Struct MultiVar 

pub struct MultiVar<const X: char, I>(/* private fields */);

A multivariate monomial in indexed variables Xᵢ, with exponents stored in a MultiDeg. The base symbol X is a const generic; the actual variables are X₀, X₁, … (displayed with subscripts).

Implementations

impl<const X: char, I> MultiVar<X, I>

pub fn var_symbol() -> char

pub fn deg_for(&self, i: usize) -> I

where I: Copy,

pub fn total_deg(&self) -> I

where I: Zero + for<'x> Add<&'x I, Output = I>,

pub fn eval<R>(&self, v: &[R]) -> R

where R: One + Mul<Output = R>, I: Copy, for<'x> &'x R: Pow<I, Output = R>,

impl<const X: char> MultiVar<X, usize>

pub fn generate(n: usize, tot_deg: usize) -> impl Iterator<Item = Self>

Trait Implementations

impl<const X: char, I: Clone> Clone for MultiVar<X, I>

fn clone(&self) -> MultiVar<X, I>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const X: char, I> Debug for MultiVar<X, I>

where I: ToPrimitive,

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

Formats the value using the given formatter.

impl<const X: char, I: Default> Default for MultiVar<X, I>

fn default() -> MultiVar<X, I>

Returns the “default value” for a type.

impl<const X: char, I> Display for MultiVar<X, I>

where I: ToPrimitive,

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

Formats the value using the given formatter.

impl<const X: char, I> Div for MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>,

type Output = MultiVar<X, I>

The resulting type after applying the / operator.

fn div(self, rhs: MultiVar<X, I>) -> Self::Output

Performs the / operation.

impl<const X: char, I> Div<&MultiVar<X, I>> for &MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>, MultiVar<X, I>: Clone,

type Output = MultiVar<X, I>

The resulting type after applying the / operator.

fn div(self, rhs: &MultiVar<X, I>) -> Self::Output

Performs the / operation.

impl<const X: char, I> Div<&MultiVar<X, I>> for MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>,

type Output = MultiVar<X, I>

The resulting type after applying the / operator.

fn div(self, rhs: &MultiVar<X, I>) -> Self::Output

Performs the / operation.

impl<const X: char, I> Div<MultiVar<X, I>> for &MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>, MultiVar<X, I>: Clone,

type Output = MultiVar<X, I>

The resulting type after applying the / operator.

fn div(self, rhs: MultiVar<X, I>) -> Self::Output

Performs the / operation.

impl<const X: char, I> DivAssign for MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>,

fn div_assign(&mut self, rhs: MultiVar<X, I>)

Performs the /= operation.

impl<const X: char, I> DivAssign<&MultiVar<X, I>> for MultiVar<X, I>

where I: Zero + for<'x> SubAssign<&'x I>,

fn div_assign(&mut self, rhs: &MultiVar<X, I>)

Performs the /= operation.

impl<const X: char, I: Eq> Eq for MultiVar<X, I>

impl<const X: char, I> From<(usize, I)> for MultiVar<X, I>

where I: Zero,

fn from(value: (usize, I)) -> Self

Converts to this type from the input type.

impl<const X: char, I> From<MultiDeg<I>> for MultiVar<X, I>

fn from(d: MultiDeg<I>) -> Self

Converts to this type from the input type.

impl<const X: char, const N: usize, I> From<[I; N]> for MultiVar<X, I>

where I: Zero,

fn from(degs: [I; N]) -> Self

Converts to this type from the input type.

impl<const X: char, I> FromIterator<(usize, I)> for MultiVar<X, I>

where I: Zero,

fn from_iter<T: IntoIterator<Item = (usize, I)>>(iter: T) -> Self

Creates a value from an iterator.

impl<const X: char, I> FromStr for MultiVar<X, I>

where I: Zero + FromStr + FromPrimitive,

type Err = ParseErr

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl<const X: char, I: Hash> Hash for MultiVar<X, I>

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

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<const X: char, I> LcKey for MultiVar<X, I>

where I: IndexType + Zero + ToPrimitive + for<'x> Add<&'x I, Output = I>,

impl<const X: char, I> MathType for MultiVar<X, I>

where I: IndexType + ToPrimitive,

fn math_symbol() -> String

impl<const X: char> Mono for MultiVar<X, usize>

type Deg = MultiDeg<usize>

Degree type — usize (ordinary) or isize (Laurent), or a tuple/vector for multivariate monomials.

fn deg(&self) -> Self::Deg

The degree (or multi-degree) of this monomial.

fn is_unit(&self) -> bool

true iff this monomial is the unit 1 (all powers zero).

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

Multiplicative inverse, if this monomial is a unit; otherwise None.

fn divides(&self, other: &Self) -> bool

true iff self divides other (componentwise on degrees).

impl<const X: char> Mono for MultiVar<X, isize>

type Deg = MultiDeg<isize>

Degree type — usize (ordinary) or isize (Laurent), or a tuple/vector for multivariate monomials.

fn deg(&self) -> Self::Deg

The degree (or multi-degree) of this monomial.

fn is_unit(&self) -> bool

true iff this monomial is the unit 1 (all powers zero).

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

Multiplicative inverse, if this monomial is a unit; otherwise None.

fn divides(&self, _other: &Self) -> bool

true iff self divides other (componentwise on degrees).

impl<const X: char, I> MonoOrd for MultiVar<X, I>

where I: Zero + Ord + for<'x> Add<&'x I, Output = I>,

fn cmp_lex(&self, other: &Self) -> Ordering

Pure lexicographic order.

fn cmp_grlex(&self, other: &Self) -> Ordering

Graded lexicographic order (compare total degree first, break ties by lex).

impl<const X: char, I> Mul for MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>,

type Output = MultiVar<X, I>

The resulting type after applying the * operator.

fn mul(self, rhs: MultiVar<X, I>) -> Self::Output

Performs the * operation.

impl<const X: char, I> Mul<&MultiVar<X, I>> for &MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>, MultiVar<X, I>: Clone,

type Output = MultiVar<X, I>

The resulting type after applying the * operator.

fn mul(self, rhs: &MultiVar<X, I>) -> Self::Output

Performs the * operation.

impl<const X: char, I> Mul<&MultiVar<X, I>> for MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>,

type Output = MultiVar<X, I>

The resulting type after applying the * operator.

fn mul(self, rhs: &MultiVar<X, I>) -> Self::Output

Performs the * operation.

impl<const X: char, I> Mul<MultiVar<X, I>> for &MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>, MultiVar<X, I>: Clone,

type Output = MultiVar<X, I>

The resulting type after applying the * operator.

fn mul(self, rhs: MultiVar<X, I>) -> Self::Output

Performs the * operation.

impl<const X: char, I> MulAssign for MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>,

fn mul_assign(&mut self, rhs: MultiVar<X, I>)

Performs the *= operation.

impl<const X: char, I> MulAssign<&MultiVar<X, I>> for MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>,

fn mul_assign(&mut self, rhs: &MultiVar<X, I>)

Performs the *= operation.

impl<const X: char, I> One for MultiVar<X, I>

where I: Zero + for<'x> AddAssign<&'x I>,

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<const X: char, I> Ord for MultiVar<X, I>

where I: Zero + Ord + for<'x> Add<&'x I, Output = I>,

fn cmp(&self, other: &Self) -> 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<const X: char, I: PartialEq> PartialEq for MultiVar<X, I>

fn eq(&self, other: &MultiVar<X, I>) -> bool

Equality operator ==.

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

Inequality operator !=.

impl<const X: char, I> PartialOrd for MultiVar<X, I>

where I: Zero + Ord + for<'x> Add<&'x I, Output = I>,

fn partial_cmp(&self, other: &Self) -> 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<const X: char, I: PartialEq> StructuralPartialEq for MultiVar<X, I>

impl<const X: char, I> TeX for MultiVar<X, I>

where I: ToPrimitive,

fn tex_math_symbol() -> String

fn tex_string(&self) -> String