Struct VirtualPairCol

pub struct VirtualPairCol<F: Field> { /* private fields */ }

An affine linear combination of columns in a PAIR (Preprocessed AIR).

This structure represents the column V with entries V[j] = Σ(w_i * V_i[j]) + c where:

• w_i are the column weights
• V_i are the columns (either preprocessed or main trace columns)
• c is a constant term

Implementations

impl<F: Field> VirtualPairCol<F>

pub const ONE: Self

A virtual column that always evaluates to the field element 1.

pub const fn new(column_weights: Vec<(PairCol, F)>, constant: F) -> Self

Creates a new virtual column with the specified column weights and constant term.

Arguments

• column_weights - Vector of (column, weight) pairs defining the linear combination
• constant - Constant term to add to the linear combination

pub fn new_preprocessed(column_weights: Vec<(usize, F)>, constant: F) -> Self

Creates a virtual column as a linear combination of preprocessed columns.

Arguments

• column_weights - Vector of (column_index, weight) pairs for preprocessed columns
• constant - Constant term to add to the combination

pub fn new_main(column_weights: Vec<(usize, F)>, constant: F) -> Self

Creates a virtual column as a linear combination of main trace columns.

Arguments

• column_weights - Vector of (column_index, weight) pairs for main trace columns
• constant - Constant term to add to the combination

pub const fn constant(x: F) -> Self

Create a virtual column whose value on every row is equal and constant.

Arguments

• x - The constant field element.

pub fn single(column: PairCol) -> Self

Creates a virtual column equal to a provided column.

Arguments

• column - The column to represent.

pub fn single_preprocessed(column: usize) -> Self

Creates a virtual column equal to a preprocessed column.

Arguments

• column - Index of the preprocessed column

pub fn single_main(column: usize) -> Self

Creates a virtual column equal to a main trace column.

Arguments

• column - Index of the main trace column

pub fn sum_main(columns: Vec<usize>) -> Self

Create a virtual column which is the sum of main trace columns.

Arguments

• columns - Vector of main trace column indices to sum

pub fn sum_preprocessed(columns: Vec<usize>) -> Self

Create a virtual column which is the sum of preprocessed columns.

Arguments

• columns - Vector of preprocessed column indices to sum

pub fn diff_preprocessed(a_col: usize, b_col: usize) -> Self

Create a virtual column which is the difference between two preprocessed columns.

Arguments

• a_col - Index of the minuend preprocessed column.
• b_col - Index of the subtrahend preprocessed column.

pub fn diff_main(a_col: usize, b_col: usize) -> Self

Create a virtual column which is the difference between two main trace columns.

Arguments

• a_col - Index of the minuend main trace column.
• b_col - Index of the subtrahend main trace column.

pub fn apply<Expr, Var>(&self, preprocessed: &[Var], main: &[Var]) -> Expr

where F: Into<Expr>, Expr: PrimeCharacteristicRing + Mul<F, Output = Expr>, Var: Into<Expr> + Copy,

Evaluates the virtual column at a given row by applying the affine linear combination to a pair of preprocessed and main trace rows.

This computes Σ(w_i * column_values[i]) + constant

Arguments

• preprocessed - Row of preprocessed values.
• main - Row of main trace values.

Trait Implementations

impl<F: Clone + Field> Clone for VirtualPairCol<F>

fn clone(&self) -> VirtualPairCol<F>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F: Debug + Field> Debug for VirtualPairCol<F>

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

Formats the value using the given formatter.