Struct PowerSeries 

pub struct PowerSeries<R: CommutativeRing> { /* private fields */ }

A fixed-truncation power series carrying its complete context.

Supported one-variable coefficient contexts keep an immutable FLINT polynomial as their primary representation. Clones share that storage, and the canonical sparse term view is materialized lazily only for inspection, serialization, or a generic algorithm. Multivariate and unsupported contexts retain the sparse truncation-aware representation.

Implementations

impl<R> PowerSeries<R>

where R: CommutativeRing + Display,

pub fn monomial_substitution( &self, monomial_map: &MonomialMap, ) -> Result<Self, SemilinearSubstitutionError>

Substitute monomials and discard transformed terms outside the fixed cap.

pub fn semilinear_substitution<M>( &self, coefficient_map: &M, monomial_map: &MonomialMap, ) -> Result<PowerSeries<M::Target>, SemilinearSubstitutionError>

where M: CoefficientMap<Source = R>,

Fuse monomial capping and coefficient mapping in one source-term stream.

A transformed exponent is rejected before its coefficient map is applied.

pub fn frobenius_lift( &self, exponent: u64, ) -> Result<Self, SemilinearSubstitutionError>

where R: CoefficientFrobeniusContext,

Apply coefficient Frobenius and x_i -> x_i^(p^exponent) with early capping.

impl<R: CommutativeRing> PowerSeries<R>

pub fn ring(&self) -> &PowerSeriesRing<R>

Exact power-series context carried by this value.

pub fn terms(&self) -> impl Iterator<Item = (&[u64], &R::Element)>

Nonzero terms in deterministic lexicographic exponent order.

pub fn map_coefficients<M>( &self, map: &M, ) -> Result<PowerSeries<M::Target>, CoefficientMappingError>

where M: CoefficientMap<Source = R>, R: Display,

Apply one checked scalar map to every retained coefficient while preserving variables, truncation identity, and exponents.

pub fn coefficient( &self, exponent: &[u64], ) -> Result<R::Element, PowerSeriesError>

Coefficient at a retained exponent position.

Asking beyond the context’s precision is an error, not a zero coefficient claim.

pub fn constant_coefficient(&self) -> R::Element

Constant coefficient.

pub fn is_zero(&self) -> bool

Whether every retained coefficient is zero.

pub fn is_one(&self) -> bool

Whether this is the multiplicative identity in its context.

pub fn nonzero_term_count(&self) -> usize

Number of stored nonzero coefficients.

pub fn to_json(&self) -> Result<String, NoetherError>

where R: Serialize, R::Element: Serialize,

Serialize this series with its complete fixed-precision context and terms.

pub fn from_json(value: &str) -> Result<Self, NoetherError>

where R: for<'de> Deserialize<'de>, R::Element: for<'de> Deserialize<'de>,

Deserialize and revalidate the context, exponent region, and coefficients.

pub fn pow(&self, exponent: u64) -> Result<Self, ContextMismatchError>

Raise this series to a nonnegative power in its fixed context.

pub fn scalar_mul(&self, scalar: &R::Element) -> Result<Self, PowerSeriesError>

Multiply every coefficient by one value from the coefficient ring.

pub fn derivative(&self, variable: usize) -> Result<Self, PowerSeriesError>

Formal derivative with respect to one variable.

pub fn compose(&self, images: &[Self]) -> Result<Self, PowerSeriesError>

Substitute one image for each variable when the images preserve the truncation ideal.

pub fn inverse(&self) -> Result<Self, UnitError>

where R: UnitInversion,

Invert a series exactly when its constant coefficient is a unit.

pub fn exact_div(&self, divisor: &Self) -> Result<Self, PowerSeriesError>

where R: UnitInversion,

Return the canonical exact quotient by a monomial times a unit series.

Fixed truncation makes division by a nonunit nonunique: coefficients beyond the dividend’s retained region cannot be recovered. For a divisor x^a u, with u(0) a unit, this method chooses the unique quotient obtained by shifting the retained dividend by a, filling the newly unknown boundary coefficients with zero, and dividing by u. It verifies the result by multiplication in this exact quotient ring. More general divisors are rejected rather than choosing a hidden term order or quotient lift.

pub fn restrict_truncation( &self, target: SeriesTruncation, ) -> Result<Self, PowerSeriesError>

Enter an explicitly coarser truncation context.

Trait Implementations

impl<R: CommutativeRing> Add<&PowerSeries<R>> for &PowerSeries<R>

type Output = Result<PowerSeries<R>, ContextMismatchError>

The resulting type after applying the + operator.

fn add(self, rhs: &PowerSeries<R>) -> Self::Output

Performs the + operation.

impl<R: Clone + CommutativeRing> Clone for PowerSeries<R>

where R::Element: Clone,

fn clone(&self) -> PowerSeries<R>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<R: CommutativeRing> Debug for PowerSeries<R>

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

Formats the value using the given formatter.

impl<'de, R> Deserialize<'de> for PowerSeries<R>

where R: CommutativeRing + Deserialize<'de>, R::Element: Deserialize<'de>,

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

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<R: CommutativeRing> Display for PowerSeries<R>

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

Formats the value using the given formatter.

impl<R: CommutativeRing> Mul<&PowerSeries<R>> for &PowerSeries<R>

type Output = Result<PowerSeries<R>, ContextMismatchError>

The resulting type after applying the * operator.

fn mul(self, rhs: &PowerSeries<R>) -> Self::Output

Performs the * operation.

impl<R: CommutativeRing> Neg for &PowerSeries<R>

type Output = Result<PowerSeries<R>, ContextMismatchError>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<R: CommutativeRing> PartialEq for PowerSeries<R>

fn eq(&self, other: &Self) -> 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<R: CommutativeRing> SemanticType for PowerSeries<R>

const TYPE_ID: &'static str = "noether/commalg/PowerSeries@1"

Versioned, language-neutral semantic identity.

fn canonical_bytes(&self) -> Result<Vec<u8>, NoetherError>

Serialize without backend- or language-specific identity.

fn describe() -> &'static TypeDescription

Return static discovery metadata for the type.

impl<R> Serialize for PowerSeries<R>

where R: CommutativeRing + Serialize, R::Element: Serialize,

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

where S: Serializer,

Serialize this value into the given Serde serializer.

impl<R: CommutativeRing> Sub<&PowerSeries<R>> for &PowerSeries<R>

type Output = Result<PowerSeries<R>, ContextMismatchError>

The resulting type after applying the - operator.

fn sub(self, rhs: &PowerSeries<R>) -> Self::Output

Performs the - operation.

impl<R: CommutativeRing> Eq for PowerSeries<R>