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EllipPy

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EllipPy is an elliptic integral library for Python, powered by Rust. All functions support numpy and parallelization. EllipPy features high accuracy and performance. For more details on testing and benchmarks, please refer to Ellip.

Quick Start

from ellippy import *
import numpy as np

ellipk(
    m=np.array([0.1, 0.2, 0.3, 0.4, 0.5])
)  # [1.61244135 1.6596236  1.71388945 1.77751937 1.85407468]

ellippiinc(phi=np.pi / 4, n=0.1, m=0.25)  # 0.8197192266707629

cel(kc=0.5, p=0.1, a=1.0, b=-1.0)  # -5.2310275365518795

elliprf(
    x=[0.1, 0.2, 0.3], y=[0.2, 0.4, 0.8], z=[0.3, 0.5, 0.7]
)  # [2.29880489 1.68455225 1.32157804]

jacobi_zeta(phi=np.pi / 3, m=0.5)  # 0.13272240254017148

To install EllipPy, use your preferred package manager:

pip install ellippy
uv add ellippy

Features

  • Legendre's complete integrals
    • ellipk: Complete elliptic integral of the first kind (K).
    • ellipe: Complete elliptic integral of the second kind (E).
    • ellipke: Simultaneous computation of the complete elliptic integrals of the first and second kind (K and E).
    • ellippi: Complete elliptic integral of the third kind (Π).
    • ellipd: Complete elliptic integral of Legendre's type (D).
  • Legendre's incomplete integrals
    • ellipf: Incomplete elliptic integral of the first kind (F).
    • ellipeinc: Incomplete elliptic integral of the second kind (E).
    • ellippiinc: Incomplete elliptic integral of the third kind (Π).
    • ellipdinc: Incomplete elliptic integral of Legendre's type (D).
  • Bulirsch's integrals
    • cel: General complete elliptic integral in Bulirsch's form.
    • cel1: Complete elliptic integral of the first kind in Bulirsch's form.
    • cel2: Complete elliptic integral of the second kind in Bulirsch's form.
    • cel3: Complete elliptic integral of the third kind in Bulirsch's form.
    • el1: Incomplete elliptic integral of the first kind in Bulirsch's form.
    • el2: Incomplete elliptic integral of the second kind in Bulirsch's form.
    • el3: Incomplete elliptic integral of the third kind in Bulirsch's form.
  • Carlson's symmetric integrals
    • elliprf: Symmetric elliptic integral of the first kind (RF).
    • elliprg: Symmetric elliptic integral of the second kind (RG).
    • elliprj: Symmetric elliptic integral of the third kind (RJ).
    • elliprc: Degenerate elliptic integral of RF (RC).
    • elliprd: Degenerate elliptic integral of the third kind (RD).
  • Miscellaneous functions
    • jacobi_zeta: Jacobi Zeta function (Z).
    • heuman_lambda: Heuman Lambda function (Λ0).

Citation

EllipPy is based on a Rust library, Ellip. The paper is published in the Journal of Open Source Software. If EllipPy is helpful to your work, please consider citing Ellip:

Pornsiriprasert, S., (2026). Ellip: An Elliptic Integral Library for Rust. Journal of Open Source Software, 11(118), 9386, https://doi.org/10.21105/joss.09386

Bibtex format:

@article{Pornsiriprasert2026,
    doi = {10.21105/joss.09386}, 
    url = {https://doi.org/10.21105/joss.09386}, 
    year = {2026}, 
    publisher = {The Open Journal}, 
    volume = {11}, number = {118}, pages = {9386},
    author = {Pornsiriprasert, Sira}, 
    title = {Ellip: An Elliptic Integral Library for Rust}, 
    journal = {Journal of Open Source Software} } 

Performance calibration

For advanced users who wish the best performance fine tuned to their specific machines, see the Python-path calibration guide for measuring Rayon and interpreter-detachment crossovers through the public API.

Metadata

Release files for ellippy 1.2.1

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Source distribution (sdist)

Source distribution for ellippy 1.2.1
File Size Uploaded Provenance
ellippy-1.2.1.tar.gz 17.1 kB Without provenance Details

Built distributions (wheels)

Table of built distributions (wheels) for ellippy 1.2.1
File
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_17_s390x.manylinux2014_s390x.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_17_armv7l.manylinux2014_armv7l.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_17_aarch64.manylinux2014_aarch64.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-pp311-pypy311_pp73-manylinux_2_12_i686.manylinux2010_i686.whl PyPy 3.11 PyPy 3.11 7.3 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp315-cp315t-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.15 CPython 3.15 free-threading Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp315-cp315t-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.15 CPython 3.15 free-threading Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp315-cp315-win32.whl CPython 3.15 CPython 3.15 Windows x86-32 Details
ellippy-1.2.1-cp315-cp315-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.15 CPython 3.15 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp315-cp315-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.15 CPython 3.15 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp314-cp314t-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.14 CPython 3.14 free-threading Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp314-cp314-win_amd64.whl CPython 3.14 CPython 3.14 Windows x86-64 Details
ellippy-1.2.1-cp314-cp314-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp314-cp314-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp314-cp314-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp314-cp314-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp314-cp314-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.14 CPython 3.14 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp314-cp314-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.14 CPython 3.14 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp314-cp314-macosx_11_0_arm64.whl CPython 3.14 CPython 3.14 macOS 11.0+ ARM64 Details
ellippy-1.2.1-cp314-cp314-macosx_10_12_x86_64.whl CPython 3.14 CPython 3.14 macOS 10.12+ x86-64 Details
ellippy-1.2.1-cp313-cp313-win_amd64.whl CPython 3.13 CPython 3.13 Windows x86-64 Details
ellippy-1.2.1-cp313-cp313-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp313-cp313-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp313-cp313-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp313-cp313-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp313-cp313-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.13 CPython 3.13 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp313-cp313-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.13 CPython 3.13 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp313-cp313-macosx_11_0_arm64.whl CPython 3.13 CPython 3.13 macOS 11.0+ ARM64 Details
ellippy-1.2.1-cp313-cp313-macosx_10_12_x86_64.whl CPython 3.13 CPython 3.13 macOS 10.12+ x86-64 Details
ellippy-1.2.1-cp312-cp312-win_amd64.whl CPython 3.12 CPython 3.12 Windows x86-64 Details
ellippy-1.2.1-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp312-cp312-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp312-cp312-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp312-cp312-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.12 CPython 3.12 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp312-cp312-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.12 CPython 3.12 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp312-cp312-macosx_11_0_arm64.whl CPython 3.12 CPython 3.12 macOS 11.0+ ARM64 Details
ellippy-1.2.1-cp312-cp312-macosx_10_12_x86_64.whl CPython 3.12 CPython 3.12 macOS 10.12+ x86-64 Details
ellippy-1.2.1-cp311-cp311-win_amd64.whl CPython 3.11 CPython 3.11 Windows x86-64 Details
ellippy-1.2.1-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp311-cp311-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp311-cp311-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp311-cp311-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp311-cp311-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.11 CPython 3.11 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp311-cp311-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.11 CPython 3.11 Linux glibc 2.12+ x86-32 Details
ellippy-1.2.1-cp311-cp311-macosx_11_0_arm64.whl CPython 3.11 CPython 3.11 macOS 11.0+ ARM64 Details
ellippy-1.2.1-cp311-cp311-macosx_10_12_x86_64.whl CPython 3.11 CPython 3.11 macOS 10.12+ x86-64 Details
ellippy-1.2.1-cp310-cp310-win_amd64.whl CPython 3.10 CPython 3.10 Windows x86-64 Details
ellippy-1.2.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ x86-64 Details
ellippy-1.2.1-cp310-cp310-manylinux_2_17_s390x.manylinux2014_s390x.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ IBM System/390x Details
ellippy-1.2.1-cp310-cp310-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ PowerPC 64-le Details
ellippy-1.2.1-cp310-cp310-manylinux_2_17_armv7l.manylinux2014_armv7l.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ ARMv7l Details
ellippy-1.2.1-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl CPython 3.10 CPython 3.10 Linux glibc 2.17+ ARM64 Details
ellippy-1.2.1-cp310-cp310-manylinux_2_12_i686.manylinux2010_i686.whl CPython 3.10 CPython 3.10 Linux glibc 2.12+ x86-32 Details

Total release size: 21.2 MB

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Release files / ellippy-1.2.1-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / ellippy-1.2.1-cp311-cp311-manylinux_2_12_i686.manylinux2010_i686.whl

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Release files / ellippy-1.2.1-cp311-cp311-macosx_10_12_x86_64.whl

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Release files / ellippy-1.2.1-cp310-cp310-win_amd64.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_17_s390x.manylinux2014_s390x.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_17_armv7l.manylinux2014_armv7l.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl

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Release files / ellippy-1.2.1-cp310-cp310-manylinux_2_12_i686.manylinux2010_i686.whl

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