Struct Polynomial

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

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impl<T: Display + One + Zero + PartialEq> Polynomial<T>

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pub fn to_display<'a, 'b>( &'b self, variable: &'a str, ) -> DisplayPolynomial<'a, 'b, T>

Examples found in repository?
examples/basic.rs (line 10)
4fn main() {
5	let a = Polynomial::new(coefficients![1f32, 2.0, 3.0, 0.0]);
6	let b = Polynomial::new(coefficients![1f32, 0.0, 1.0]);
7	let (q, r) = a.div_rem(&b);
8	println!(
9		"({0}) / ({1}) = ({1}) * ({2}) + {3}",
10		a.to_display("ω"),
11		b.to_display("ω"),
12		q.to_display("ω"),
13		r.to_display("ω")
14	);
15
16	let x = Complex::new(0f32, 1.0);
17	let e = a.eval(x);
18	println!("{} = {} for x = {}", a.to_display("x"), e, x);
19
20	let d = a.eval_der(1f32, 2);
21	println!("({})'' = {} for z = {}", a.to_display("z"), d, 1f32);
22}
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impl<T> Polynomial<T>

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pub fn order(&self) -> i32

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pub fn reverse_coeffs(&self) -> &SmallVec<[T; 8]>

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pub fn into_coeffs(self) -> SmallVec<[T; 8]>

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pub fn into_reverse_coeffs(self) -> SmallVec<[T; 8]>

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pub fn coeffs(&self) -> SmallVec<[T; 8]>
where T: Clone,

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pub fn new(coefficients: SmallVec<[T; 8]>) -> Self
where T: Zero,

Examples found in repository?
examples/basic.rs (line 5)
4fn main() {
5	let a = Polynomial::new(coefficients![1f32, 2.0, 3.0, 0.0]);
6	let b = Polynomial::new(coefficients![1f32, 0.0, 1.0]);
7	let (q, r) = a.div_rem(&b);
8	println!(
9		"({0}) / ({1}) = ({1}) * ({2}) + {3}",
10		a.to_display("ω"),
11		b.to_display("ω"),
12		q.to_display("ω"),
13		r.to_display("ω")
14	);
15
16	let x = Complex::new(0f32, 1.0);
17	let e = a.eval(x);
18	println!("{} = {} for x = {}", a.to_display("x"), e, x);
19
20	let d = a.eval_der(1f32, 2);
21	println!("({})'' = {} for z = {}", a.to_display("z"), d, 1f32);
22}
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pub fn new_reversed(rev_coeffs: SmallVec<[T; 8]>) -> Self
where T: Zero,

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pub fn eval<X, Y>(&self, x: X) -> Y
where T: Zero, for<'l, 'r> &'l T: Mul<&'r X, Output = Y>, X: for<'r> MulAssign<&'r X> + One, Y: AddAssign + Zero,

Examples found in repository?
examples/basic.rs (line 17)
4fn main() {
5	let a = Polynomial::new(coefficients![1f32, 2.0, 3.0, 0.0]);
6	let b = Polynomial::new(coefficients![1f32, 0.0, 1.0]);
7	let (q, r) = a.div_rem(&b);
8	println!(
9		"({0}) / ({1}) = ({1}) * ({2}) + {3}",
10		a.to_display("ω"),
11		b.to_display("ω"),
12		q.to_display("ω"),
13		r.to_display("ω")
14	);
15
16	let x = Complex::new(0f32, 1.0);
17	let e = a.eval(x);
18	println!("{} = {} for x = {}", a.to_display("x"), e, x);
19
20	let d = a.eval_der(1f32, 2);
21	println!("({})'' = {} for z = {}", a.to_display("z"), d, 1f32);
22}
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pub fn eval_precise<X, Y>(&self, x: X) -> Y
where T: Zero + Clone + Into<Y>, for<'l> &'l X: Pow<i32, Output = X>, Y: MulAddAssign<X, Y> + Zero, for<'l> &'l T: Mul<X, Output = Y>,

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pub fn eval_der<X, Y>(&self, x: X, n: i32) -> Y
where T: Zero + FromPrimitive + for<'r> Mul<&'r X, Output = Y>, for<'l> &'l T: Mul<T, Output = T>, X: for<'r> MulAssign<&'r X> + One, Y: AddAssign + Zero,

Examples found in repository?
examples/basic.rs (line 20)
4fn main() {
5	let a = Polynomial::new(coefficients![1f32, 2.0, 3.0, 0.0]);
6	let b = Polynomial::new(coefficients![1f32, 0.0, 1.0]);
7	let (q, r) = a.div_rem(&b);
8	println!(
9		"({0}) / ({1}) = ({1}) * ({2}) + {3}",
10		a.to_display("ω"),
11		b.to_display("ω"),
12		q.to_display("ω"),
13		r.to_display("ω")
14	);
15
16	let x = Complex::new(0f32, 1.0);
17	let e = a.eval(x);
18	println!("{} = {} for x = {}", a.to_display("x"), e, x);
19
20	let d = a.eval_der(1f32, 2);
21	println!("({})'' = {} for z = {}", a.to_display("z"), d, 1f32);
22}
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pub fn eval_der_precise<X, Y>(&self, x: X, n: i32) -> Y
where T: Zero + FromPrimitive + Into<Y>, for<'l, 'l> &'l T: Mul<T, Output = T> + Mul<X, Output = Y>, for<'l> &'l X: Pow<i32, Output = X>, Y: MulAddAssign<X, Y> + Zero + Clone,

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pub fn div_rem(&self, rhs: &Self) -> (Self, Self)
where T: Zero + Clone + for<'r> AddAssign<&'r T> + SubAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T> + Div<&'r T, Output = T>,

Examples found in repository?
examples/basic.rs (line 7)
4fn main() {
5	let a = Polynomial::new(coefficients![1f32, 2.0, 3.0, 0.0]);
6	let b = Polynomial::new(coefficients![1f32, 0.0, 1.0]);
7	let (q, r) = a.div_rem(&b);
8	println!(
9		"({0}) / ({1}) = ({1}) * ({2}) + {3}",
10		a.to_display("ω"),
11		b.to_display("ω"),
12		q.to_display("ω"),
13		r.to_display("ω")
14	);
15
16	let x = Complex::new(0f32, 1.0);
17	let e = a.eval(x);
18	println!("{} = {} for x = {}", a.to_display("x"), e, x);
19
20	let d = a.eval_der(1f32, 2);
21	println!("({})'' = {} for z = {}", a.to_display("z"), d, 1f32);
22}

Trait Implementations§

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impl<T> Add<&Polynomial<T>> for &Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero + Clone,

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type Output = Polynomial<T>

The resulting type after applying the + operator.
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fn add(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the + operation. Read more
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impl<T> Add<&Polynomial<T>> for Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the + operator.
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fn add(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the + operation. Read more
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impl<T> Add<Polynomial<T>> for &Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the + operator.
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fn add(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the + operation. Read more
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impl<T> Add for Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the + operator.
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fn add(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the + operation. Read more
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impl<T> AddAssign<&Polynomial<T>> for Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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fn add_assign(&mut self, rhs: &Polynomial<T>)

Performs the += operation. Read more
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impl<T> AddAssign for Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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fn add_assign(&mut self, rhs: Polynomial<T>)

Performs the += operation. Read more
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impl<T: Clone> Clone for Polynomial<T>

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<T: Debug> Debug for Polynomial<T>

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

Formats the value using the given formatter. Read more
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impl Mul<&Polynomial<BigInt>> for &BigInt

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type Output = Polynomial<BigInt>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigInt>) -> Polynomial<BigInt>

Performs the * operation. Read more
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impl Mul<&Polynomial<BigInt>> for BigInt

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type Output = Polynomial<BigInt>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigInt>) -> Polynomial<BigInt>

Performs the * operation. Read more
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impl Mul<&Polynomial<BigUint>> for &BigUint

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type Output = Polynomial<BigUint>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigUint>) -> Polynomial<BigUint>

Performs the * operation. Read more
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impl Mul<&Polynomial<BigUint>> for BigUint

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type Output = Polynomial<BigUint>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigUint>) -> Polynomial<BigUint>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<f32>>> for &Complex<f32>

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type Output = Polynomial<Complex<f32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<f32>>) -> Polynomial<Complex<f32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<f32>>> for Complex<f32>

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type Output = Polynomial<Complex<f32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<f32>>) -> Polynomial<Complex<f32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<f64>>> for &Complex<f64>

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type Output = Polynomial<Complex<f64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<f64>>) -> Polynomial<Complex<f64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<f64>>> for Complex<f64>

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type Output = Polynomial<Complex<f64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<f64>>) -> Polynomial<Complex<f64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i16>>> for &Complex<i16>

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type Output = Polynomial<Complex<i16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i16>>) -> Polynomial<Complex<i16>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i16>>> for Complex<i16>

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type Output = Polynomial<Complex<i16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i16>>) -> Polynomial<Complex<i16>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i32>>> for &Complex<i32>

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type Output = Polynomial<Complex<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i32>>) -> Polynomial<Complex<i32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i32>>> for Complex<i32>

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type Output = Polynomial<Complex<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i32>>) -> Polynomial<Complex<i32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i64>>> for &Complex<i64>

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type Output = Polynomial<Complex<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i64>>) -> Polynomial<Complex<i64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i64>>> for Complex<i64>

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type Output = Polynomial<Complex<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i64>>) -> Polynomial<Complex<i64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i8>>> for &Complex<i8>

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type Output = Polynomial<Complex<i8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i8>>) -> Polynomial<Complex<i8>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<i8>>> for Complex<i8>

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type Output = Polynomial<Complex<i8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<i8>>) -> Polynomial<Complex<i8>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<isize>>> for &Complex<isize>

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type Output = Polynomial<Complex<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<isize>>) -> Polynomial<Complex<isize>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<isize>>> for Complex<isize>

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type Output = Polynomial<Complex<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<isize>>) -> Polynomial<Complex<isize>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u16>>> for &Complex<u16>

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type Output = Polynomial<Complex<u16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u16>>) -> Polynomial<Complex<u16>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u16>>> for Complex<u16>

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type Output = Polynomial<Complex<u16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u16>>) -> Polynomial<Complex<u16>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u32>>> for &Complex<u32>

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type Output = Polynomial<Complex<u32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u32>>) -> Polynomial<Complex<u32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u32>>> for Complex<u32>

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type Output = Polynomial<Complex<u32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u32>>) -> Polynomial<Complex<u32>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u64>>> for &Complex<u64>

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type Output = Polynomial<Complex<u64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u64>>) -> Polynomial<Complex<u64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u64>>> for Complex<u64>

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type Output = Polynomial<Complex<u64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u64>>) -> Polynomial<Complex<u64>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u8>>> for &Complex<u8>

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type Output = Polynomial<Complex<u8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u8>>) -> Polynomial<Complex<u8>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<u8>>> for Complex<u8>

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type Output = Polynomial<Complex<u8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<u8>>) -> Polynomial<Complex<u8>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<usize>>> for &Complex<usize>

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type Output = Polynomial<Complex<usize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<usize>>) -> Polynomial<Complex<usize>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Complex<usize>>> for Complex<usize>

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type Output = Polynomial<Complex<usize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Complex<usize>>) -> Polynomial<Complex<usize>>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<BigInt>>> for &BigRational

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type Output = Polynomial<Ratio<BigInt>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigRational>) -> Polynomial<BigRational>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<BigInt>>> for BigRational

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type Output = Polynomial<Ratio<BigInt>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<BigRational>) -> Polynomial<BigRational>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<i32>>> for &Rational32

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type Output = Polynomial<Ratio<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational32>) -> Polynomial<Rational32>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<i32>>> for Rational32

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type Output = Polynomial<Ratio<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational32>) -> Polynomial<Rational32>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<i64>>> for &Rational64

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type Output = Polynomial<Ratio<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational64>) -> Polynomial<Rational64>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<i64>>> for Rational64

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type Output = Polynomial<Ratio<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational64>) -> Polynomial<Rational64>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<isize>>> for &Rational

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type Output = Polynomial<Ratio<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational>) -> Polynomial<Rational>

Performs the * operation. Read more
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impl Mul<&Polynomial<Ratio<isize>>> for Rational

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type Output = Polynomial<Ratio<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<Rational>) -> Polynomial<Rational>

Performs the * operation. Read more
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impl<T> Mul<&Polynomial<T>> for &Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the * operation. Read more
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impl<T> Mul<&Polynomial<T>> for Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the * operation. Read more
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impl Mul<&Polynomial<f32>> for &f32

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type Output = Polynomial<f32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<f32>) -> Polynomial<f32>

Performs the * operation. Read more
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impl Mul<&Polynomial<f32>> for f32

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type Output = Polynomial<f32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<f32>) -> Polynomial<f32>

Performs the * operation. Read more
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impl Mul<&Polynomial<f64>> for &f64

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type Output = Polynomial<f64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<f64>) -> Polynomial<f64>

Performs the * operation. Read more
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impl Mul<&Polynomial<f64>> for f64

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type Output = Polynomial<f64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<f64>) -> Polynomial<f64>

Performs the * operation. Read more
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impl Mul<&Polynomial<i16>> for &i16

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type Output = Polynomial<i16>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i16>) -> Polynomial<i16>

Performs the * operation. Read more
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impl Mul<&Polynomial<i16>> for i16

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type Output = Polynomial<i16>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i16>) -> Polynomial<i16>

Performs the * operation. Read more
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impl Mul<&Polynomial<i32>> for &i32

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type Output = Polynomial<i32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i32>) -> Polynomial<i32>

Performs the * operation. Read more
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impl Mul<&Polynomial<i32>> for i32

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type Output = Polynomial<i32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i32>) -> Polynomial<i32>

Performs the * operation. Read more
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impl Mul<&Polynomial<i64>> for &i64

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type Output = Polynomial<i64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i64>) -> Polynomial<i64>

Performs the * operation. Read more
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impl Mul<&Polynomial<i64>> for i64

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type Output = Polynomial<i64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i64>) -> Polynomial<i64>

Performs the * operation. Read more
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impl Mul<&Polynomial<i8>> for &i8

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type Output = Polynomial<i8>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i8>) -> Polynomial<i8>

Performs the * operation. Read more
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impl Mul<&Polynomial<i8>> for i8

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type Output = Polynomial<i8>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<i8>) -> Polynomial<i8>

Performs the * operation. Read more
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impl Mul<&Polynomial<isize>> for &isize

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type Output = Polynomial<isize>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<isize>) -> Polynomial<isize>

Performs the * operation. Read more
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impl Mul<&Polynomial<isize>> for isize

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type Output = Polynomial<isize>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<isize>) -> Polynomial<isize>

Performs the * operation. Read more
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impl Mul<&Polynomial<u16>> for &u16

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type Output = Polynomial<u16>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u16>) -> Polynomial<u16>

Performs the * operation. Read more
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impl Mul<&Polynomial<u16>> for u16

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type Output = Polynomial<u16>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u16>) -> Polynomial<u16>

Performs the * operation. Read more
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impl Mul<&Polynomial<u32>> for &u32

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type Output = Polynomial<u32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u32>) -> Polynomial<u32>

Performs the * operation. Read more
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impl Mul<&Polynomial<u32>> for u32

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type Output = Polynomial<u32>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u32>) -> Polynomial<u32>

Performs the * operation. Read more
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impl Mul<&Polynomial<u64>> for &u64

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type Output = Polynomial<u64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u64>) -> Polynomial<u64>

Performs the * operation. Read more
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impl Mul<&Polynomial<u64>> for u64

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type Output = Polynomial<u64>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u64>) -> Polynomial<u64>

Performs the * operation. Read more
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impl Mul<&Polynomial<u8>> for &u8

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type Output = Polynomial<u8>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u8>) -> Polynomial<u8>

Performs the * operation. Read more
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impl Mul<&Polynomial<u8>> for u8

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type Output = Polynomial<u8>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<u8>) -> Polynomial<u8>

Performs the * operation. Read more
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impl Mul<&Polynomial<usize>> for &usize

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type Output = Polynomial<usize>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<usize>) -> Polynomial<usize>

Performs the * operation. Read more
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impl Mul<&Polynomial<usize>> for usize

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type Output = Polynomial<usize>

The resulting type after applying the * operator.
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fn mul(self, rhs: &Polynomial<usize>) -> Polynomial<usize>

Performs the * operation. Read more
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impl<T> Mul<&T> for &Polynomial<T>
where T: Zero, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &T) -> Polynomial<T>

Performs the * operation. Read more
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impl<T> Mul<&T> for Polynomial<T>
where T: for<'r> Mul<&'r T, Output = T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: &T) -> Polynomial<T>

Performs the * operation. Read more
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impl Mul<Polynomial<BigInt>> for &BigInt

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type Output = Polynomial<BigInt>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigInt>) -> Polynomial<BigInt>

Performs the * operation. Read more
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impl Mul<Polynomial<BigInt>> for BigInt

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type Output = Polynomial<BigInt>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigInt>) -> Polynomial<BigInt>

Performs the * operation. Read more
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impl Mul<Polynomial<BigUint>> for &BigUint

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type Output = Polynomial<BigUint>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigUint>) -> Polynomial<BigUint>

Performs the * operation. Read more
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impl Mul<Polynomial<BigUint>> for BigUint

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type Output = Polynomial<BigUint>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigUint>) -> Polynomial<BigUint>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<f32>>> for &Complex<f32>

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type Output = Polynomial<Complex<f32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<f32>>) -> Polynomial<Complex<f32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<f32>>> for Complex<f32>

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type Output = Polynomial<Complex<f32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<f32>>) -> Polynomial<Complex<f32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<f64>>> for &Complex<f64>

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type Output = Polynomial<Complex<f64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<f64>>) -> Polynomial<Complex<f64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<f64>>> for Complex<f64>

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type Output = Polynomial<Complex<f64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<f64>>) -> Polynomial<Complex<f64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i16>>> for &Complex<i16>

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type Output = Polynomial<Complex<i16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i16>>) -> Polynomial<Complex<i16>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i16>>> for Complex<i16>

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type Output = Polynomial<Complex<i16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i16>>) -> Polynomial<Complex<i16>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i32>>> for &Complex<i32>

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type Output = Polynomial<Complex<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i32>>) -> Polynomial<Complex<i32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i32>>> for Complex<i32>

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type Output = Polynomial<Complex<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i32>>) -> Polynomial<Complex<i32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i64>>> for &Complex<i64>

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type Output = Polynomial<Complex<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i64>>) -> Polynomial<Complex<i64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i64>>> for Complex<i64>

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type Output = Polynomial<Complex<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i64>>) -> Polynomial<Complex<i64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i8>>> for &Complex<i8>

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type Output = Polynomial<Complex<i8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i8>>) -> Polynomial<Complex<i8>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<i8>>> for Complex<i8>

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type Output = Polynomial<Complex<i8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<i8>>) -> Polynomial<Complex<i8>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<isize>>> for &Complex<isize>

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type Output = Polynomial<Complex<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<isize>>) -> Polynomial<Complex<isize>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<isize>>> for Complex<isize>

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type Output = Polynomial<Complex<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<isize>>) -> Polynomial<Complex<isize>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u16>>> for &Complex<u16>

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type Output = Polynomial<Complex<u16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u16>>) -> Polynomial<Complex<u16>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u16>>> for Complex<u16>

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type Output = Polynomial<Complex<u16>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u16>>) -> Polynomial<Complex<u16>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u32>>> for &Complex<u32>

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type Output = Polynomial<Complex<u32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u32>>) -> Polynomial<Complex<u32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u32>>> for Complex<u32>

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type Output = Polynomial<Complex<u32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u32>>) -> Polynomial<Complex<u32>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u64>>> for &Complex<u64>

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type Output = Polynomial<Complex<u64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u64>>) -> Polynomial<Complex<u64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u64>>> for Complex<u64>

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type Output = Polynomial<Complex<u64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u64>>) -> Polynomial<Complex<u64>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u8>>> for &Complex<u8>

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type Output = Polynomial<Complex<u8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u8>>) -> Polynomial<Complex<u8>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<u8>>> for Complex<u8>

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type Output = Polynomial<Complex<u8>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<u8>>) -> Polynomial<Complex<u8>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<usize>>> for &Complex<usize>

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type Output = Polynomial<Complex<usize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<usize>>) -> Polynomial<Complex<usize>>

Performs the * operation. Read more
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impl Mul<Polynomial<Complex<usize>>> for Complex<usize>

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type Output = Polynomial<Complex<usize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Complex<usize>>) -> Polynomial<Complex<usize>>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<BigInt>>> for &BigRational

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type Output = Polynomial<Ratio<BigInt>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigRational>) -> Polynomial<BigRational>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<BigInt>>> for BigRational

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type Output = Polynomial<Ratio<BigInt>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<BigRational>) -> Polynomial<BigRational>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<i32>>> for &Rational32

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type Output = Polynomial<Ratio<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational32>) -> Polynomial<Rational32>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<i32>>> for Rational32

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type Output = Polynomial<Ratio<i32>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational32>) -> Polynomial<Rational32>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<i64>>> for &Rational64

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type Output = Polynomial<Ratio<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational64>) -> Polynomial<Rational64>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<i64>>> for Rational64

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type Output = Polynomial<Ratio<i64>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational64>) -> Polynomial<Rational64>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<isize>>> for &Rational

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type Output = Polynomial<Ratio<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational>) -> Polynomial<Rational>

Performs the * operation. Read more
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impl Mul<Polynomial<Ratio<isize>>> for Rational

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type Output = Polynomial<Ratio<isize>>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<Rational>) -> Polynomial<Rational>

Performs the * operation. Read more
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impl<T> Mul<Polynomial<T>> for &Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the * operation. Read more
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impl Mul<Polynomial<f32>> for &f32

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type Output = Polynomial<f32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<f32>) -> Polynomial<f32>

Performs the * operation. Read more
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impl Mul<Polynomial<f32>> for f32

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type Output = Polynomial<f32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<f32>) -> Polynomial<f32>

Performs the * operation. Read more
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impl Mul<Polynomial<f64>> for &f64

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type Output = Polynomial<f64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<f64>) -> Polynomial<f64>

Performs the * operation. Read more
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impl Mul<Polynomial<f64>> for f64

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type Output = Polynomial<f64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<f64>) -> Polynomial<f64>

Performs the * operation. Read more
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impl Mul<Polynomial<i16>> for &i16

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type Output = Polynomial<i16>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i16>) -> Polynomial<i16>

Performs the * operation. Read more
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impl Mul<Polynomial<i16>> for i16

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type Output = Polynomial<i16>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i16>) -> Polynomial<i16>

Performs the * operation. Read more
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impl Mul<Polynomial<i32>> for &i32

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type Output = Polynomial<i32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i32>) -> Polynomial<i32>

Performs the * operation. Read more
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impl Mul<Polynomial<i32>> for i32

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type Output = Polynomial<i32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i32>) -> Polynomial<i32>

Performs the * operation. Read more
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impl Mul<Polynomial<i64>> for &i64

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type Output = Polynomial<i64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i64>) -> Polynomial<i64>

Performs the * operation. Read more
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impl Mul<Polynomial<i64>> for i64

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type Output = Polynomial<i64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i64>) -> Polynomial<i64>

Performs the * operation. Read more
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impl Mul<Polynomial<i8>> for &i8

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type Output = Polynomial<i8>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i8>) -> Polynomial<i8>

Performs the * operation. Read more
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impl Mul<Polynomial<i8>> for i8

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type Output = Polynomial<i8>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<i8>) -> Polynomial<i8>

Performs the * operation. Read more
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impl Mul<Polynomial<isize>> for &isize

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type Output = Polynomial<isize>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<isize>) -> Polynomial<isize>

Performs the * operation. Read more
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impl Mul<Polynomial<isize>> for isize

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type Output = Polynomial<isize>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<isize>) -> Polynomial<isize>

Performs the * operation. Read more
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impl Mul<Polynomial<u16>> for &u16

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type Output = Polynomial<u16>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u16>) -> Polynomial<u16>

Performs the * operation. Read more
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impl Mul<Polynomial<u16>> for u16

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type Output = Polynomial<u16>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u16>) -> Polynomial<u16>

Performs the * operation. Read more
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impl Mul<Polynomial<u32>> for &u32

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type Output = Polynomial<u32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u32>) -> Polynomial<u32>

Performs the * operation. Read more
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impl Mul<Polynomial<u32>> for u32

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type Output = Polynomial<u32>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u32>) -> Polynomial<u32>

Performs the * operation. Read more
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impl Mul<Polynomial<u64>> for &u64

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type Output = Polynomial<u64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u64>) -> Polynomial<u64>

Performs the * operation. Read more
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impl Mul<Polynomial<u64>> for u64

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type Output = Polynomial<u64>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u64>) -> Polynomial<u64>

Performs the * operation. Read more
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impl Mul<Polynomial<u8>> for &u8

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type Output = Polynomial<u8>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u8>) -> Polynomial<u8>

Performs the * operation. Read more
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impl Mul<Polynomial<u8>> for u8

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type Output = Polynomial<u8>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<u8>) -> Polynomial<u8>

Performs the * operation. Read more
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impl Mul<Polynomial<usize>> for &usize

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type Output = Polynomial<usize>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<usize>) -> Polynomial<usize>

Performs the * operation. Read more
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impl Mul<Polynomial<usize>> for usize

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type Output = Polynomial<usize>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<usize>) -> Polynomial<usize>

Performs the * operation. Read more
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impl<T> Mul<T> for &Polynomial<T>
where T: Zero, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: T) -> Polynomial<T>

Performs the * operation. Read more
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impl<T> Mul<T> for Polynomial<T>
where T: for<'r> Mul<&'r T, Output = T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: T) -> Polynomial<T>

Performs the * operation. Read more
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impl<T> Mul for Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the * operator.
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fn mul(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the * operation. Read more
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impl<T> MulAssign<&Polynomial<T>> for Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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fn mul_assign(&mut self, rhs: &Polynomial<T>)

Performs the *= operation. Read more
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impl<T> MulAssign for Polynomial<T>
where T: Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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fn mul_assign(&mut self, rhs: Polynomial<T>)

Performs the *= operation. Read more
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impl<T> Neg for &Polynomial<T>
where T: Zero, for<'l> &'l T: Neg<Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn neg(self) -> Polynomial<T>

Performs the unary - operation. Read more
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impl<T> Neg for Polynomial<T>
where T: Zero, for<'l> &'l T: Neg<Output = T>,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn neg(self) -> Polynomial<T>

Performs the unary - operation. Read more
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impl<T> One for Polynomial<T>
where T: One + Zero + AddAssign, for<'l, 'r> &'l T: Mul<&'r T, Output = T>,

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fn one() -> Self

Returns the multiplicative identity element of Self, 1. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl<T: Ord> Ord for Polynomial<T>

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

This method returns an Ordering between self and other. Read more
1.21.0 · Source§

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

Compares and returns the maximum of two values. Read more
1.21.0 · Source§

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

Compares and returns the minimum of two values. Read more
1.50.0 · Source§

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

Restrict a value to a certain interval. Read more
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impl<T: PartialEq> PartialEq for Polynomial<T>

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fn eq(&self, other: &Polynomial<T>) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<T: PartialOrd> PartialOrd for Polynomial<T>

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

This method returns an ordering between self and other values if one exists. Read more
1.0.0 · Source§

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

Tests less than (for self and other) and is used by the < operator. Read more
1.0.0 · Source§

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

Tests less than or equal to (for self and other) and is used by the <= operator. Read more
1.0.0 · Source§

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

Tests greater than (for self and other) and is used by the > operator. Read more
1.0.0 · Source§

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

Tests greater than or equal to (for self and other) and is used by the >= operator. Read more
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impl<T> Sub<&Polynomial<T>> for &Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero + Clone,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the - operation. Read more
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impl<T> Sub<&Polynomial<T>> for Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: &Polynomial<T>) -> Polynomial<T>

Performs the - operation. Read more
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impl<T> Sub<Polynomial<T>> for &Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero + Clone,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the - operation. Read more
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impl<T> Sub for Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero,

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type Output = Polynomial<T>

The resulting type after applying the - operator.
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fn sub(self, rhs: Polynomial<T>) -> Polynomial<T>

Performs the - operation. Read more
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impl<T> SubAssign<&Polynomial<T>> for Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero,

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fn sub_assign(&mut self, rhs: &Polynomial<T>)

Performs the -= operation. Read more
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impl<T> SubAssign for Polynomial<T>
where T: for<'r> SubAssign<&'r T> + Zero,

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fn sub_assign(&mut self, rhs: Polynomial<T>)

Performs the -= operation. Read more
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impl<T> Zero for Polynomial<T>
where T: for<'r> AddAssign<&'r T> + Zero,

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fn zero() -> Self

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl<T: Eq> Eq for Polynomial<T>

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impl<T> StructuralPartialEq for Polynomial<T>

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impl<T> Freeze for Polynomial<T>
where T: Freeze,

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impl<T> RefUnwindSafe for Polynomial<T>
where T: RefUnwindSafe,

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impl<T> Send for Polynomial<T>
where T: Send,

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impl<T> Sync for Polynomial<T>
where T: Sync,

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impl<T> Unpin for Polynomial<T>
where T: Unpin,

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impl<T> UnwindSafe for Polynomial<T>

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T, Base> RefNum<Base> for T
where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base>,