Struct Rational 

pub struct Rational(/* private fields */);

任意精度有理数，规范形见模块文档。

Implementations

impl Rational

pub fn zero() -> Rational

pub fn one() -> Rational

pub fn from_integer(v: &Integer) -> Rational

pub fn from_ints(n: &Integer, d: &Integer) -> Option<Rational>

由整数分子分母构造并规范化；d = 0 返回 None。

pub fn is_zero(&self) -> bool

pub fn is_one(&self) -> bool

pub fn is_negative(&self) -> bool

pub fn sign(&self) -> i32

pub fn num(&self) -> Integer

pub fn den(&self) -> Integer

pub fn neg(&self) -> Rational

pub fn abs(&self) -> Rational

pub fn inv(&self) -> Option<Rational>

乘法逆元；零无逆元。

pub fn add(&self, other: &Rational) -> Rational

pub fn sub(&self, other: &Rational) -> Rational

pub fn mul(&self, other: &Rational) -> Rational

pub fn div(&self, other: &Rational) -> Option<Rational>

有理数相除；除零返回 None。

pub fn pow(&self, exp: u32) -> Rational

非负整数幂。规模守卫由调用方（expr 层）负责。

pub fn pow_reduced(&self, exp: u32) -> Rational

非负整数幂（快速路径）：既约有理数的幂仍既约——gcd(num,den)^m = 1， 无需再跑 gcd。大幂折叠产生几万比特常数时 gcd 是平方级瓶颈 （perf_probe case 1431 实测），此路径跳过它。

落位判定必须与 from_big_parts 一致：分母按 u64 判（不是 i64）， 否则同值出现两种表示，破坏“规范形与表示无关“（29^13 案例实测）。

pub fn to_f64(&self) -> f64

f64 近似（数值交叉验证路径；大数经十进制字符串中转，精度为 f64 语义）。

pub fn inv_reduced(&self) -> Option<Rational>

乘法逆元（快速路径，前提：自身既约——Rational 规范形保证）；零无逆元。 逆元的既约性继承自原数，跳过 gcd。

pub fn cmp_integer(&self, o: &Integer) -> Ordering

与整数比较：self - o 的符号。

Trait Implementations

impl Clone for Rational

fn clone(&self) -> Rational

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Rational

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

Formats the value using the given formatter.

impl Display for Rational

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

Formats the value using the given formatter.

impl Eq for Rational

impl Field for Rational

fn inv(&self) -> Option<Rational>

impl Hash for Rational

fn hash<H>(&self, state: &mut H)

where H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for Rational

fn cmp(&self, other: &Rational) -> 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.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

impl PartialEq for Rational

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Rational

fn partial_cmp(&self, other: &Rational) -> 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 Ring for Rational

fn zero() -> Rational

fn one() -> Rational

fn from_i64_coeff(v: i64) -> Rational

由 i64 构造系数（poly 偏导的指数乘子等用途）。

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

fn sub(&self, other: &Rational) -> Rational

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

fn neg(&self) -> Rational

fn is_zero(&self) -> bool

fn is_one(&self) -> bool

fn pow_u32(&self, e: u32) -> Rational

非负整数幂；默认重复乘，实现方可覆写快速路径。

impl StructuralPartialEq for Rational