Struct Polynomial

pub struct Polynomial<T> { /* private fields */ }

多项式

Implementations

impl<T: Clone> Polynomial<T>

pub fn new(coe: &Vec<T>) -> Self

pub fn get_coe(&self) -> &Vec<T>

pub fn get_coe_mut(&mut self) -> &mut Vec<T>

pub fn multiply_by<U, V>(&self, num: U, degree: usize) -> Polynomial<V>

where T: Mul<U, Output = V>, U: Clone, V: Clone + Zero,

(ax^2+bx-c).multiply_by(d, e) => adx^(2+e)+bdx^(1+e)-cdx^e

pub fn multiply_left_by<U, V>(&self, num: U, degree: usize) -> Polynomial<V>

where U: Clone + Mul<T, Output = V>, V: Clone + Zero,

(ax^2+bx-c).multiply_left_by(d, e) => dax^(2+e)+dbx^(1+e)-dcx^e

pub fn divide_by<U, V>(&self, num: U) -> Polynomial<V>

where T: Div<U, Output = V>, U: Clone, V: Clone,

(ax^2+bx-c).divide_by(d) => a/dx^2+b/dx-c/d

pub fn divide_left_by<U, V>(&self, num: U) -> Polynomial<V>

where T: DivLeft<U, Output = V>, U: Clone, V: Clone,

(ax^2+bx-c).divide_left_by(d) => a\dx^2+b\dx-c\d

pub fn value<U, V>(&self, num: U) -> V

where T: Mul<U, Output = V>, U: Clone + Mul<Output = U> + One, V: Clone + Add<Output = V>,

(ax^2+bx+c).value(n) = an^2+bn+c

pub fn value_left<U, V>(&self, num: U) -> V

where U: Clone + Mul<Output = U> + Mul<T, Output = V> + One, V: Clone + Add<Output = V>,

(ax^2+bx+c).value_left(n) = n^2a+nb+c

impl<T: Clone + Zero> Polynomial<T>

pub fn adjust(&self) -> Self

(0x^3+2x^2-4).adjust() = 2x^2-4

pub fn similar_adjust(&self, precision: f64) -> Self

((3e-8)x^3+(1e-3)x^2-(2e-8)x+3).similar_adjust(1e-6) = (1e-3)x^2-(2e-8)x+3

impl<T> Polynomial<T>

where T: Clone + Div<Output = T> + Sub<Output = T> + Mul<Output = T> + Add<Output = T> + Zero + One + PartialEq,

pub fn gcd(&self, other: &Self) -> Self

pub fn gcde(&self, other: &Self) -> (Self, Self, Self)

返回(gcd, x, y)使得 self * x + other * y = self.gcd(other)

pub fn similar_gcd(&self, other: &Self, precision: f64) -> Self

pub fn similar_gcde(&self, other: &Self, precision: f64) -> (Self, Self, Self)

impl Polynomial<Fraction>

pub fn primitive(&self) -> Polynomial<i128>

有理数多项式的本原化

impl Polynomial<i8>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<i16>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<i32>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<i64>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<i128>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<isize>

pub fn rational_roots(&self) -> Vec<Fraction>

求所有有理根

impl Polynomial<f64>

pub fn derived(&self) -> Polynomial<f64>

求导

pub fn integral(&self) -> Polynomial<f64>

积分

pub fn real_roots(&self, x_precision: f64, y_precision: f64) -> Vec<f64>

求所有实数根

Trait Implementations

impl<T, U, V> Add<Polynomial<U>> for Polynomial<T>

where T: Clone + Add<U, Output = V> + Zero, U: Clone + Zero, V: Clone,

type Output = Polynomial<V>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Clone> Clone for Polynomial<T>

fn clone(&self) -> Polynomial<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Con> Con for Polynomial<T>

where <T as Con>::Output: Clone,

type Output = Polynomial<<T as Con>::Output>

fn con(&self) -> Self::Output

where <T as Con>::Output: Clone,

impl<T: Debug> Debug for Polynomial<T>

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

Formats the value using the given formatter.

impl<T: Display> Display for Polynomial<T>

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

Formats the value using the given formatter.

impl<T, U, V> Div<Polynomial<U>> for Polynomial<T>

where T: Clone + Div<U, Output = V> + Sub<Output = T> + Zero + PartialEq, U: Clone + Mul<V, Output = T> + Zero, V: Clone + Zero,

type Output = (Polynomial<V>, Polynomial<T>)

The resulting type after applying the / operator.

fn div(self, other: Polynomial<U>) -> Self::Output

Performs the / operation.

impl<T, U, V> DivLeft<Polynomial<U>> for Polynomial<T>

where T: Clone + DivLeft<U, Output = V> + Sub<Output = T> + Zero + PartialEq, U: Clone + Zero, V: Clone + Mul<U, Output = T> + Zero,

type Output = (Polynomial<V>, Polynomial<T>)

fn div_left(&self, other: &Polynomial<U>) -> Self::Output

impl<T: Latex> Latex for Polynomial<T>

fn latex(&self) -> String

impl<T, U, V> Mul<Polynomial<U>> for Polynomial<T>

where T: Clone + Mul<U, Output = V>, U: Clone, V: Clone + Add<Output = V>,

type Output = Polynomial<V>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: Neg> Neg for Polynomial<T>

where <T as Neg>::Output: Clone,

type Output = Polynomial<<T as Neg>::Output>

fn neg(&self) -> Self::Output

where <T as Neg>::Output: Clone,

impl<T: Clone + One + Zero + PartialEq> One for Polynomial<T>

fn get_one(&self) -> Self

fn eq_one(&self) -> bool

fn similar_one(&self, precision: f64) -> bool

impl<T: PartialEq> PartialEq for Polynomial<T>

fn eq(&self, other: &Self) -> 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<T: Clone + Mul<Output = T> + Add<Output = T> + One + Zero + PartialEq> Pow for Polynomial<T>

type Output = Polynomial<T>

fn pow(&self, power: u32) -> Self::Output

impl<T, U, V> Rem<Polynomial<U>> for Polynomial<T>

where T: Clone + Div<U, Output = V> + Sub<Output = T> + Zero + PartialEq, U: Clone + Mul<V, Output = T> + Zero, V: Clone + Zero,

type Output = Polynomial<T>

The resulting type after applying the % operator.

fn rem(self, other: Polynomial<U>) -> Self::Output

Performs the % operation.

impl<T: Similar> Similar for Polynomial<T>

fn similar(&self, other: &Self, precision: f64) -> bool

impl<T, U, V> Sub<Polynomial<U>> for Polynomial<T>

where T: Clone + Sub<U, Output = V> + Zero, U: Clone + Zero, V: Clone,

type Output = Polynomial<V>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: Clone + Add<Output = T> + Zero> Sum for Polynomial<T>

fn sum<U>(iter: U) -> Self

where U: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T: Clone + Zero + PartialEq> Zero for Polynomial<T>

fn get_zero(&self) -> Self

fn eq_zero(&self) -> bool

fn similar_zero(&self, precision: f64) -> bool

impl<T: Eq> Eq for Polynomial<T>