Trait zksnark::field::Polynomial

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pub trait Polynomial<T>: From<Vec<T>> + Deref<Target = [T]>where
    T: Field,{
    fn coefficients(&self) -> Vec<T> { ... }
    fn degree(&self) -> usize { ... }
    fn evaluate(&self, x: T) -> T { ... }
    fn remove_leading_zeros(&mut self) { ... }
}

Expand description

A line, Polynomial, represented as a vector of Field elements where the position in the vector determines the power of the exponent.

Remarks

If you want examples of how to implement a Polynomial go to the Z251 module.

The polynomial is represented as a list of coefficients where the powers of “x” are implicit.

For Example: [1, 3, 0, 5] is f(x) = 1 + 3x + 5x^3

Note

use zksnark::field::z251::Z251;
use zksnark::field::*;

// The (*) is overloaded to give you back an array
let tmp = vec![1,2,0,4].into_iter()
                       .map(Z251::from)
                       .collect::<Vec<_>>();

assert_eq!(*tmp, [1.into(),2.into(),0.into(),4.into()]);

Run

Provided Methods§

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fn coefficients(&self) -> Vec<T>

This defines how to turn a Polynomial into a vector of Field. In other words, it gives you back the coefficients of the Polynomial.

However, since Deref is required for Polynomial you may prefer to get the coefficients through an iterator.

Examples

use zksnark::field::z251::Z251;
use zksnark::field::*;

// Get coefficients through an iterator
let poly = vec![1,2,0,4].into_iter()
                        .map(Z251::from)
                        .collect::<Vec<_>>();

let mut iter = poly.iter();

assert_eq!(iter.next(), Some(&Z251::from(1)));

Run

source

fn degree(&self) -> usize

Returns the highest exponent of the polynomial.

Examples

Basic usage:

use zksnark::field::z251::Z251;
use zksnark::field::*;

// [1, 2, 0, 4] would be f(x) = 1 + 2x + 0x^2 + 4x^3
// Thus the degree is 3
assert_eq!(
    vec![1, 2, 0, 4]
        .into_iter()
        .map(Z251::from)
        .collect::<Vec<_>>()
        .degree(),
    3
);
// [1, 1, 1, 1, 9] would be f(x) = 1 + x + x^2 + x^3 + 9x^4
// Thus the degree is 4
assert_eq!(
    vec![1, 1, 1, 1, 9]
        .into_iter()
        .map(Z251::from)
        .collect::<Vec<_>>()
        .degree(),
    4
);

Run

source

fn evaluate(&self, x: T) -> T

Takes the polynomial and evaluates it at the specified value.

Examples

Basic usage:

use zksnark::field::z251::Z251;
use zksnark::field::*;

// [1, 1, 1] would be f(x) = 1 + x + x^2 thus f(2) = 1 + 2 + 2^2
assert_eq!(
   vec![1, 1, 1]
       .into_iter()
       .map(Z251::from)
       .collect::<Vec<_>>()
       .evaluate(Z251::from(2)),
   Z251::from(7)
);
// [1, 1, 4] would be f(x) = 1 + x + 4x^2 thus f(2) = 1 + 2 + 4*2^2
assert_eq!(
    vec![1, 1, 4]
        .into_iter()
        .map(Z251::from)
        .collect::<Vec<_>>()
        .evaluate(Z251::from(2)),
    Z251::from(19)
);

// (1, 2, 3, 4) would be f(x) = 1 + 2x + 3x^2 + 4x^3
// thus f(3) = 1 + 2 * 3 + 3 * 3^2 + 4 * 3^3
assert_eq!(
    (1..5)
        .map(Z251::from)
        .collect::<Vec<_>>()
        .evaluate(Z251::from(3)),
    Z251::from(142)
);