Struct MPZBase 

pub struct MPZBase;

Available on crate feature mpir only.

Arbitrary-precision integer ring, implemented by binding to the well-known and heavily optimized library mpir (fork of gmp).

TODO: Remove Copy at next breaking release.

Implementations

impl MPZBase

pub fn from_le_bytes(&self, dst: &mut MPZEl, input: &[u8])

Interprets the bytes in input as little endian bytes and returns the nonnegative integer represented by them.

pub fn from_base_u64_repr(&self, dst: &mut MPZEl, input: &[u64])

Interprets the u64 as digits w.r.t. base 2^64 (with least-significant digit first) and returns the nonnegative integer represented by them.

pub fn abs_base_u64_repr_len(&self, src: &MPZEl) -> usize

pub fn abs_base_u64_repr(&self, src: &MPZEl, out: &mut [u64])

Inverse to MPZBase::from_base_u64_repr().

pub fn to_le_bytes_len(&self, src: &MPZEl) -> usize

pub fn to_le_bytes(&self, src: &MPZEl, out: &mut [u8])

Inverse to MPZBase::from_le_bytes().

Trait Implementations

impl Clone for MPZBase

fn clone(&self) -> MPZBase

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MPZBase

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

Formats the value using the given formatter.

impl Default for MPZBase

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for MPZBase

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl DivisibilityRing for MPZBase

fn checked_left_div( &self, lhs: &Self::Element, rhs: &Self::Element, ) -> Option<Self::Element>

Checks whether there is an element x such that rhs * x = lhs, and returns it if it exists.

fn balance_factor<'a, I>(&self, elements: I) -> Option<Self::Element>

where I: Iterator<Item = &'a Self::Element>, Self: 'a,

Function that computes a “balancing” factor of a sequence of ring elements. The only use of the balancing factor is to increase performance, in particular, dividing all elements in the sequence by this factor should make them “smaller” resp. cheaper to process.

type PreparedDivisorData = ()

Additional data associated to a fixed ring element that can be used to speed up division by this ring element.

fn divides_left(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether there is an element x such that rhs * x = lhs. If you need such an element, consider using DivisibilityRing::checked_left_div().

fn divides(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Same as DivisibilityRing::divides_left(), but requires a commutative ring.

fn checked_div( &self, lhs: &Self::Element, rhs: &Self::Element, ) -> Option<Self::Element>

Same as DivisibilityRing::checked_left_div(), but requires a commutative ring.

fn is_unit(&self, x: &Self::Element) -> bool

Returns whether the given element is a unit, i.e. has an inverse.

fn prepare_divisor(&self, _: &Self::Element) -> Self::PreparedDivisorData

“Prepares” an element of this ring for division.

fn checked_left_div_prepared( &self, lhs: &Self::Element, rhs: &Self::Element, _rhs_prep: &Self::PreparedDivisorData, ) -> Option<Self::Element>

Same as DivisibilityRing::checked_left_div() but for a prepared divisor.

fn divides_left_prepared( &self, lhs: &Self::Element, rhs: &Self::Element, _rhs_prep: &Self::PreparedDivisorData, ) -> bool

Same as DivisibilityRing::divides_left() but for a prepared divisor.

fn is_unit_prepared(&self, x: &PreparedDivisor<Self>) -> bool

Same as DivisibilityRing::is_unit() but for a prepared divisor.

fn invert(&self, el: &Self::Element) -> Option<Self::Element>

If the given element is a unit, returns its inverse, otherwise None.

impl EuclideanRing for MPZBase

fn euclidean_div_rem( &self, lhs: Self::Element, rhs: &Self::Element, ) -> (Self::Element, Self::Element)

Computes euclidean division with remainder.

fn euclidean_rem( &self, lhs: Self::Element, rhs: &Self::Element, ) -> Self::Element

Computes only the remainder of euclidean division.

fn euclidean_div( &self, lhs: Self::Element, rhs: &Self::Element, ) -> Self::Element

Computes euclidean division without remainder.

fn euclidean_deg(&self, val: &Self::Element) -> Option<usize>

Defines how “small” an element is. For details, see EuclideanRing.

impl EvalPolyLocallyRing for MPZBase

type LocalComputationData<'ring> = RingValue<ZnBase<RingValue<AsFieldBase<RingValue<ZnBase>>>, RingRef<'ring, MPZBase>>> where Self: 'ring

Available on crate feature unstable-enable only.

A collection of prime ideals of the ring, and additionally any data required to reconstruct a small ring element from its projections onto each prime ideal.

type LocalRing<'ring> = RingValue<AsFieldBase<RingValue<ZnBase>>> where Self: 'ring

Available on crate feature unstable-enable only.

type LocalRingBase<'ring> = AsFieldBase<RingValue<ZnBase>> where Self: 'ring

Available on crate feature unstable-enable only.

The type of the ring we get once quotienting by a prime ideal.

fn ln_pseudo_norm(&self, el: &Self::Element) -> f64

Available on crate feature unstable-enable only.

Computes (an upper bound of) the natural logarithm of the pseudo norm of a ring element.

fn local_computation<'ring>( &'ring self, ln_pseudo_norm_bound: f64, ) -> Self::LocalComputationData<'ring>

Available on crate feature unstable-enable only.

Sets up the context for a new polynomial evaluation, whose output should have pseudo norm less than the given bound.

fn local_ring_at<'ring>( &self, computation: &Self::LocalComputationData<'ring>, i: usize, ) -> Self::LocalRing<'ring>

where Self: 'ring,

Available on crate feature unstable-enable only.

Returns the i-th local ring belonging to the given computation.

fn local_ring_count<'ring>( &self, computation: &Self::LocalComputationData<'ring>, ) -> usize

where Self: 'ring,

Available on crate feature unstable-enable only.

Returns the number k of local rings that are required to get the correct result of the given computation.

fn reduce<'ring>( &self, computation: &Self::LocalComputationData<'ring>, el: &Self::Element, ) -> Vec<<Self::LocalRingBase<'ring> as RingBase>::Element>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes the map R -> R1 x ... x Rk, i.e. maps the given element into each of the local rings.

fn lift_combine<'ring>( &self, computation: &Self::LocalComputationData<'ring>, el: &[<Self::LocalRingBase<'ring> as RingBase>::Element], ) -> Self::Element

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes a preimage under the map R -> R1 x ... x Rk, i.e. a ring element x that reduces to each of the given local rings under the map EvalPolyLocallyRing::reduce().

impl FiniteRingSpecializable for MPZBase

fn specialize<O: FiniteRingOperation<Self>>(op: O) -> O::Output

Available on crate feature unstable-enable only.

fn is_finite_ring() -> bool

Available on crate feature unstable-enable only.

impl HashableElRing for MPZBase

fn hash<H: Hasher>(&self, el: &Self::Element, h: &mut H)

Hashes the given ring element.

impl IntCast<MPZBase> for MPZBase

fn cast(&self, _from: &MPZBase, el: MPZEl) -> MPZEl

Maps the given integer into this ring.

impl IntCast<MPZBase> for RustBigintRingBase

fn cast(&self, from: &MPZBase, el: MPZEl) -> RustBigint

Maps the given integer into this ring.

impl IntCast<MPZBase> for StaticRingBase<i128>

fn cast(&self, from: &MPZBase, el: MPZEl) -> i128

Maps the given integer into this ring.

impl IntCast<MPZBase> for StaticRingBase<i16>

fn cast(&self, _: &MPZBase, el: MPZEl) -> i16

Maps the given integer into this ring.

impl IntCast<MPZBase> for StaticRingBase<i32>

fn cast(&self, _: &MPZBase, el: MPZEl) -> i32

Maps the given integer into this ring.

impl IntCast<MPZBase> for StaticRingBase<i64>

fn cast(&self, from: &MPZBase, el: MPZEl) -> i64

Maps the given integer into this ring.

impl IntCast<MPZBase> for StaticRingBase<i8>

fn cast(&self, _: &MPZBase, el: MPZEl) -> i8

Maps the given integer into this ring.

impl IntCast<RustBigintRingBase> for MPZBase

fn cast(&self, _: &RustBigintRingBase, el: RustBigint) -> Self::Element

Maps the given integer into this ring.

impl IntCast<StaticRingBase<i128>> for MPZBase

fn cast(&self, _: &StaticRingBase<i128>, el: i128) -> MPZEl

Maps the given integer into this ring.

impl IntCast<StaticRingBase<i16>> for MPZBase

fn cast(&self, _: &StaticRingBase<i16>, el: i16) -> MPZEl

Maps the given integer into this ring.

impl IntCast<StaticRingBase<i32>> for MPZBase

fn cast(&self, _: &StaticRingBase<i32>, el: i32) -> MPZEl

Maps the given integer into this ring.

impl IntCast<StaticRingBase<i64>> for MPZBase

fn cast(&self, _: &StaticRingBase<i64>, el: i64) -> Self::Element

Maps the given integer into this ring.

impl IntCast<StaticRingBase<i8>> for MPZBase

fn cast(&self, _: &StaticRingBase<i8>, el: i8) -> MPZEl

Maps the given integer into this ring.

impl IntegerPolyGCDRing for MPZBase

type LocalRingAsZnBase<'ring> = <MPZBase as PolyGCDLocallyDomain>::LocalRingBase<'ring> where Self: 'ring

Available on crate feature unstable-enable only.

It would be much preferrable if we could restrict associated types from supertraits, this is just a workaround (and an ugly one at that)

type LocalRingAsZn<'ring> = <MPZBase as PolyGCDLocallyDomain>::LocalRing<'ring> where Self: 'ring

Available on crate feature unstable-enable only.

fn local_ring_as_zn<'a, 'ring>( &self, local_field: &'a Self::LocalRing<'ring>, ) -> &'a Self::LocalRingAsZn<'ring>

where Self: 'ring,

Available on crate feature unstable-enable only.

fn local_ring_into_zn<'ring>( &self, local_field: Self::LocalRing<'ring>, ) -> Self::LocalRingAsZn<'ring>

where Self: 'ring,

Available on crate feature unstable-enable only.

fn principal_ideal_generator<'ring>( &self, p: &Self::SuitableIdeal<'ring>, ) -> El<BigIntRing>

where Self: 'ring,

Available on crate feature unstable-enable only.

impl IntegerRing for MPZBase

fn to_float_approx(&self, el: &Self::Element) -> f64

Computes a float value that is “close” to the given integer.

fn from_float_approx(&self, el: f64) -> Option<Self::Element>

Computes a value that is “close” to the given float. However, no guarantees are made on the definition of close, in particular, this does not have to be the closest integer to the given float, and cannot be used to compute rounding. It is also implementation-defined when to return None, although this is usually the case on infinity and NaN.

fn mul_pow_2(&self, el: &mut Self::Element, power: usize)

Multiplies the element by a power of two.

fn euclidean_div_pow_2(&self, el: &mut Self::Element, power: usize)

Computes the euclidean division by a power of two, always rounding to zero (note that euclidean division requires that |remainder| < |divisor|, and thus would otherwise leave multiple possible results).

fn abs_is_bit_set(&self, el: &Self::Element, bit: usize) -> bool

Return whether the i-th bit in the two-complements representation of abs(value) is 1.

fn abs_highest_set_bit(&self, value: &Self::Element) -> Option<usize>

Returns the index of the highest set bit in the two-complements representation of abs(value), or None if the value is zero.

fn abs_lowest_set_bit(&self, value: &Self::Element) -> Option<usize>

Returns the index of the lowest set bit in the two-complements representation of abs(value), or None if the value is zero.

fn rounded_div(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

Computes the rounded division, i.e. rounding to the closest integer. In the case of a tie (i.e. round(0.5)), we round towards +/- infinity.

fn get_uniformly_random_bits<G: FnMut() -> u64>( &self, log2_bound_exclusive: usize, rng: G, ) -> Self::Element

Computes a uniformly random integer in [0, 2^log_bound_exclusive - 1], assuming that rng provides uniformly random values in the whole range of u64.

fn representable_bits(&self) -> Option<usize>

Returns n such that this ring can represent at least [-2^n, ..., 2^n - 1]. Returning None means that the size of representable integers is unbounded.

fn ceil_div(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

Computes the division lhs / rhs, rounding towards + infinity.

fn floor_div(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

Computes the division lhs / rhs, rounding towards - infinity.

fn power_of_two(&self, power: usize) -> Self::Element

Returns the value 2^power in this integer ring.

fn parse(&self, string: &str, base: u32) -> Result<Self::Element, ()>

Parses the given string as a number.

impl InterpolationBaseRing for MPZBase

type ExtendedRing<'a> = RingRef<'a, MPZBase> where Self: 'a

Available on crate feature unstable-enable only.

type ExtendedRingBase<'a> = MPZBase where Self: 'a

Available on crate feature unstable-enable only.

The type of the extension ring we can switch to to get more points.

fn in_base<'a, S>(&self, _ext_ring: S, el: El<S>) -> Option<Self::Element>

where Self: 'a, S: RingStore<Type = Self::ExtendedRingBase<'a>>,

Available on crate feature unstable-enable only.

fn in_extension<'a, S>(&self, _ext_ring: S, el: Self::Element) -> El<S>

where Self: 'a, S: RingStore<Type = Self::ExtendedRingBase<'a>>,

Available on crate feature unstable-enable only.

fn interpolation_points<'a>( &'a self, count: usize, ) -> (Self::ExtendedRing<'a>, Vec<El<Self::ExtendedRing<'a>>>)

Available on crate feature unstable-enable only.

Returns count points such that the difference between any two of them is a non-zero-divisor.

impl OrderedRing for MPZBase

fn cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering

Returns whether lhs is Ordering::Less, Ordering::Equal or Ordering::Greater than rhs.

fn is_neg(&self, value: &Self::Element) -> bool

Returns whether value < 0.

fn abs_cmp(&self, lhs: &Self::Element, rhs: &Self::Element) -> Ordering

Returns whether abs(lhs) is Ordering::Less, Ordering::Equal or Ordering::Greater than abs(rhs).

fn is_leq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs <= rhs.

fn is_geq(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs >= rhs.

fn is_lt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs < rhs.

fn is_gt(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

Returns whether lhs > rhs.

fn is_pos(&self, value: &Self::Element) -> bool

Returns whether value > 0.

fn abs(&self, value: Self::Element) -> Self::Element

Returns the absolute value of value, i.e. value if value >= 0 and -value otherwise.

fn max<'a>( &self, fst: &'a Self::Element, snd: &'a Self::Element, ) -> &'a Self::Element

Returns the larger one of fst and snd.

impl PartialEq for MPZBase

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PolyGCDLocallyDomain for MPZBase

type LocalRing<'ring> = RingValue<ZnBase<RingValue<MPZBase>>> where Self: 'ring

Available on crate feature unstable-enable only.

type LocalRingBase<'ring> = ZnBase<RingValue<MPZBase>> where Self: 'ring

Available on crate feature unstable-enable only.

The type of the local ring once we quotiented out a power of a prime ideal.

type LocalFieldBase<'ring> = AsFieldBase<RingValue<ZnBase>> where Self: 'ring

Available on crate feature unstable-enable only.

The type of the field we get by quotienting out a power of a prime ideal.

type LocalField<'ring> = RingValue<AsFieldBase<RingValue<ZnBase>>> where Self: 'ring

Available on crate feature unstable-enable only.

type SuitableIdeal<'ring> = i64 where Self: 'ring

Available on crate feature unstable-enable only.

An ideal of the ring for which we know a decomposition into maximal ideals, and can use Hensel lifting to lift values to higher powers of this ideal.

fn reconstruct_ring_el<'local, 'element, 'ring, V1, V2>( &self, _p: &Self::SuitableIdeal<'ring>, from: V1, _e: usize, x: V2, ) -> Self::Element

where Self: 'ring, V1: VectorFn<&'local Self::LocalRing<'ring>>, V2: VectorFn<&'element El<Self::LocalRing<'ring>>>,

Available on crate feature unstable-enable only.

Computes a “small” element x in R such that x mod mi^e is equal to the given value, for every maximal ideal mi over I. In cases where the factors of polynomials in R[X] do not necessarily have coefficients in R, this function might have to do rational reconstruction.

fn maximal_ideal_factor_count<'ring>( &self, _p: &Self::SuitableIdeal<'ring>, ) -> usize

where Self: 'ring,

Available on crate feature unstable-enable only.

Returns the number of maximal ideals in the primary decomposition of ideal.

fn lift_partial<'ring>( &self, _p: &Self::SuitableIdeal<'ring>, from: (&Self::LocalRingBase<'ring>, usize), to: (&Self::LocalRingBase<'ring>, usize), max_ideal_idx: usize, x: El<Self::LocalRing<'ring>>, ) -> El<Self::LocalRing<'ring>>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes any element y in R / mi^to_e such that y = x mod mi^from_e. In particular, y does not have to be “short” in any sense, but any lift is a valid result.

fn local_field_at<'ring>( &self, p: &Self::SuitableIdeal<'ring>, max_ideal_idx: usize, ) -> Self::LocalField<'ring>

where Self: 'ring,

Available on crate feature unstable-enable only.

Returns R / mi, where mi is the i-th maximal ideal over I.

fn local_ring_at<'ring>( &self, p: &Self::SuitableIdeal<'ring>, e: usize, max_ideal_idx: usize, ) -> Self::LocalRing<'ring>

where Self: 'ring,

Available on crate feature unstable-enable only.

Returns R / mi^e, where mi is the i-th maximal ideal over I.

fn random_suitable_ideal<'ring, F>( &'ring self, rng: F, ) -> Self::SuitableIdeal<'ring>

where F: FnMut() -> u64,

Available on crate feature unstable-enable only.

Returns an ideal sampled at random from the interval of all supported ideals.

fn base_ring_to_field<'ring>( &self, _ideal: &Self::SuitableIdeal<'ring>, from: &Self::LocalRingBase<'ring>, to: &Self::LocalFieldBase<'ring>, max_ideal_idx: usize, x: El<Self::LocalRing<'ring>>, ) -> El<Self::LocalField<'ring>>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes the isomorphism between the ring and field representations of R / mi

fn field_to_base_ring<'ring>( &self, _ideal: &Self::SuitableIdeal<'ring>, from: &Self::LocalFieldBase<'ring>, to: &Self::LocalRingBase<'ring>, max_ideal_idx: usize, x: El<Self::LocalField<'ring>>, ) -> El<Self::LocalRing<'ring>>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes the isomorphism between the ring and field representations of R / mi

fn reduce_ring_el<'ring>( &self, _p: &Self::SuitableIdeal<'ring>, to: (&Self::LocalRingBase<'ring>, usize), max_ideal_idx: usize, x: Self::Element, ) -> El<Self::LocalRing<'ring>>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes the reduction map

fn reduce_partial<'ring>( &self, _p: &Self::SuitableIdeal<'ring>, from: (&Self::LocalRingBase<'ring>, usize), to: (&Self::LocalRingBase<'ring>, usize), max_ideal_idx: usize, x: El<Self::LocalRing<'ring>>, ) -> El<Self::LocalRing<'ring>>

where Self: 'ring,

Available on crate feature unstable-enable only.

Computes the reduction map

fn heuristic_exponent<'ring, 'a, I>( &self, p: &i64, poly_deg: usize, coefficients: I, ) -> usize

where I: Iterator<Item = &'a Self::Element>, Self: 'a + 'ring,

Available on crate feature unstable-enable only.

Returns an exponent e such that we hope that the factors of a polynomial of given degree, involving the given coefficient can already be read of (via PolyGCDLocallyDomain::reconstruct_ring_el()) their reductions modulo I^e. Note that this is just a heuristic, and if it does not work, the implementation will gradually try larger e. Thus, even if this function returns constant 1, correctness will not be affected, but giving a good guess can improve performance

fn dbg_ideal<'ring>( &self, p: &Self::SuitableIdeal<'ring>, out: &mut Formatter<'_>, ) -> Result

where Self: 'ring,

Available on crate feature unstable-enable only.

impl PrincipalIdealRing for MPZBase

fn extended_ideal_gen( &self, lhs: &Self::Element, rhs: &Self::Element, ) -> (Self::Element, Self::Element, Self::Element)

Computes a Bezout identity for the generator g of the ideal (lhs, rhs) as g = s * lhs + t * rhs.

fn checked_div_min( &self, lhs: &Self::Element, rhs: &Self::Element, ) -> Option<Self::Element>

Similar to DivisibilityRing::checked_left_div() this computes a “quotient” q of lhs and rhs, if it exists. However, we impose the additional constraint that this quotient be minimal, i.e. there is no q' with q' | q properly and q' * rhs = lhs.

fn annihilator(&self, val: &Self::Element) -> Self::Element

Returns the (w.r.t. divisibility) smallest element x such that x * val = 0.

fn create_elimination_matrix( &self, a: &Self::Element, b: &Self::Element, ) -> ([Self::Element; 4], Self::Element)

Creates a matrix A of unit determinant such that A * (a, b)^T = (d, 0). Returns (A, d).

fn ideal_gen(&self, lhs: &Self::Element, rhs: &Self::Element) -> Self::Element

Computes a generator g of the ideal (lhs, rhs) = (g), also known as greatest common divisor.

fn ideal_gen_with_controller<Controller>( &self, lhs: &Self::Element, rhs: &Self::Element, _: Controller, ) -> Self::Element

where Controller: ComputationController,

As PrincipalIdealRing::ideal_gen(), this computes a generator of the ideal (lhs, rhs). However, it additionally accepts a ComputationController to customize the performed computation.

fn lcm(&self, lhs: &Self::Element, rhs: &Self::Element) -> Self::Element

Computes a generator of the ideal (lhs) ∩ (rhs), also known as least common multiple.

impl RingBase for MPZBase

type Element = MPZEl

Type of elements of the ring

fn clone_el(&self, val: &Self::Element) -> Self::Element

fn mul_ref(&self, lhs: &Self::Element, rhs: &Self::Element) -> Self::Element

fn negate_inplace(&self, lhs: &mut Self::Element)

fn zero(&self) -> Self::Element

fn one(&self) -> Self::Element

fn sub_ref_fst(&self, lhs: &Self::Element, rhs: Self::Element) -> Self::Element

fn sub_ref_snd(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

fn add_assign(&self, lhs: &mut Self::Element, rhs: Self::Element)

fn add_assign_ref(&self, lhs: &mut Self::Element, rhs: &Self::Element)

fn mul_assign(&self, lhs: &mut Self::Element, rhs: Self::Element)

fn mul_assign_ref(&self, lhs: &mut Self::Element, rhs: &Self::Element)

fn mul_assign_int(&self, lhs: &mut Self::Element, rhs: i32)

fn sub(&self, lhs: Self::Element, rhs: Self::Element) -> Self::Element

fn from_int(&self, value: i32) -> Self::Element

fn eq_el(&self, lhs: &Self::Element, rhs: &Self::Element) -> bool

fn is_zero(&self, val: &Self::Element) -> bool

fn is_one(&self, val: &Self::Element) -> bool

fn is_neg_one(&self, val: &Self::Element) -> bool

fn is_noetherian(&self) -> bool

Returns whether the ring is noetherian, i.e. every ideal is finitely generated.

fn is_commutative(&self) -> bool

Returns whether the ring is commutative, i.e. a * b = b * a for all elements a, b. Note that addition is assumed to be always commutative.

fn is_approximate(&self) -> bool

Returns whether this ring computes with approximations to elements. This would usually be the case for rings that are based on f32 or f64, to represent real or complex numbers.

fn dbg_within<'a>( &self, value: &Self::Element, out: &mut Formatter<'a>, _env: EnvBindingStrength, ) -> Result

Writes a human-readable representation of value to out, taking into account the possible context to place parenthesis as needed.

fn characteristic<I: IntegerRingStore + Copy>( &self, other_ZZ: I, ) -> Option<El<I>>

where I::Type: IntegerRing,

Returns the characteristic of this ring as an element of the given implementation of ZZ.

fn sub_assign_ref(&self, lhs: &mut Self::Element, rhs: &Self::Element)

fn neg_one(&self) -> Self::Element

fn fma( &self, lhs: &Self::Element, rhs: &Self::Element, summand: Self::Element, ) -> Self::Element

Fused-multiply-add. This computes summand + lhs * rhs.

fn dbg<'a>(&self, value: &Self::Element, out: &mut Formatter<'a>) -> Result

Writes a human-readable representation of value to out.

fn square(&self, value: &mut Self::Element)

fn negate(&self, value: Self::Element) -> Self::Element

fn sub_assign(&self, lhs: &mut Self::Element, rhs: Self::Element)

fn mul_int(&self, lhs: Self::Element, rhs: i32) -> Self::Element

fn mul_int_ref(&self, lhs: &Self::Element, rhs: i32) -> Self::Element

fn fma_int( &self, lhs: &Self::Element, rhs: i32, summand: Self::Element, ) -> Self::Element

Fused-multiply-add with an integer. This computes summand + lhs * rhs.

fn sub_self_assign(&self, lhs: &mut Self::Element, rhs: Self::Element)

Computes lhs := rhs - lhs.

fn sub_self_assign_ref(&self, lhs: &mut Self::Element, rhs: &Self::Element)

Computes lhs := rhs - lhs.

fn add_ref(&self, lhs: &Self::Element, rhs: &Self::Element) -> Self::Element

fn add_ref_fst(&self, lhs: &Self::Element, rhs: Self::Element) -> Self::Element

fn add_ref_snd(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

fn add(&self, lhs: Self::Element, rhs: Self::Element) -> Self::Element

fn sub_ref(&self, lhs: &Self::Element, rhs: &Self::Element) -> Self::Element

fn mul_ref_fst(&self, lhs: &Self::Element, rhs: Self::Element) -> Self::Element

fn mul_ref_snd(&self, lhs: Self::Element, rhs: &Self::Element) -> Self::Element

fn mul(&self, lhs: Self::Element, rhs: Self::Element) -> Self::Element

fn pow_gen<R: RingStore>( &self, x: Self::Element, power: &El<R>, integers: R, ) -> Self::Element

where R::Type: IntegerRing,

Raises x to the power of an arbitrary, nonnegative integer given by a custom integer ring implementation.

fn sum<I>(&self, els: I) -> Self::Element

where I: IntoIterator<Item = Self::Element>,

Sums the elements given by the iterator.

fn prod<I>(&self, els: I) -> Self::Element

where I: IntoIterator<Item = Self::Element>,

Computes the product of the elements given by the iterator.

impl SerializableElementRing for MPZBase

fn deserialize<'de, D>( &self, deserializer: D, ) -> Result<Self::Element, D::Error>

where D: Deserializer<'de>,

Available on crate feature unstable-enable only.

Deserializes an element of this ring from the given deserializer.

fn serialize<S>( &self, el: &Self::Element, serializer: S, ) -> Result<S::Ok, S::Error>

where S: Serializer,

Available on crate feature unstable-enable only.

Serializes an element of this ring to the given serializer.

impl Serialize for MPZBase

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl Copy for MPZBase

impl Domain for MPZBase

impl Eq for MPZBase

impl StructuralPartialEq for MPZBase