commalg · PowerSeries¶

28 accepted declarations. Python and Rust forms, contracts, evidence, failure boundaries, and checked usages are kept together below.

Worked example¶

The complete checked program Calculate in a fixed-cap multivariate weighted power-series ring uses this API directly.

# SPDX-License-Identifier: MIT
# Copyright (c) 2026 Benjamin Antieau and Deven Manam
"""Calculate in a fixed-cap multivariate weighted power-series ring."""

from noether import Z
from noether.commalg import PowerSeriesRing, SeriesTruncation


def main() -> None:
    ring = PowerSeriesRing(
        Z,
        ["x", "y", "z"],
        SeriesTruncation.weighted_degree([1, 2, 3], 6),
    )
    x, y, z = ring.generators()
    assert (x**6).is_zero()
    assert not (x**2 * z + y * z).is_zero()
    value = (1 + x + y).pow(4)
    print(f"{value}; coefficient capacity <= {ring.coefficient_capacity_bound()}")


if __name__ == "__main__":
    main()

Run it with .venv/bin/python examples/17_weighted_power_series.py.

`commalg.PowerSeries`¶

A sparse power series carrying its coefficient and truncation context.

PythonRust

class PowerSeries

noether::commalg::PowerSeries · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_acceptance_workload.py:14 · validation/unit/commalg/test_acceptance_workload.py:55 · validation/unit/commalg/test_context_tower_workload.py:80 · validation/unit/commalg/test_context_tower_workload.py:9 · validation/unit/commalg/test_power_series_facade.py:12 · validation/unit/commalg/test_power_series_facade.py:200

`commalg.PowerSeries.add`¶

Add another compatible value to this value.

Detailed contract

Returns the argument unchanged.

PythonRust

(self, other: PowerSeries[C] | Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries::add · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/infra/test_discovery.py:211 · validation/unit/infra/test_public_api_index.py:293

`commalg.PowerSeries.mul`¶

Multiply this value by another compatible value.

PythonRust

(self, other: PowerSeries[C] | Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries::mul · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/infra/test_public_api_index.py:214

`commalg.PowerSeries.neg`¶

Return the additive inverse of this value.

PythonRust

(self) -> PowerSeries[C]

noether::commalg::PowerSeries::neg · Direct Rust declaration

fn neg(self) -> Self::Output

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

`commalg.PowerSeries.pow`¶

Raise this value to the supplied power.

PythonRust

(self, exponent: int, modulus: None=None) -> PowerSeries[C]

noether::commalg::PowerSeries · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

`commalg.PowerSeries.radd`¶

Add this value to a compatible value on its left.

PythonRust

(self, other: Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

`commalg.PowerSeries.rmul`¶

Multiply this value by a compatible value on its left.

PythonRust

(self, other: Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

`commalg.PowerSeries.rsub`¶

Subtract this value from a compatible value on its left.

PythonRust

(self, other: Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries · Python projection

Python projection convenience over this Rust mathematical type

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

`commalg.PowerSeries.sub`¶

Subtract another compatible value from this value.

PythonRust

(self, other: PowerSeries[C] | Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries::sub · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/infra/test_discovery.py:212

`commalg.PowerSeries.coefficient`¶

Compute coefficient for this PowerSeries.

Detailed contract

Coefficient at a retained exponent position. Asking beyond the context’s precision is an error, not a zero coefficient claim.

PythonRust

(self, exponent: Sequence[int]) -> Coefficient

noether::commalg::PowerSeries::coefficient · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/17_weighted_power_series.py:19 · examples/22_matroids_and_tutte.py:11 · examples/22_matroids_and_tutte.py:12 · examples/22_matroids_and_tutte.py:13 · examples/33_simplicial_cohomology_operations.py:31 · validation/unit/combin/test_acceptance_workload.py:45

`commalg.PowerSeries.compose`¶

Compose this PowerSeries with another compatible map.

Detailed contract

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

PythonRust

(self, images: Sequence[PowerSeries[C]] | Mapping[str, PowerSeries[C]]) -> PowerSeries[C]

noether::commalg::PowerSeries::compose · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_context_tower_workload.py:3 · validation/unit/commalg/test_polynomial_facade.py:200 · validation/unit/commalg/test_power_series_facade.py:151 · validation/unit/commalg/test_power_series_facade.py:245 · validation/unit/commalg/test_power_series_facade.py:248 · validation/unit/groups/test_permutation_group_facade.py:41

`commalg.PowerSeries.constant_coefficient`¶

Compute constant coefficient for this PowerSeries.

Detailed contract

Constant coefficient.

PythonRust

(self) -> Coefficient

noether::commalg::PowerSeries::constant_coefficient · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_polynomial_facade.py:364 · validation/unit/commalg/test_polynomial_facade.py:371 · validation/unit/commalg/test_polynomial_ideal_facade.py:413 · validation/unit/commalg/test_power_series_facade.py:129 · validation/unit/commalg/test_power_series_facade.py:152 · validation/unit/commalg/test_power_series_facade.py:196

`commalg.PowerSeries.derivative`¶

Compute derivative for this PowerSeries.

Detailed contract

Formal derivative with respect to one variable.

PythonRust

(self, variable: int | str) -> PowerSeries[C]

noether::commalg::PowerSeries::derivative · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_polynomial_facade.py:216 · validation/unit/commalg/test_power_series_facade.py:134 · validation/unit/commalg/test_power_series_facade.py:135 · validation/unit/commalg/test_power_series_facade.py:136 · validation/unit/infra/test_macaulay2_benchmark_protocol.py:636 · validation/unit/numthy/test_padic_ring_facade.py:176

`commalg.PowerSeries.exact_div`¶

Compute exact div for this PowerSeries.

Detailed contract

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.

PythonRust

(self, divisor: PowerSeries[C] | Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries::exact_div · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_polynomial_facade.py:451 · validation/unit/commalg/test_polynomial_facade.py:464 · validation/unit/commalg/test_polynomial_facade.py:483 · validation/unit/commalg/test_polynomial_facade.py:485 · validation/unit/commalg/test_polynomial_facade.py:497 · validation/unit/commalg/test_polynomial_facade.py:502

`commalg.PowerSeries.frobenius_lift`¶

Compute frobenius lift for this PowerSeries.

Detailed contract

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

PythonRust

(self, exponent: int) -> PowerSeries[C]

noether::commalg::PowerSeries::frobenius_lift · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_polynomial_facade.py:244 · validation/unit/commalg/test_power_series_facade.py:271 · validation/unit/commalg/test_power_series_facade.py:298 · validation/bench/sage_power_series.py:127

`commalg.PowerSeries.from_json`¶

Deserialize and revalidate a fixed-precision power series.

Detailed contract

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

PythonRust

(cls, value: str) -> PowerSeries[C]

noether::commalg::PowerSeries::from_json · Direct Rust declaration

pub fn from_json(value: &str) -> Result<Self, NoetherError>where R: for<'de> Deserialize<'de>, R::Element: for<'de> Deserialize<'de>,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106 · validation/unit/combin/test_graph_facade.py:25 · validation/unit/combinatorics/test_kashiwara_crystal.py:32

`commalg.PowerSeries.inverse`¶

Compute inverse for this PowerSeries.

Detailed contract

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

PythonRust

(self) -> PowerSeries[C]

noether::commalg::PowerSeries::inverse · Direct Rust declaration

pub fn inverse(&self) -> Result<Self, UnitError>where R: UnitInversion,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/distributed/f2_linear_algebra.py:37 · examples/distributed/f2_linear_algebra.py:39 · validation/unit/commalg/test_context_tower_workload.py:121 · validation/unit/commalg/test_context_tower_workload.py:122 · validation/unit/commalg/test_context_tower_workload.py:75 · validation/unit/commalg/test_context_tower_workload.py:77

`commalg.PowerSeries.is_one`¶

Test whether this PowerSeries is one.

Detailed contract

Whether this is the multiplicative identity in its context.

PythonRust

(self) -> bool

noether::commalg::PowerSeries::is_one · Direct Rust declaration

pub fn is_one(&self) -> bool

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_rational_function_facade.py:31 · validation/unit/commalg/test_residue_ring_facade.py:25 · validation/unit/numthy/test_number_field_facade.py:29 · validation/corpus/commalg/evolution-algebra-isomorphism.py:34 · validation/corpus/numthy/diagonal-quadric-local-density-sums.py:36

`commalg.PowerSeries.is_zero`¶

Test whether this PowerSeries is zero.

Detailed contract

Whether every retained coefficient is zero.

PythonRust

(self) -> bool

noether::commalg::PowerSeries::is_zero · Direct Rust declaration

pub fn is_zero(&self) -> bool

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/17_weighted_power_series.py:16 · examples/17_weighted_power_series.py:17 · examples/39_kahler_differentials.py:20 · validation/unit/commalg/test_graded_commutative_facade.py:26 · validation/unit/commalg/test_kahler_differentials.py:113 · validation/unit/commalg/test_kahler_differentials.py:38

`commalg.PowerSeries.monomial_substitution`¶

Compute monomial substitution for this PowerSeries.

Detailed contract

Substitute monomials and discard transformed terms outside the fixed cap.

PythonRust

(self, monomial_map: MonomialMap) -> PowerSeries[C]

noether::commalg::PowerSeries::monomial_substitution · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_polynomial_facade.py:247

`commalg.PowerSeries.nonzero_term_count`¶

Return the nonzero term count recorded by this PowerSeries.

Detailed contract

Number of stored nonzero coefficients.

PythonRust

(self) -> int

noether::commalg::PowerSeries::nonzero_term_count · Direct Rust declaration

pub fn nonzero_term_count(&self) -> usize

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/27_weight_characters.py:26 · validation/unit/commalg/test_acceptance_workload.py:50 · validation/unit/commalg/test_acceptance_workload.py:52 · validation/unit/commalg/test_context_tower_workload.py:139 · validation/unit/commalg/test_context_tower_workload.py:142 · validation/unit/commalg/test_polynomial_facade.py:436

`commalg.PowerSeries.pow`¶

Raise a fixed-truncation series to a nonnegative integer power.

Detailed contract

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

PythonRust

(self, exponent: int) -> PowerSeries[C]

noether::commalg::PowerSeries::pow · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	released
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/17_weighted_power_series.py:18 · validation/unit/commalg/test_polynomial_ideal_facade.py:368 · validation/unit/commalg/test_polynomial_ideal_facade.py:369 · validation/unit/commalg/test_polynomial_ideal_facade.py:370 · validation/unit/commalg/test_polynomial_ideal_facade.py:373 · validation/unit/commalg/test_polynomial_ideal_facade.py:381

`commalg.PowerSeries.restrict_truncation`¶

Compute restrict truncation for this PowerSeries.

Detailed contract

Enter an explicitly coarser truncation context.

PythonRust

(self, target: SeriesTruncation) -> PowerSeries[C]

noether::commalg::PowerSeries::restrict_truncation · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_acceptance_workload.py:52 · validation/unit/commalg/test_context_tower_workload.py:142 · validation/unit/commalg/test_power_series_facade.py:138

`commalg.PowerSeries.ring`¶

Return the ring recorded by this PowerSeries.

Detailed contract

Exact power-series context carried by this value.

PythonRust

(self) -> PowerSeriesRing[C]

noether::commalg::PowerSeries::ring · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/11_qadic_witt_vectors.py:3 · examples/13_chinese_remainder_theorem.py:10 · examples/13_chinese_remainder_theorem.py:12 · examples/13_chinese_remainder_theorem.py:9 · examples/14_weighted_polynomials.py:10 · examples/14_weighted_polynomials.py:11

`commalg.PowerSeries.scalar_mul`¶

Compute scalar mul for this PowerSeries.

Detailed contract

Multiply every coefficient by one value from the coefficient ring.

PythonRust

(self, scalar: Coefficient) -> PowerSeries[C]

noether::commalg::PowerSeries::scalar_mul · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_intersection_theory.py:30 · validation/unit/commalg/test_intersection_theory.py:37 · validation/unit/commalg/test_intersection_theory.py:51 · validation/unit/commalg/test_power_series_facade.py:152 · validation/unit/numthy/test_elliptic_curve_facade.py:36 · validation/bench/macaulay2_derived.py:693

`commalg.PowerSeries.semilinear_substitution`¶

Compute semilinear substitution for this PowerSeries.

Detailed contract

Fuse monomial capping and coefficient mapping in one source-term stream. A transformed exponent is rejected before its coefficient map is applied.

PythonRust

(self, coefficient_map: CoefficientFrobenius, monomial_map: MonomialMap) -> PowerSeries[C]

noether::commalg::PowerSeries::semilinear_substitution · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/commalg/test_power_series_facade.py:278 · validation/unit/commalg/test_power_series_facade.py:285 · validation/unit/numthy/test_padic_local_field_facade.py:163 · validation/unit/numthy/test_padic_local_field_facade.py:166

`commalg.PowerSeries.terms`¶

Compute terms for this PowerSeries.

Detailed contract

Nonzero terms in deterministic lexicographic exponent order.

PythonRust

(self) -> list[tuple[list[int], Coefficient]]

noether::commalg::PowerSeries::terms · Direct Rust declaration

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

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: examples/07_integer_factorization.py:14 · examples/40_exterior_algebra.py:43 · validation/unit/combin/test_acceptance_workload.py:45 · validation/unit/combin/test_acceptance_workload.py:81 · validation/unit/combinatorics/test_boundary.py:31 · validation/unit/combinatorics/test_boundary.py:44

`commalg.PowerSeries.to_json`¶

Serialize this series with its complete fixed-precision context.

Detailed contract

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

PythonRust

(self) -> str

noether::commalg::PowerSeries::to_json · Direct Rust declaration

pub fn to_json(&self) -> Result<String, NoetherError>where R: Serialize, R::Element: Serialize,

Contract	Value
Guarantee	checked deterministic result
Determinism	deterministic
Availability	default CPU build
Domain implementation crates	noether, flint-core, groebner-kernel, module-core, poly-core, resolution-kernel
GIL	attached / bounded
Semantic ID	noether/commalg/PowerSeries@1

Executable usage: validation/unit/category/test_category.py:14 · validation/unit/category/test_category.py:15 · validation/unit/combin/test_acceptance_workload.py:30 · validation/unit/combin/test_acceptance_workload.py:65 · validation/unit/combin/test_acceptance_workload.py:86 · validation/unit/combin/test_graph_facade.py:106

commalg · PowerSeries¶

Worked example¶

commalg.PowerSeries¶

commalg.PowerSeries.__add__¶

commalg.PowerSeries.__mul__¶

commalg.PowerSeries.__neg__¶

commalg.PowerSeries.__pow__¶

commalg.PowerSeries.__radd__¶

commalg.PowerSeries.__rmul__¶

commalg.PowerSeries.__rsub__¶

commalg.PowerSeries.__sub__¶

commalg.PowerSeries.coefficient¶

commalg.PowerSeries.compose¶

commalg.PowerSeries.constant_coefficient¶

commalg.PowerSeries.derivative¶

commalg.PowerSeries.exact_div¶

commalg.PowerSeries.frobenius_lift¶

commalg.PowerSeries.from_json¶

commalg.PowerSeries.inverse¶

commalg.PowerSeries.is_one¶

commalg.PowerSeries.is_zero¶

commalg.PowerSeries.monomial_substitution¶

commalg.PowerSeries.nonzero_term_count¶

commalg.PowerSeries.pow¶

commalg.PowerSeries.restrict_truncation¶

commalg.PowerSeries.ring¶

commalg.PowerSeries.scalar_mul¶

commalg.PowerSeries.semilinear_substitution¶

commalg.PowerSeries.terms¶

commalg.PowerSeries.to_json¶

`commalg.PowerSeries`¶

`commalg.PowerSeries.add`¶

`commalg.PowerSeries.mul`¶

`commalg.PowerSeries.neg`¶

`commalg.PowerSeries.pow`¶

`commalg.PowerSeries.radd`¶

`commalg.PowerSeries.rmul`¶

`commalg.PowerSeries.rsub`¶

`commalg.PowerSeries.sub`¶

`commalg.PowerSeries.coefficient`¶

`commalg.PowerSeries.compose`¶

`commalg.PowerSeries.constant_coefficient`¶

`commalg.PowerSeries.derivative`¶

`commalg.PowerSeries.exact_div`¶

`commalg.PowerSeries.frobenius_lift`¶

`commalg.PowerSeries.from_json`¶

`commalg.PowerSeries.inverse`¶

`commalg.PowerSeries.is_one`¶

`commalg.PowerSeries.is_zero`¶

`commalg.PowerSeries.monomial_substitution`¶

`commalg.PowerSeries.nonzero_term_count`¶

`commalg.PowerSeries.pow`¶

`commalg.PowerSeries.restrict_truncation`¶

`commalg.PowerSeries.ring`¶

`commalg.PowerSeries.scalar_mul`¶

`commalg.PowerSeries.semilinear_substitution`¶

`commalg.PowerSeries.terms`¶

`commalg.PowerSeries.to_json`¶