Struct binius_core::tensor_algebra::TensorAlgebra

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pub struct TensorAlgebra<F, FE>
where
    F: Field,
    FE: ExtensionField<F>,
{
    pub elems: Vec<FE>,
    /* private fields */
}
Expand description

An element of the tensor algebra defined as the tensor product of FE and FE as fields.

A tensor algebra element is a length $D$ vector of FE field elements, where $D$ is the degree of FE as an extension of F. The algebra has a “vertical subring” and a “horizontal subring”, which are both isomorphic to FE as a field.

See DP24 Section 2 for further details.

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§elems: Vec<FE>

Implementations§

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impl<F, FE> TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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pub fn new(elems: Vec<FE>) -> Self

Constructs an element from a vector of vertical subring elements.

§Preconditions
  • elems must have length FE::DEGREE, otherwise this will pad or truncate.
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pub const fn kappa() -> usize

Returns $\kappa$, the base-2 logarithm of the extension degree.

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pub fn byte_size() -> usize

Returns the byte size of an element.

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pub fn one() -> Self

Returns the multiplicative identity element, one.

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pub fn vertical_elems(&self) -> &[FE]

Returns a slice of the vertical subfield elements composing the tensor algebra element.

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pub fn tensor(vertical: FE, horizontal: FE) -> Self

Tensor product of a vertical subring element and a horizontal subring element.

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pub fn from_vertical(x: FE) -> Self

Constructs a TensorAlgebra in the vertical subring.

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pub fn try_extract_vertical(&self) -> Option<FE>

If the algebra element lives in the vertical subring, this returns it as a field element.

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pub fn scale_vertical(self, scalar: FE) -> Self

Multiply by an element from the vertical subring.

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impl<F, FE> TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F> + PackedExtension<F>, FE::Scalar: ExtensionField<F>,

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pub fn scale_horizontal(self, scalar: FE) -> Self

Multiply by an element from the vertical subring.

Internally, this performs a transpose, vertical scaling, then transpose sequence. If multiple horizontal scaling operations are required and performance is a concern, it may be better for the caller to do the transposes directly and amortize their cost.

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pub fn transpose(self) -> Self

Transposes the algebra element.

A transpose flips the vertical and horizontal subring elements.

Trait Implementations§

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impl<F, FE> Add<&TensorAlgebra<F, FE>> for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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type Output = TensorAlgebra<F, FE>

The resulting type after applying the + operator.
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fn add(self, rhs: &Self) -> Self

Performs the + operation. Read more
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impl<F, FE> AddAssign<&TensorAlgebra<F, FE>> for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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fn add_assign(&mut self, rhs: &Self)

Performs the += operation. Read more
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impl<F, FE> Clone for TensorAlgebra<F, FE>
where F: Field + Clone, FE: ExtensionField<F> + Clone,

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fn clone(&self) -> TensorAlgebra<F, FE>

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<F, FE> Debug for TensorAlgebra<F, FE>
where F: Field + Debug, FE: ExtensionField<F> + Debug,

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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<F, FE> Default for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl<F, FE> PartialEq for TensorAlgebra<F, FE>
where F: Field + PartialEq, FE: ExtensionField<F> + PartialEq,

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fn eq(&self, other: &TensorAlgebra<F, FE>) -> bool

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<F, FE> Sub<&TensorAlgebra<F, FE>> for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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type Output = TensorAlgebra<F, FE>

The resulting type after applying the - operator.
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fn sub(self, rhs: &Self) -> Self

Performs the - operation. Read more
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impl<F, FE> SubAssign<&TensorAlgebra<F, FE>> for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation. Read more
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impl<'a, F, FE> Sum<&'a TensorAlgebra<F, FE>> for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

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fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.
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impl<F, FE> Eq for TensorAlgebra<F, FE>
where F: Field + Eq, FE: ExtensionField<F> + Eq,

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impl<F, FE> StructuralPartialEq for TensorAlgebra<F, FE>
where F: Field, FE: ExtensionField<F>,

Auto Trait Implementations§

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impl<F, FE> Freeze for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static,

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impl<F, FE> RefUnwindSafe for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + RefUnwindSafe, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + RefUnwindSafe,

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impl<F, FE> Send for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static,

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impl<F, FE> Sync for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static,

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impl<F, FE> Unpin for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + Unpin, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + Unpin,

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impl<F, FE> UnwindSafe for TensorAlgebra<F, FE>
where FE: MulAssign<F> + SubAssign<F> + AddAssign<F> + Mul<F, Output = FE, Output = FE, Output = FE> + Sub<F, Output = FE, Output = FE, Output = FE> + Add<F, Output = FE, Output = FE, Output = FE> + TryInto<F> + From<F> + Field<Output = FE> + WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a FE> + for<'a> SubAssign<&'a FE> + for<'a> AddAssign<&'a FE> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a FE> + for<'a> Sum<&'a FE> + for<'a> Mul<&'a FE> + for<'a> Sub<&'a FE> + for<'a> Add<&'a FE> + Product + Sum + Mul + Sub + Add + Neg + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + UnwindSafe, <FE as WithUnderlier>::Underlier: PackScalar<FE> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, <F as WithUnderlier>::Underlier: PackScalar<F> + UnderlierType + Sync + Send + Zeroable + NoUninit + Random + Copy + Clone + ConstantTimeEq + Eq + PartialEq + Default + Debug + Sized + 'static, F: WithUnderlier + Zeroable + InvertOrZero + Square + for<'a> MulAssign<&'a F> + for<'a> SubAssign<&'a F> + for<'a> AddAssign<&'a F> + MulAssign + SubAssign + AddAssign + for<'a> Product<&'a F> + for<'a> Sum<&'a F> + for<'a> Mul<&'a F, Output = F, Output = F> + for<'a> Sub<&'a F, Output = F, Output = F> + for<'a> Add<&'a F, Output = F, Output = F> + Product + Sum + Mul + Sub + Add + Neg<Output = F> + Debug + Sync + Send + Default + Clone + Copy + Eq + PartialEq + 'static + UnwindSafe,

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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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where T: ?Sized,

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Returns the argument unchanged.

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Instruments this type with the provided [Span], returning an Instrumented wrapper. Read more
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Calls U::from(self).

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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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const ALIGN: usize = _

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unsafe fn init(init: <T as Pointable>::Init) -> usize

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