Enum free_algebra::FreeInv

pub enum FreeInv<T: Eq> {
    Id(T),
    Inv(T),
}

Wraps a type T and symbolically inverts elements.

Used for constructing FreeGroup

Variants

Id(T)

Wraps an instance of type T

Inv(T)

The symbolic inverse of an object of type T

Methods

impl<T: Eq> FreeInv<T>

pub fn is_inv(&self) -> bool

Returns true if self is inverted

use free_algebra::FreeInv::*;

assert!(Inv('a').is_inv());
assert!(!Id('a').is_inv());

pub fn is_id(&self) -> bool

Returns true if self is non-inverted

use free_algebra::FreeInv::*;

assert!(Id('a').is_id());
assert!(!Inv('a').is_id());

Trait Implementations

impl<T: Eq> MonoidRule<FreeInv<T>> for InvRule

fn apply(string: Vec<FreeInv<T>>, letter: FreeInv<T>) -> Vec<FreeInv<T>>

Applies the operation rule to the product of a word and a single letter

fn apply_many(word1: Vec<C>, word2: Vec<C>) -> Vec<C>

Applies the operation rule to the product of two words

fn apply_iter<I: Iterator<Item = C>>(word: Vec<C>, letters: I) -> Vec<C>

Applies the operation rule to the product of a word and a sequence of letters

impl<T: Eq> InvMonoidRule<FreeInv<T>> for InvRule

fn invert(letter: FreeInv<T>) -> FreeInv<T>

Inverts a letter x such that x * x.invert() == 1

impl<T: Eq> AssociativeMonoidRule<FreeInv<T>> for InvRule

impl<T: Eq> AsRef<T> for FreeInv<T>

Provides a reference to this type's inner T

Note that this does not convey any information regarding the state of inversion

fn as_ref(&self) -> &T

Performs the conversion.

impl<T: Eq> AsMut<T> for FreeInv<T>

Provides a mutable reference to this type's inner T

Note that this does not convey any information regarding the state of inversion

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

Performs the conversion.

impl<T: Eq> From<T> for FreeInv<T>

fn from(t: T) -> Self

Performs the conversion.

impl<C: Eq, P: One + Neg<Output = P>> From<FreeInv<C>> for FreePow<C, P>

fn from(inv: FreeInv<C>) -> Self

Performs the conversion.

impl<T: Clone + Eq> Clone for FreeInv<T>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Copy + Eq> Copy for FreeInv<T>

impl<T: Eq> Eq for FreeInv<T>

impl<T: PartialEq + Eq> PartialEq<FreeInv<T>> for FreeInv<T>

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &FreeInv<T>) -> bool

This method tests for !=.

impl<T: Eq> PartialEq<T> for FreeInv<T>

fn eq(&self, rhs: &T) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<T: Eq + Display> Display for FreeInv<T>

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

Formats the value using the given formatter.

impl<T: Debug + Eq> Debug for FreeInv<T>

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

Formats the value using the given formatter.

impl<T: Eq> Div<FreeInv<T>> for FreeInv<T>

type Output = FreeGroup<T>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> FreeGroup<T>

Performs the / operation.

impl<T: Eq> Div<MonoidalString<FreeInv<T>, InvRule>> for FreeInv<T>

type Output = FreeGroup<T>

The resulting type after applying the / operator.

fn div(self, rhs: FreeGroup<T>) -> FreeGroup<T>

Performs the / operation.

impl<T: Eq> Mul<FreeInv<T>> for FreeInv<T>

type Output = FreeGroup<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> FreeGroup<T>

Performs the * operation.

impl<T: Eq> Mul<MonoidalString<FreeInv<T>, InvRule>> for FreeInv<T>

type Output = FreeGroup<T>

The resulting type after applying the * operator.

fn mul(self, rhs: FreeGroup<T>) -> FreeGroup<T>

Performs the * operation.

impl<T: Hash + Eq> Hash for FreeInv<T>

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, 

Feeds a slice of this type into the given [Hasher].

impl<T: Eq> StructuralPartialEq for FreeInv<T>

impl<T: Eq> StructuralEq for FreeInv<T>

impl<T: Eq> Inv for FreeInv<T>

type Output = Self

The result after applying the operator.

fn inv(self) -> Self

Returns the multiplicative inverse of self.