn try_int_pow(&self, a: &Self::Set, n: &Integer) -> Option<Self::Set>

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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<S> RightCancellativeMultiplicationSignature for S
where S: CancellativeMultiplicationSignature,

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fn try_right_divide( &self, a: &<S as SetSignature>::Set, b: &<S as SetSignature>::Set, ) -> Option<<S as SetSignature>::Set>

Try to find x such that a = x * b.
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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<Ring> RingToFinitelyFreeModuleSignature for Ring
where Ring: RingSignature,

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fn free_module(&self, n: usize) -> FinitelyFreeModuleStructure<Self, &Self>

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fn into_free_module(self, n: usize) -> FinitelyFreeModuleStructure<Self, Self>

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impl<RS> RingToMultiPolynomialRingSignature for RS
where RS: RingEqSignature,

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fn multivariable_polynomial_ring(&self) -> MultiPolynomialStructure<Self, &Self>

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fn into_multivariable_polynomial_ring( self, ) -> MultiPolynomialStructure<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<S> TryLeftReciprocalSignature for S
where S: TryReciprocalSignature + CommutativeMultiplicationSignature,

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fn try_left_reciprocal( &self, a: &<S as SetSignature>::Set, ) -> Option<<S as SetSignature>::Set>

x such that x*a=1 or None if no such x exists.
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impl<S> TryRightReciprocalSignature for S
where S: TryReciprocalSignature + CommutativeMultiplicationSignature,

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fn try_right_reciprocal( &self, a: &<S as SetSignature>::Set, ) -> Option<<S as SetSignature>::Set>

x such that a*x=1 or None if no such x exists.
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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<R> ZeroEqSignature for R
where R: ZeroSignature + EqSignature,

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fn is_zero(&self, a: &Self::Set) -> bool

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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,

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impl<R> RingEqSignature for R
where R: RingSignature + EqSignature,

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impl<Ring> RingUnitsSignature for Ring
where Ring: RingSignature + TryReciprocalSignature,

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impl<R> SemiRingEqSignature for R
where R: SemiRingSignature + EqSignature,