Struct ProvenancePoly 

pub struct ProvenancePoly { /* private fields */ }

A provenance polynomial: a finite sum of monomials with natural-number coefficients.

Stored in normal form: monomials with zero coefficient are dropped; like terms are merged.

The empty polynomial is 0 (additive identity). The polynomial {Monomial::one() -> 1} is the multiplicative identity 1.

Custom serde: serialized as a sorted array of {"monomial": ..., "coefficient": n} entries, since JSON objects require string keys.

Implementations

impl ProvenancePoly

pub fn zero() -> Self

Additive identity: the polynomial 0.

pub fn one() -> Self

Multiplicative identity: the polynomial 1.

pub fn singleton(var: impl Into<String>) -> Self

Polynomial consisting of a single variable with coefficient 1.

pub fn from_monomial(monomial: Monomial, coefficient: u64) -> Self

Polynomial consisting of a single monomial with the given coefficient. If the coefficient is 0, returns zero().

pub fn terms(&self) -> impl Iterator<Item = (&Monomial, &u64)>

Iterate (monomial, coefficient) in monomial-sorted order.

pub fn term_count(&self) -> usize

Number of distinct monomials with positive coefficient.

pub fn is_zero(&self) -> bool

Whether this is the additive identity.

pub fn coefficient(&self, monomial: &Monomial) -> u64

Coefficient of a specific monomial, or 0 if not present.

pub fn support(&self) -> BTreeSet<String>

Support: the set of variables appearing in any monomial with positive coefficient.

This is what Theorem 2 bounds under retraction: for any retracted set Y, support(retract(p, Y)) is a subset of support(p).

pub fn insert_term(&mut self, monomial: Monomial, coefficient: u64)

Add a single term in place, merging like monomials.

pub fn retract<S: AsRef<str>>(&self, retracted: &BTreeSet<S>) -> Self

Retract every variable in retracted by the substitution x -> 0. This is the homomorphism rho_Y from docs/THEORY.md Section 6.

Operationally: any monomial containing a retracted variable is dropped. Monomials with no retracted variables are kept with their coefficients unchanged.

Trait Implementations

impl Add<&ProvenancePoly> for &ProvenancePoly

type Output = ProvenancePoly

The resulting type after applying the + operator.

fn add(self, other: &ProvenancePoly) -> ProvenancePoly

Performs the + operation.

impl Add for ProvenancePoly

type Output = ProvenancePoly

The resulting type after applying the + operator.

fn add(self, other: ProvenancePoly) -> ProvenancePoly

Performs the + operation.

impl AddAssign<&ProvenancePoly> for ProvenancePoly

fn add_assign(&mut self, other: &ProvenancePoly)

Performs the += operation.

impl Clone for ProvenancePoly

fn clone(&self) -> ProvenancePoly

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ProvenancePoly

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

Formats the value using the given formatter.

impl Default for ProvenancePoly

fn default() -> ProvenancePoly

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for ProvenancePoly

fn deserialize<D: Deserializer<'de>>(deserializer: D) -> Result<Self, D::Error>

Deserialize this value from the given Serde deserializer.

impl Display for ProvenancePoly

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

Formats the value using the given formatter.

impl Mul<&ProvenancePoly> for &ProvenancePoly

type Output = ProvenancePoly

The resulting type after applying the * operator.

fn mul(self, other: &ProvenancePoly) -> ProvenancePoly

Performs the * operation.

impl Mul for ProvenancePoly

type Output = ProvenancePoly

The resulting type after applying the * operator.

fn mul(self, other: ProvenancePoly) -> ProvenancePoly

Performs the * operation.

impl MulAssign<&ProvenancePoly> for ProvenancePoly

fn mul_assign(&mut self, other: &ProvenancePoly)

Performs the *= operation.

impl PartialEq for ProvenancePoly

fn eq(&self, other: &ProvenancePoly) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for ProvenancePoly

fn serialize<S: Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error>

Serialize this value into the given Serde serializer.

impl Eq for ProvenancePoly

impl StructuralPartialEq for ProvenancePoly