Struct ArithmeticCongruenceMonoid

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pub struct ArithmeticCongruenceMonoid<T>where
    for<'b> T: TBounds + Ops<T, T> + Ops<&'b T, T> + AssignOps<&'b T>,
    for<'a, 'a, 'b> &'a T: Ops<T, T> + Ops<&'b T, T>,
{ /* private fields */ }

Expand description

Arithmetic congruence monoid implementation.

Implementations§

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impl<T> ArithmeticCongruenceMonoid<T>
where for<'b> T: TBounds + Ops<T, T> + Ops<&'b T, T> + AssignOps<&'b T>, for<'a, 'a, 'b> &'a T: Ops<T, T> + Ops<&'b T, T>,

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pub fn new(a: T, b: T) -> Result<ArithmeticCongruenceMonoid<T>, ACMError<T>>

Construct a new ACM with components $a$ and $b$ satisfying $a\equiv a^2\pmod b$.

§Examples

// A valid ACM (1 % 4 == 1 == 1*1 % 4)
assert!(acm::ArithmeticCongruenceMonoid::new(1, 4).is_ok());

// An invalid ACM (2 % 4 == 2 != 0 == 2*2 % 4)
assert!(acm::ArithmeticCongruenceMonoid::new(2, 4).is_err());

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pub fn a(&self) -> &T

Returns the $a$ component of the ACM.

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pub fn b(&self) -> &T

Returns the $b$ component of the ACM.

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pub fn contains(&self, x: &T) -> bool

Returns true if n is an element of the ACM.

§Examples

let acm = acm::ArithmeticCongruenceMonoid::new(1, 4).unwrap();
assert!( acm.contains(&5));
assert!(!acm.contains(&6));

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pub fn nearest<U: Into<T>>(&self, s: U) -> T

Returns the nearst ACM element less-than or equal to $s$. If $s < a$, returns $a$.

§Examples

let acm = acm::ArithmeticCongruenceMonoid::new(1, 4).unwrap();
assert_eq!(acm.nearest(0), 1);
assert_eq!(acm.nearest(1), 1);
assert_eq!(acm.nearest(5), 5);
assert_eq!(acm.nearest(6), 5);

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pub fn iter(&self) -> ACMElementIterator<T> ⓘ

Returns an iterator over ACM elements.

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pub fn iter_from(&self, s: T) -> ACMElementIterator<T> ⓘ

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pub fn ith<U: Into<T>>(&self, i: U) -> T

Returns the $n$th ACM element.

§Examples

let acm = acm::ArithmeticCongruenceMonoid::new(1, 4).unwrap();
assert_eq!(acm.ith(0), 1);
assert_eq!(acm.ith(1), 5);
assert_eq!(acm.ith(56), 225);

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pub fn index(&self, n: T) -> Option<T>

Get ACM element index of an integer.

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pub fn divisors(&self, n: T) -> Vec<T>

Returns the ACM element divisors of an integer n.

§Examples

let acm = acm::ArithmeticCongruenceMonoid::new(1, 4).unwrap();
assert_eq!(acm.divisors(225), [1, 9, 5, 25, 45, 225]);

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pub fn factor<U: Into<T>>(&mut self, n: U) -> &Vec<Vec<T>>

Returns a reference to the vector of ACM atom factorizations of an integer n. If n is not an element of the ACM then the vector will be empty. Because factorization results are stored internally to the ACM in order to reduce computational costs, using factor requires that the ACM binding be declared mutable.

§Examples

let mut acm = acm::ArithmeticCongruenceMonoid::new(3, 6).unwrap();
assert_eq!(acm.factor(1),   &[[]]);
assert_eq!(acm.factor(2),   &[[]; 0]);
assert_eq!(acm.factor(3),   &[[3]]);
assert_eq!(acm.factor(9),   &[[3, 3]]);
assert_eq!(acm.factor(225), &[[15, 15], [3, 75]]);

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pub fn atomic(&mut self, n: &T) -> bool

Returns true if n is atomic under the ACM (is an ACM element, and cannot be expressed as a product of smaller ACM atoms). Because of underlying usage of factor, using atomic requires that the ACM binding be declared mutable.

§Examples

let mut acm = acm::ArithmeticCongruenceMonoid::new(1, 4).unwrap();
assert!( acm.contains(&5)  &&  acm.atomic(&5));
assert!(!acm.contains(&15) && !acm.atomic(&15));
assert!( acm.contains(&25) && !acm.atomic(&25));