Struct Polynomial 

pub struct Polynomial {
    pub map: BTreeMap<Monomial, Rational>,
}

Uniquely reduced form of a symbolic polynomial expression.

A Laurent polynomial $P_b$ is realized as the sum of products of a Rational coefficient $C_m$ and a primitive Laurent Monomial $M_m$ (i.e., an element of an ordered polynomial basis).

P_b \equiv \sum_m C_m M_m

All operators (e.g., Add, Mul) implemented for Polynomial reduce an arbitrary expression into this unique form.

Fields

map: BTreeMap<Monomial, Rational>

Symbolic storage.

Implementations

impl Polynomial

pub fn one() -> Self

The one.

pub fn is_zero(&self) -> bool

Whether this polynomial is zero.

pub fn is_one(&self) -> bool

Whether this polynomial is one.

pub fn alt(self) -> Self

Extends the symbol space.

pub fn cdm(self, mark: char) -> Self

Appends combining diacritical mark to all symbols.

pub fn swp(self) -> Self

Swaps lowercase and uppercase symbols.

pub fn ops(&self) -> (usize, usize)

Returns the number of (multiplications, additions).

pub fn gcd(&self) -> Rational

GCD of coefficients.

pub fn lcm(&self) -> Rational

LCM of coefficients.

pub fn signed_gcd(&self) -> Rational

GCD and predominant sign of coefficients.

pub fn signed_lcd(&self) -> Rational

LCD and predominant sign of coefficients.

Trait Implementations

impl Add for Polynomial

type Output = Polynomial

The resulting type after applying the + operator.

fn add(self, other: Self) -> Self::Output

Performs the + operation.

impl AddAssign for Polynomial

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl Clone for Polynomial

fn clone(&self) -> Polynomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Polynomial

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

Formats the value using the given formatter.

impl Default for Polynomial

fn default() -> Polynomial

Returns the “default value” for a type.

impl Div<Rational> for Polynomial

type Output = Polynomial

The resulting type after applying the / operator.

fn div(self, other: Rational) -> Self::Output

Performs the / operation.

impl Div<i32> for Polynomial

type Output = Polynomial

The resulting type after applying the / operator.

fn div(self, other: i32) -> Self::Output

Performs the / operation.

impl DivAssign<Rational> for Polynomial

fn div_assign(&mut self, other: Rational)

Performs the /= operation.

impl DivAssign<i32> for Polynomial

fn div_assign(&mut self, other: i32)

Performs the /= operation.

impl From<Factorization> for Polynomial

fn from(f: Factorization) -> Self

Converts to this type from the input type.

impl From<Polynomial> for Factorization

fn from(p: Polynomial) -> Self

Converts to this type from the input type.

impl From<Polynomial> for Tree

fn from(p: Polynomial) -> Self

Converts to this type from the input type.

impl<M, S> FromIterator<M> for Polynomial

where M: IntoIterator<Item = S>, S: Into<Symbol>,

fn from_iter<P: IntoIterator<Item = M>>(iter: P) -> Self

Creates a value from an iterator.

impl Mul<Rational> for Polynomial

type Output = Polynomial

The resulting type after applying the * operator.

fn mul(self, other: Rational) -> Self::Output

Performs the * operation.

impl Mul<i32> for Polynomial

type Output = Polynomial

The resulting type after applying the * operator.

fn mul(self, other: i32) -> Self::Output

Performs the * operation.

impl Mul for Polynomial

type Output = Polynomial

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Self::Output

Performs the * operation.

impl MulAssign<Rational> for Polynomial

fn mul_assign(&mut self, other: Rational)

Performs the *= operation.

impl MulAssign<i32> for Polynomial

fn mul_assign(&mut self, other: i32)

Performs the *= operation.

impl MulAssign for Polynomial

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl Neg for Polynomial

type Output = Polynomial

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for Polynomial

fn cmp(&self, other: &Polynomial) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Polynomial

fn eq(&self, other: &Polynomial) -> 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 PartialOrd for Polynomial

fn partial_cmp(&self, other: &Polynomial) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Sub for Polynomial

type Output = Polynomial

The resulting type after applying the - operator.

fn sub(self, other: Self) -> Self::Output

Performs the - operation.

impl SubAssign for Polynomial

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl Eq for Polynomial

impl StructuralPartialEq for Polynomial